cuaderno de ejercicios - ramaeco.files.wordpress.com€¦ · Índice de ejercicios pÁg. tema 3 –...

Colegio Los Peñascales Prof. Daniel de las Heras NOMBRE DEL ALUMNO/A

CUADERNO

DE

EJERCICIOS

ECONOMÍA

DE LA EMPRESA

2º BACHILLERATO

CURSO 2012 - 2013

COLEGIO LOS PEÑASCALES

PROFESOR: DANIEL DE LAS HERAS

Colegio Los Peñascales Prof. Daniel de las Heras

2

ÍNDICE DE EJERCICIOS

PÁG.

TEMA 3 – DERECHOS PREFERENTES DE SUSCRIPCIÓN 3

TEMA 4 – TOMA DE DECISIÓN 6

TEMA 4 – PRODUCTIVIDAD 8

TEMA 4 – PUNTO MUERTO 10

TEMA 7 – MODELO WILSON 14

TEMA 9 – SELECCIÓN DE INVERSIONES 15

TEMA 9 – PERIODO MEDIO DE MADURACIÓN 18

TEMA 10 – BALANCES 20

TEMA 11 – FONDO DE MANIOBRA 21

TEMA 11 – FONDO DE MANIOBRA Y RATIOS 25

TEMA 12 – ANÁLISIS ECONÓMICO 29

EXAMEN DE SELECTIVIDAD 30


3

TEMA 3 - PROBLEMAS DE DERECHO PREFERENTE DE

SUSCRIPCIÓN HOJA 1

!" #$%&'()&*$%+,-+.% /+.%0&*&$%$'(12$)% *3% 4$(25$1.% ($)$%(60&)% $0732)2)%83&9$%'$7328$)2$"%:1%

4$(25$1%$85&*%0&%1$%289&)*2;8%&*%0&%<="===>%02920206*%&8%?="===%$44268&*"%+453$1'&85&.%&*5$*%

$44268&*%4652@$8%&8%A61*$%$%B>"%#$%$'(12$42;8%0&%4$(25$1%&*%0&%C"===%$44268&*%83&9$*%$%1$%($)"%

/2%38%$442682*5$%52&8&%!?"===%$44268&*.%)&*(680&D%

$" E$16)%86'28$1%0&%1$%$442;8"%

F" E$16)%0&1%0&)&4G6%0&%*3*4)2(42;8"%4" HI3J85$*%$44268&*%(3&0&%*3*4)2F2)%&1%$442682*5$%K%$%73L%46*5&M%0" HI3J856%6F5&80)N$%(6)% 1$%9&85$%0&% *3*%0&)&4G6*.% *2%&1%$442682*5$%0&420&%86%$4302)%$% 1$%

$'(12$42;8M%

!"#$%&'()*+,*-*./0123*4!*-*1/5123*67#8%&'(*5*8*93*

%:*;8<8=*>)111?5*-*9@)11123*A:*B(<C7D8=*9@)111?1/51*-*5)E112*

?" -8$%*642&0$0%$8;82'$.%52&8&%38%4$(25$1%0&%!=="===>.%02920206%&8%!="===%$44268&*"%:1%9$16)%$1%

73&%4652@$8%024G$*%&*%$44268&*%&*%0&%!?>"%/&%0&420&%$'(12$)%&1%4$(25$1%&8%?"===%$44268&*%$%1$%

($)"% :1% /)"% #;(&@.% $852O36% $442682*5$% 52&8&% P"===% $44268&*"% :Q(124$% 73&% 643))2)J% &8% 16*%

*2O32&85&*%4$*6*D%

$" +430&%$%1$%$'(12$42;8%0&%4$(25$1"%

F" R6%$430&%$%1$%$'(12$42;8%K%9&80&%16*%0&)&4G6*"%

4" S32&)&%$0732)2)%!"===%$44268&*%0&%1$%$'(12$42;8"%

0" S32&)&%$0732)2)%P==%$44268&*%0&%1$%$'(12$42;8"%

!"#$%&'()*+,*-*99/0F23*4!*-*1/>>23*67#8%&'(*.*8*93*8:*;8<8=*E11?1/>>*-*@052*

G:*B(<C7D8=*5)111?1/>>*-*9)>@123*

%:*H"IJC8*A7C7%K"D*-*9)111?1/>>*-*>>12*L*H"IJC8*8%%&"(7D*9)111?91*-*91)11123*M",8#*-*91)>>12*

A:*+7(,8*A7C7%K"D*-*@)111?1/>>*-*0012*L*H"IJC8*8%%&"(7D*511?91*-*5)11123*M",8#*-*>)>512*J8<8*

T" -8$%&'()&*$%52&8&%38%4$(25$1%0&%C="===>%K%&1%9$16)%86'28$1%0&%1$*%$44268&*%&*%0&%C>"%:1%9$16)%

0&%4652@$42;8%0&%1$*%$44268&*%$453$1'&85&%&*%0&%B>"%:*5$%&'()&*$%0&420&%$'(12$)%4$(25$1%&8%

C"===% $44268&*% $% 1$% ($)"% /3(68&'6*% 73&% 38% $442682*5$% (6*&&% T"===% $44268&*% $85&*% 0&% 1$%

$'(12$42;8"%S3L%643))2)J%&468;'24$'&85&%$%024G6%$442682*5$%&8%&*56*%4$*6*D%

$" +430&%$%1$%$'(12$42;8%0&%4$(25$1"%

F" R6%$430&%$%1$%$'(12$42;8%K%9&80&%16*%0&)&4G6*"%

4" S32&)&%$0732)2)%?"===%$44268&*%0&%1$%$'(12$42;8"%

!"#$%&'()*+,*-*./0F23*4!*-*1/>>23*67#8%&'(*@*8*93*8:*;8<8=*9).11?.*-*F).1123*G:*B(<C7D8=*>)111?1/>>*-*9)1112*

%:*H"IJC8*A7C7%K"D*-*9)111?1/>>*-*>>12*L*H"IJC8*8%%&"(7D*@)111?.*-*91)11123*M",8#*-*91)>>12*

P" U&$12@$%&1%()6F1&'$%$85&)26)%*3(682&806%73&%1$%$'(12$42;8%0&%4$(25$1%*&%)&$12@$%&'252&806%1$*%

83&9$*%$44268&*%!=V%*6F)&%1$%($)"%

!"#$%&'()*+,*-*./E>23*4!*-*1/9F23*67#8%&'(*@*8*9*

8:*;8<8=*9).11?./.*-*E)@.123*G:*B(<C7D8=*>)111?1/9F*-*.912*

%:*H"IJC8*A7C7%K"D*-*9)111?1/9F*-*9F12*L*H"IJC8*8%%&"(7D*@)111?./.*-*99)11123*M",8#*-*99)9F12*


4

PROBLEMAS DE DERECHOS PREFERENTES DE

SUSCRIPCIÓN HOJA 2

!" #$%&'()&*$%W+XY.%/"+".%0&024$0$%$% 1$% Z$F)24$42;8%0&%4$1@$06%0&%(2&1.%*&%&843&85)$%&8%38$%

Z$*&% 0&% &Q($8*2;8"% +85&% 1$% 8&4&*20$0% 0&% 83&9$*% 289&)*268&*.% *&% (1$85&$% )&$12@$)% 38$%

$'(12$42;8% 0&% 4$(25$1% 0&% C="===% $44268&*% 468% 38% 9$16)% 0&% &'2*2;8% 0&% T% &3)6*[$442;8"% #$%

*253$42;8%0&%1$%&'()&*$.%$85&*%0&%1$%$'(12$42;8.%&*%1$%*2O32&85&D%I$(25$1%*642$1%C=="===%&3)6*\%

U&*&)9$*%]=="===%&3)6*\%8^'&)6%0&%$44268&*%?=="==="%%

_$)52&806%0&%1$%28Z6)'$42;8%$85&)26)%*&%(20&D%%

`%E$16)%86'28$1%0&%1$*%$44268&*"%

`%E$16)%0&%1$*%$44268&*%$85&*%0&%1$%$'(12$42;8"%

`%E$16)%0&%1$*%$44268&*%0&*(3L*%0&%1$%$'(12$42;8"%

`%E$16)%0&1%0&)&4G6%()&Z&)&85&%0&%*3*4)2(42;8"%

!"#$%#&#'!()*!+#,#-.#!//)0-12##&#3445444#,#6445444#&#6734#18902#

:"#;1#()<1-#1+#=!+09#*1>9)/05#?2*1#=!+09#21#/!+/8+!#<1#+!#2)@8)1-*1#A09B!C#

$*#&#D!*9)B0-)0#%1*0#,#-.#<1#!//)0-12#

E)1-<0#1+#(!*9)B0-)0#-1*0#+!#28B!#<1+#/!()*!+#F#+!2#91219=!2#G12#<1/)97#+02#91/89202#(90()02"#

$*#&#3445444#H#I445444#,#6445444#&#J#18902#

/"#KL09!#*1-1B02#M81#/!+/8+!9#1+#-81=0#(!*9)B0-)0#-1*05#;1-#1-#/81-*!#M81#1+#/!()*!+#21#L!#!B(+)!<0#

F#(09#*!-*0#21#L!#B0<)A)/!<0#28#=!+095#?+#/!()*!+#!B(+)!<0#219NC#345444#!//)0-12#O#P#18902#&#Q3454445#F#

/0B0#!-*12#1+#/!()*!+#19!#<1#3445444#189027#1+#/!()*!+#<12(8R2#<1#+!#!B(+)!/)>-#219N#+!#28B!C#3445444#

H#Q345444#&#J345444#S5#

K<1BN2#1+#-TB190#<1#!//)0-12#<12(8R2#<1#+!#!B(+)!/)>-#219NC#6445444#G!-*19)0912#!#+!#!B(+)!/)>-"#H#

345444#GM81#20-#+!2#M81#21#!B(+U!-"5#D09#*!-*07#1+#=!+09#<1#+!#!//)>-#<12(8R2#<1#+!#!B(+)!/)>-#12C#

$*#&#D!*9)B0-)0#%1*0#,#-.#<1#!//)0-12#

$*#&#J345444#H#I445444#,#6345444#&#37V4#18902#

<"#?+#<191/L0#(91A191-*1#<1#282/9)(/)>-#+0#(0<1B02#L!++!9#912*!-<0#1+#=!+09#!-*12#<1#+!#!B(+)!/)>-#F#

1+#=!+09#<12(8R2#<1#+!#!B(+)!/)>-C#

WE#&#$!+09#!-*12#!B(+)!/)>-#X#$!+09#<12(8R2#!B(+)!/)>-#&#J#Y#37V4#&#47J4#18902#

?" #$%&'()&*$%aa%*&%(1$85&$%$0732)2)%83&9$*%28*5$1$4268&*%()6034529$*"%_$)$%Z28$842$)%1$*%425$0$*%

289&)*268&*% 1$% a385$% ,&8&)$1% 0&% $442682*5$*% 0&420&% $'(12$)% &1% 4$(25$1% &8% !"===% $44268&*%

83&9$*%468%38%9$16)%0&%&'2*2;8%0&%!=%&3)6*%(6)%$442;8"%:1%8^'&)6%0&%$44268&*%$85&*%0&%1$%

$'(12$42;8%&*%0&%C"==="%#6*%9$16)&*%0&%16*%Z6806*%()6(26*%$85&*%0&%1$%$'(12$42;8%*68D%I$(25$1%

C="===%&3)6*%K%U&*&)9$*%!="===%&3)6*"%I68%1$%28Z6)'$42;8%$85&)26)%*&%(20&D%

$b I$1431&%&1%9$16)%0&1%0&)&4G6%0&%*3*4)2(42;8"%Fb /2%38%$442682*5$%$852O36%(6*&&%?"===%$44268&*%H43J85$*%$44268&*%83&9$*%(60)N$%*3*4)2F2)%*2%

0&420&%$4302)%$%1$%$'(12$42;8%0&%4$(25$1M%

!"#$%&'()*+,*-!*.*/012*34*5,*2//*+%%&"(67*


5

T" -8$%&'()&*$%0&*&$%$'(12$)%&1%4$(25$1%&8%TC=%$44268&*%468%38%9$16)%0&%&'2*2;8%0&%?]=%&3)6*%

(6)%$442;8"%:1%8^'&)6%0&%$44268&*%$85&*%0&%1$%$'(12$42;8%&*%0&%!"]C="%#6*%9$16)&*%$85&*%0&%1$%

$'(12$42;8%*68D%4$(25$1%TC="===%&3)6*%K%)&*&)9$*%!]C"===%&3)6*"%I68%1$%28Z6)'$42;8%$85&)26)%

*&%(20&D%

$" I$1431$)%&1%9$16)%0&1%0&)&4G6%0&%*3*4)2(42;8"%

F" /2%38%$442682*5$%$852O36%(6*&&%!]C%$44268&*.%HI3J85$*%$44268&*%83&9$*%(60)N$%*3*4)2F2)%

*2%0&420&%$4302)%$%1$%$'(12$42;8%0&%4$(25$1M%

!"#$%&'()*+,*-!*.8*34*5,*18*+%%&"(67*

P" #$% *642&0$0% $8;82'$%S-cRd+%0&*&$% $'(12$)% *3% 8&O6426"% _$)$% Z28$842$)% 1$% 83&9$% 289&)*2;8%

0&420&%&Z&453$)%38$%$'(12$42;8%0&%4$(25$1%'&02$85&%1$%&'2*2;8%0&%83&9$*%$44268&*"%:1%4$(25$1%

$85&*%0&%1$%$'(12$42;8%&*%0&%!=="===%&3)6*%K%468*5$%0&%?="===%$44268&*.%1$*%43$1&*%4652@$8%&8%

A61*$%$%<%&3)6*%(6)%$442;8"%/&%&'25&8%!="===%$44268&*%83&9$*%$%1$%($).%&*%0&42).%(6)%*3%9$16)%

86'28$1"%:1%/)"%a2'L8&@.%$852O36%$442682*5$%K%52531$)%0&%P"===%$44268&*.%$430&%$%1$%$'(12$42;8%

0&%4$(25$1"%/&%(20&D%

e$b%E$16)%86'28$1%0&%1$*%$44268&*\%eFb%HI3J85$*%$44268&*%83&9$*%(60)J%*3*4)2F2)%&8%Z3842;8%0&%

1$*% $852O3$*% 73&% K$% (6*&&M\% e4b% HI3J1% *&)N$% *3% 46*5&M\% e0b% HS3L% *&% &852&80&% (6)% 0&)&4G6*%

()&Z&)&85&*%0&%*3*4)2(42;8M%

!"#$%&'()*+,*9:*.*834*5,*;)///*+%%&"(674*%,*</)///*6$="7*

*


6

TEMA 4 - PROBLEMAS DE TOMA DE DECISIONES

!" -8%&'()&*$)26%0&%&*(&45J4316*%52&8&%73&%6)O$82@$)%38%46842&)56%K%*&%1&%6Z)&4&8%1$*%6(4268&*%

0&% G$4&)16% $1% $2)&% 12F)&% 6% &8% 38% ($F&11;8% 43F2&)56"% #6*% F&8&Z2426*% 9$8% $% 0&(&80&)% 0&% 1$%

$*2*5&842$% 0&1% (^F1246% K% L*5$% $% *3% 9&@% 0&1% 412'$.% 73&% (3&0&% *&)% 468% 11392$.% 468% 83F&*% 6%

*61&$06"% #6*% )&*315$06*% &*(&)$06*% *2% 16% 6)O$82@$% $1% $2)&% 12F)&% *68% !="===.% C="===% K% BC"===%

&3)6*%*2%&1%52&'(6%&*%113926*6.%83F1$06%6%*61&$06%)&*(&4529$'&85&"%/2%&1%46842&)56%*&%)&$12@$%

&8%($F&11;8%43F2&)56.%16*%)&*315$06*%*&)N$8%PC"===.%P="===%K%TC"===%&3)6*%($)$%4$0$%&*5$06%

412'J5246"%

/&%(20&D%

$b I68Z2O3)$)%1$%'$5)2@%0&%0&42*2;8"%

Fb HS3L% 0&42*2;8% 0&F&% 56'$)% &1% &'()&*$)26% *2% 35212@$% 16*% 42846% 4)25&)26*% 0&% 56'$% 0&%

0&42*268&*%&8%$'F2&85&%0&%284&)5203'F)&M%

!"#$%&'()*+,*-./&0&/1+*2*3+4.##'(*567)888,9*4,*:31&0&/1+*2*;&<.*#&4<.*5=7)888,9*

%,*>+3#+%.*2*;&<.*#&4<.*5?@)A78,9*B,*C$<D&%E*2*;&<.*#&4<.*57@)A78,9*.,*!+F+G.*2*-+4.##'(*568)888,*

?" #$% &'()&*$% X2O25$1f6% /"+"% *&% (1$85&$% 1$% $0732*242;8% 0&% 38% 83&96% &732(6.% (302&806% &1&O2)%

&85)&% 1$*% 5)&*% $15&)8$529$*% +.% A% 6% I"% #6*% )&*315$06*% 46'6% 468*&43&842$% 0&% 1$% &1&442;8% 0&1%

&732(6% 0&(&80&8% 0&1% 46'(6)5$'2&856% 0&% 1$% 0&'$80$% 73&% (3&0&% *&)% $15$.% 468% 38$%

()6F$F2120$0%0&1%T=V\%'&02$.%468%38$%()6F$F2120$0%0&1%PCV\%6%F$g$.%468%38$%()6F$F2120$0%0&1%

?CV"%X&%5$1%Z6)'$D%

- /2% &12O&% +.% 16*% F&8&Z2426*% *&)J8% 0&% T=="===% 3"'".% ?=="===% 3"'"% 6% !=="===% 3"'".% *2% 1$%

0&'$80$%&*%$15$.%'&02$%6%F$g$%)&*(&4529$'&85&"%

- /2% &12O&% A.% 16*% F&8&Z2426*% *&)J8% 0&% ?C="===% 3"'".% ?P="===% 3"'"% 6% !B="===% 3"'".% *2% 1$%

0&'$80$%&*%$15$.%'&02$%6%F$g$%)&*(&4529$'&85&"%

- /2% &12O&% I.% 16*% F&8&Z2426*% *&)J8% 0&% ??C"===% 3"'".% ?=C"===% 3"'"% 6% !]C"===% 3"'".% *2% 1$%

0&'$80$%&*%$15$.%'&02$%6%F$g$%)&*(&4529$'&85&"%

/&%(20&%*&1&44268$)%386%0&%16*%5)&*%&732(6*%&8%16*%*2O32&85&*%4$*6*D%

$b d&82&806%&8%43&85$%1$*%()6F$F2120$0&*%73&%'&%0$8"%

Fb /3(682&806% 73&% 86% 4686@46% 1$*% ()6F$F2120$0&*% K% (6)% 5$856% &84685)J806'&% &8% 38%

$'F2&85&%0&%284&)5203'F)&"%e-5212@$)%16*%42846%4)25&)26*%73&%46864&*b"%

eI6&Z242&85&%0&%6(52'2*'6%0&%=.<b%

!"#$%&'()*;04&.(1.*B.*<&./G"*2*H/1<+1.G&+*I*5AA6)888,9*+,*-./&0&/1+*2*J*5@K7)888,94,*:31&0&/1+*2*;*

5688)888,9*%,*>+3#+%.*2*I*5A@=)===,9*B,*C$<D&%E*2*;*5A=8)888,9*.,*!+F+G.*2*;*"*J*5K7)888,*

T" -8$% &'()&*$% 0&024$0$% $% 1$% Z$F)24$42;8% 0&% 4$1@$06% 52&8&% 73&% $8$12@$)% &85)&% 02Z&)&85&*%

&*5)$5&O2$*%0&%()603442;8.%$73&11$%73&%1&%()6(6)4268&%'J*%9&85$*.%K.%&8%468*&43&842$.%'J*%

F&8&Z2426*"%#6*%(6*2F1&*%()603456*%*68D%F65$*.%@$($56*%K%*$80$12$*"%#$%0&42*2;8%1$%0&F&%56'$)%

&8% Z3842;8% 0&% 1$*% ()&0244268&*% 0&1% 52&'(6% 73&% G$O$% &8% 16*% ();Q2'6*%'&*&*.% K$% 73&% &*56%

0&5&)'28$)J%73&%*&%9&80$%'J*%38%()603456%3%65)6"%#6*%&*5$06*%0&% 1$%8$53)$1&@$%()&92*56*%

*68%5)&*D%52&'(6%Z)N6.%86)'$1%K%4J1206"%


7

:8% &1% '6'&856% 0&% 56'$)% 1$% 0&42*2;8% &1% &'()&*$)26% 86% *$F&% 468% *&O3)20$0% &1% &*5$06% 0&%

52&'(6.% (&)6% 468*315$806% 16*%&*5$06*% 412'J5246*% 0&% 16*%^152'6*% $h6*% 11&O$% $% 1$*% *2O32&85&*%

&*52'$4268&*%&8%Z6)'$%0&%()6F$F2120$0D%&Q2*5&%38%T=V%0&%()6F$F2120$0%0&%73&%&1%52&'(6%*&$%

Z)N6.%38%PCV%0&%73&%*&$%86)'$1.%K%38%?CV%0&%73&%*&$%4J1206"%

_6)% 65)6% 1$06.% 1$% &Q(&)2&842$% &8% &1% *&456)% 1&% (&)'25&% &*52'$)% 16*% )&*315$06*% &*(&)$06*% &8%

43$856%$%9&85$*.%K%&*56%1&%(&)'25&%&1$F6)$)%1$*%*2O32&85&*%()&0244268&*%6%0&*&81$4&*D%

#$%Z$F)24$42;8%0&%F65$*%1&%0$)N$%386*%F&8&Z2426*%e&8%&3)6*b%0&%B="===.%!C"===%K%?"C==.%*2%&1%

52&'(6%&*%Z)N6.%86)'$1%6%4J1206%)&*(&4529$'&85&"%

#$%Z$F)24$42;8%0&%@$($56*%1&%0$)N$%386*%F&8&Z2426*%e&8%&3)6*b%0&%C"===.%T="===%K%!="===.%*2%&1%

52&'(6%&*%Z)N6.%86)'$1%6%4J1206%)&*(&4529$'&85&"%

#$%Z$F)24$42;8%0&%*$80$12$*%1&%0$)N$%386*%F&8&Z2426*%e&8%&3)6*b%0&%`C"===.%]"C==%K%C="===.%*2%

&1%52&'(6%&*%Z)N6.%86)'$1%6%4J1206%)&*(&4529$'&85&"%

d&82&806%&8%43&85$%&*56*%0$56*.%*&%(20&D%

$b%/253$42;8%0&%)2&*O6"%I$1431$)%16*%9$16)&*%&*(&)$06*%0&%4$0$%38$%0&%1$*%&*5)$5&O2$*"%

Fb% /253$42;8% 0&% 284&)5203'F)&"% -5212@$% 16*% 42846% 4)25&)26*% &*5302$06*"% I6&Z242&85&% 0&%

6(52'2*'6%&*%=.]"%

!"#$%&'()*+,-&.(/.*0.*1&.23"*4*5"/62*789):;9<=*6<*>.2&,&2/6*4*?6@6/"2*79)AAA<=*-<*B@/&,)*4*5"/62*

7CA)AAA<=*%<*D6@#6%.*4*5"/62*789)9;9<=*0<*E$1F&%G*4*5"/62*7H8);9A<=*.<*!6I63.*4*5"/62*7H;)9AA<*

P" -8$%&'()&*$%52&8&%43$5)6%6(4268&*%0&%164$12@$42;8%0&%38$%83&9$%ZJF)24$"%+%4685283$42;8%*&%

)&46O&% 1$%'$5)2@% 0&% 0&42*2;8% 0&% 16*% 46*5&*% 73&% 5&80)N$% 024G$% &'()&*$% 0&(&802&806% 0&% 1$%

&*5)$5&O2$%e+.%A%6%Ib%73&%)&$124&%1$%46'(&5&842$D%

# >* ?* @*

?$=A"7* Q4# QP# 66#

>#5+%6B6* 64# Z# Q3#

C+==+A"(+* QI# Q3# Q[#

@DE&F* 6Q# Q6# QQ#

:*5302$%0680&%*&%164$12@$)N$%1$%ZJF)24$%*&O^8%16*%4)25&)26*%(&*2'2*5$.%6(52'2*5$%K%#$(1$4&"%

!"#$%&'()*6<*>.2&,&2/6*4*J61163"(6*7KL<=*-<*B@/&,&2/6*4*+#-6%./.*7M<=*%<*D6@#6%.*4*+#-6%./.*"*NO0&G*7KHPC<*

%


8

TEMA 6 - PROBLEMAS DE PRODUCTIVIDAD

Q5 \!<9)++02#D912*12#1+#(!2!<0#!]0#*1-U!#8-!#(+!-*)++!#<1#34#*9!:!^!<09127#/!<!#8-0#<1#+02#/8!+12#*9!:!^>#Q5IJ4#L09!27#!+/!-_N-<021#8-#=0+8B1-#<1#(90<8//)>-#<1#VV45444# +!<9)++025#?2*1#!]0#L!#*1-)<0#8-!#

(+!-*)++!#<1#63#*9!:!^!<0912#BN2#M81#L!-#*9!:!^!<0#1+#B)2B0#-TB190#<1#L09!2#M81#1+#!]0#(!2!<07#F#

28#(90<8//)>-#L!#2)<0#<1#36[5444#+!<9)++025#E1#<121!#!-!+)_!9# +!#1=0+8/)>-#<1# +!#(90<8/*)=)<!<#<1# +!#

B!-0#<1#0:9!#<1#12*!#1B(912!5#

65 `-#!@9)/8+*09#K7#(!9!#/021/L!9#8-!#A)-/!#<1#Q3#a1/*N91!2#(91/)2!#6#/021/L!<09!2#<89!-*1#*912#<U!27#*9!:!^!-<0# 3# L09!2# !+# <U!7# F# <02# *9!:!^!<0912# *9!:!^!-<0# J# L09!2# !+# <U!5# b*90# !@9)/8+*09# c# (!9!#

/021/L!9#8-!#A)-/!#<1#6Q#L1/*N91!27#8*)+)_!#*912#/021/L!<09!2#<89!-*1#/8!*90#<U!27#*9!:!^!-<0#[#L09!2#

!+#<U!7#F#*912#*9!:!^!<0912#*9!:!^!-<0#+!2#B)2B!2#L09!2#!+#<U!5#K=19)@8!9#+!#(90<8/*)=)<!<#(09#L09!#<1#

+!#B!M8)-!9)!#F#<1#+02#*9!:!^!<0912#1-#/!<!#1B(912!7#/0B1-*!9#1+#9128+*!<05#\02#d)+02#(09#L1/*N91!#

20-#)@8!+12#(!9!#+02#<02#!@9)/8+*09125#

P5 ;912#1B(912!2#!8*0B0=)+U2*)/!2#(9121-*!-#+!2#2)@8)1-*12#(+!-*)++!2C#

?B(912!#KC#;)1-1#Q3#*9!:!^!<0912#/0-#8-!#^09-!<!#+!:09!+#<1#Q5V44#L09!2#!-8!+12#F#8-!#(90<8//)>-#

<1#Z45P44#/0/L125#

?B(912!#cC#;)1-1#Q6#*9!:!^!<0912#/0-#8-!#^09-!<!#+!:09!+#<1#Q5J44#L09!2#!-8!+12#F#8-!#(90<8//)>-#

<1#IJ5[44#/0/L125#

?B(912!#'C#;)1-1#QV#*9!:!^!<0912#/0-#8-!#^09-!<!#+!:09!+#<1#Q5334#L09!2#!-8!+12#F#8-!#(90<8//)>-#

<1#[65VJ4#/0/L125#

!5 '!+/8+!#+!#(90<8/*)=)<!<#<1#/!<!#1B(912!5#

:5 ?O(912!#1-#*R9B)-02#(09/1-*8!+12#/8N-*0#BN2#(90<8/*)=!#12#+!#1B(912!#M81#(9121-*!#8-!#B!F09#

(90<8/*)=)<!<#912(1/*0#!#+!2#0*9!2#<025#

V5 \!#1B(912!#e81:+12#\K#?Ef`g%K#E5K5#21#<1<)/!#!#A!:9)/!9#B81:+12#<1#0A)/)-!5#W89!-*1#1+#(9121-*1#

!]0#L!#A!:9)/!<0#345444#B81:+12#F#28#(+!-*)++!#12#<1#644#*9!:!^!<09125#'!+/8+!9#+!#(90<8/*)=)<!<#<1+#

*9!:!^0# 1-# 12*!# 1B(912!5# E1@T-# +!2# T+*)B!2# 12*!<U2*)/!2# (8:+)/!<!2# +!# (90<8/*)=)<!<# <1+# 21/*09# <1+#

B81:+1#<1#0A)/)-!#1-#+!#_0-!#12#<1#Q34#B81:+12#(09#*9!:!^!<09#F#!]05#?-#:!21#!#12*02#<!*02#h12#12*!#

1B(912!#/0B(1*)*)=!#<1-*90#<1+#21/*09#<1+#B81:+1#<1#0A)/)-!i#hD09#M8Ri##

!"#$%&'()*@.1*I7D8DL,C8G8N8A"C)*!&*7D*%"IJ7,&,&O8*

35 '\'7#E5K5#12#8-!#1B(912!#<1<)/!<!#!#+!#1+!:09!/)>-#<1#(09*N*)+125#\!#(+!-*)++!#12#<1#Q6#*9!:!^!<09127#

/0-#8-!#^09-!<!#+!:09!+#<1#Q5344#L09!2#!-8!+12#/!<!#8-0#<1#1++025#?-#1+#!]0#64437#+!#1B(912!#0:*8=0#

8-#=0+8B1-#<1#(90<8//)>-#<1#Q6J5444#8-)<!<125#?-#1+#!]0#644J7#/0-*9!*>#!#P#-81=02#*9!:!^!<09127#F#

1+#=0+8B1-#<1#(90<8//)>-#A81#<1#6465344#8-)<!<125#

!5 b:*1-19#+!#(90<8/*)=)<!<#<1#+!#B!-0#<1#0:9!#1-#1+#!]0#6443#F#1-#1+#!]0#644J5#

:5 h'8N+#L!#2)<0#+!#=!9)!/)>-#(09/1-*8!+#<1#+!#(90<8/*)=)<!<#<1+#!]0#6443#!+#644Ji#!"#$%&'()*8:*F*$(LK*7(*@11.*P*Q*$(LK*7(*@1103**G:**@E/.FR*


9

J5 \!#1B(912!#'bjKE#EK7#<1<)/!<!#!# +!# A!:9)/!/)>-#<1#B>=)+127# *)1-1#8-!#(+!-*)++!#<1#QJ#*9!:!^!<0912#

/0-#8-!#^09-!<!#+!:09!+7#/!<!#8-07#<1#Q5P34#L09!2#!-8!+125#?-#1+#!]0#644P#<)/L!#1B(912!#+0@9>#8-#

=0+8B1-#<1#(90<8//)>-#<1#IZ5Z64#B>=)+125#E1#()<1C#

!5 '!+/8+1#+!#(90<8/*)=)<!<#<1#+!#B!-0#<1#0:9!#<1#12*!#1B(912!5#

:5 E)# +!# (90<8/*)=)<!<# B1<)!# <1# +!# B!-0# <1# 0:9!# <1# 12*1# 21/*09# 1-# 1+# !]0# 644P# A81# <1# V76#

B>=)+12,L09!7#!-!+)/1#+!#2)*8!/)>-#<1#12*!#1B(912!5#

!"#$%&'()*8:*>/F*$(LK*

I5 E1# 2!:1# M81# +!# 1B(912!# k7# (!9!# 0:*1-19# 8-!# (90<8//)>-# <1# QV5444# 8-)<!<127# 21# -1/12)*!-# Q4#

*9!:!^!<0912# !# ^09-!<!# /0B(+1*!# G0/L0# L09!2"# <89!-*1# QZ# <U!2l#B)1-*9!2# M81# +!# 1B(912!# m7# (!9!#

0:*1-19#12!#B)2B!#(90<8//)>-#F#*9!:!^!-<0#*!B:)R-#!#^09-!<!#/0B(+1*!#21#-1/12)*!-#I#*9!:!^!<0912#

<89!-*1#64#<U!2#h'8N+#12#+!#(90<8/*)=)<!<#<1#!B:!2#1B(912!2#912(1/*0#!+#A!/*09#*9!:!^0i#

!"#$%&'()*SIJC7D8*T*7D*Q/@9*$(LK*P*SIJC7D8*U*7D*9@/.*$(LK*

[5 `-!# 1B(912!# 0:*8=07# 1-# 1+# !]0# 644P7# (90<8/*02# (09# =!+09# <1# V645444# 189027# 8*)+)_!-<0# (!9!# 1++0#

Q65444# L09!2# <1#B!-0# <1# 0:9!5# ?-# /!B:)07# 1-# 1+# !]0# 644V7# 1+# =!+09# <1# +!# (90<8//)>-# !2/1-<)># !#

JP45444#189027#/0-28B)1-<0#Q35444#L09!2#<1#B!-0#<1#0:9!5#h?-#M8R#(09/1-*!^1#F#21-*)<0#=!9)># +!#

(90<8/*)=)<!<#1-#1+#!]0#644V7#/0-#912(1/*0#!+#644Pi##

!"#$%&'()*;V@11>:*-*>.3*;V@115:*-*5@3*@1R*

Z5 `-!#1B(912!#M81#A!:9)/!#8-#20+0#(90<8/*0#0:*)1-1#P54[4#8-)<!<12#<)!9)!2#<1+#B)2B07#M81#=1-<1#!#

J764#18902#+!#8-)<!<5#D!9!#28#A!:9)/!/)>-#/0-28B1#<)!9)!B1-*1#V5344#n@#<1#B!*19)!+127#/8F0#(91/)0#

12#<1#67[4#18902#1+#n@57#F#1B(+1!#!#QJ#*9!:!^!<0912#/8F0#/02*1#(!9!#+!#1B(912!#12#<1#J3#18902#<)!9)02#

(09#*9!:!^!<095#'!+/8+!#+!#(90<8/*)=)<!<#@+0:!+#<1#+!#1B(912!#F#+!#(90<8/*)=)<!<#<1#+!#B!-0#<1#0:9!5#

!"#$%&'()*;*VW:*-*1/.0*7$C"DLK3*;*VXY:*-*9Q@/.$()L,C8G)*

Q45 `-!#1B(912!#M81#A!:9)/!#8-#20+0#(90<8/*07#0:*)1-1#36P#8-)<!<12#<)!9)!2#<1+#B)2B07#M81#=1-<1#!#P#S#

+!#8-)<!<5#D!9!#28#A!:9)/!/)>-#/0-28B1#<)!9)!B1-*1#QI3#n@5#<1#B!*19)!+127#/8F0#(91/)0#12#<1#6#S#1+#

n@5#F#1B(+1!#Q6#*9!:!^!<0912#/8F0#/02*1#12#<1#3[#S#<)!9)02#(09#*9!:!^!<095#'!+/8+!#+!#(90<8/*)=)<!<#

@+0:!+#<1#+!#1B(912!7#+!#(90<8/*)=)<!<#<1#+!#B!-0#<1#0:9!7#F#/0B(!9!#+!#(90<8/*)=)<!<#@+0:!+#<1#+!#

1B(912!#/0-#+!#<1+#21/*09#M81#12#<1#Q7P37#/0B1-*1#+!2#(02):+12#/!82!2#<1#12!#<)A191-/)!5#

!"#$%&'()*;W*-*9*7$C"LAZ83*;)*XY*-*5>/0*$(&A)L,C8G)*

QQ5 \!#1B(912!#K%'b#EK7#M81#A!:9)/!#B!*19)!+#<1#(!(1+19U!#*)1-1#(91=)2*0#/91!9#8-!#-81=!#1B(912!#(!9!#

A!:9)/!9# /8!<19-027# F# 1-# 28# (9)B19# !]0# 12(19!# (90<8/)9# Q345444#8-)<!<127# (!9!# +0# /8!+# 21# 12*8<)!#

12*!2#*912#!+*19-!*)=!2C#

K+*19-!*)=!#QC#1B(+1!9#Z#*9!:!^!<0912#!#*)1B(0#/0B(+1*0#/0-#8-!#^09-!<!#+!:09!+#<1#65444#L09!2#

!+#!]0#(09#*9!:!^!<095#

K+*19-!*)=!#6C#1B(+1!9#[#*9!:!^!<0912#!#*)1B(0#/0B(+1*0#/0-#8-!#^09-!<!#+!:09!+#<1#Q5[44#L09!2#

!+#!]0#(09#*9!:!^!<09#F#6#*9!:!^!<0912#!#*)1B(0#(!9/)!+#G34o"5#

K+*19-!*)=!# PC# 1B(+1!9# !# 3# *9!:!^!<0912# !# *)1B(0# /0B(+1*0# F# J# *9!:!^!<0912# !# *)1B(0# (!9/)!+#

GJ4o"#/0-#8-!#^09-!<!#+!:09!+#<1#65444#L09!2#!+#!]0#(09#*9!:!^!<09#G^09-!<!#/0B(+1*!"5#

E1#()<1C#

!5 g-<)M81#+!#!+*19-!*)=!#M81#(9121-*!#8-!#(90<8/*)=)<!<#BN2#A!=09!:+15#

:5 ?O(9121#1-#*R9B)-02#(09/1-*8!+12#/8N-*0#BN2#(90<8/*)=!#12#+!#!+*19-!*)=!#1+1@)<!#912(1/*0#!#+!2#

0*9!2#<025#

/5 g-<)M81#!+@8-!#<1#+!2#9!_0-12#M81#+0#1O(+)M81-5#!"#$%&'()*8:*E/>>*$(LK/*Q/@.*$(LK*P*E/F@*$(LK3**G:**99/15R*P*0/1FR*


10

TEMA 6 - EJERCICIOS DE PUNTO MUERTO

!" -8$%&'()&*$%0&024$0$%$%1$%Z$F)24$42;8%0&%4$1@$06%0&(6)5296%*&%(1$85&$%1$%6(42;8%0&%()60342)%

6% 46'()$)% 16*% 46)068&*% 73&% 11&9$% 2846)(6)$06% *3% '60&16% d?==T% e4$0$% @$($56% 11&9$% 38%

46)0;8b"%Y5)$%&'()&*$%1&%46F)$%=.<>%(6)%4$0$%46)0;8"%_)60342)16*%5&80)N$%386*%46*5&*%Z2g6*%

$83$1&*%0&%B===>%K%38%46*5&%9$)2$F1&%3825$)26%0&%=.?>%

/&%(20&D%

$b%H+%($)52)%0&%73L%8^'&)6%0&%($)&*%0&%@$($56*%&*%()&Z&)2F1&%Z$F)24$)%16*%46)068&*M%

Fb% /3(682&806% 38$% ()603442;8% $83$1% 0&% C===% ($)&*% 0&% @$($56*.% 4$1431&% &1% 46*5&% 0&%

Z$F)24$42;8%K%&1%46*5&%0&%$0732*242;8%0&%16*%46)068&*"%

4b% U&()&*&85$42;8% O)JZ24$% 0&% 16*% F&8&Z2426*% 6% (L)020$*% 6F5&8206*% *2% *&% ()6034&8% 16*%

46)068&*%8&4&*$)26*%($)$%16*%($)&*%0&%@$($56*%*&h$1$06*%&8%&1%$($)5$06%$85&)26)"%

?" -8$%&'()&*$.%0&024$0$%$%1$%Z$F)24$42;8%0&%g&)*L2*%0&%(3856.%73&%9&80&%$%38%()&426%3825$)26%

0&%BC%>.%52&8&%386*%46*5&*%Z2g6*%565$1&*%0&%B]"?==%>%K%386*%46*5&*%9$)2$F1&*%3825$)26*%0&%?T%>"%

:*52'$806%1$%()603442;8%$83$1%&8%P"===%3820$0&*"%

/&%(20&D%

$" I$1431&%&1%(3856%'3&)56%K%)$@68&%*3%*2O82Z24$06"%

F" U&()&*L85&16%O)JZ24$'&85&"%

4" I$1431&%&1%)&*315$06%*3(682&806%73&%1$%&'()&*$%9&802&)$%560$%*3%()603442;8"%

T" #$%&'()&*$%/_YUd%/"+".%0&024$0$%$% 1$% Z$F)24$42;8%K%9&85$%0&% )6($%0&(6)529$.% *&%(1$85&$% 1$%

(6*2F2120$0%0&%&1$F6)$)%&11$%'2*'$%&1%4$1@$06%0&(6)5296%73&%G$*5$%$G6)$%46'()$%$%38%()&426%

3825$)26% 0&% <% >"% :8% &1% 4$*6% 0&% 73&% 0&420$% Z$F)24$)16% &11$% '2*'$% 5&80)N$% 73&% $Z)685$)% 16*%

*2O32&85&*%46*5&*D%

• +17321&)%0&%8$9&%2803*5)2$1%?C"===.=%>%• /3&106*%K%*$1$)26*%0&%&'(1&$06*%Z2g6*%TC"===.=%>%

• I6*5&%0&%46'()$%0&%'$5&)2$*%()2'$*%e46*5&%3825$)26b%?.=%>%

• I68*3'6%0&%&8&)ON$%e46*5&%3825$)26b%!.=%>%

• +'6)52@$42;8%$83$1%0&%'$7328$)2$%!"C==.=%>%

I68% &*5$% &*5)3453)$% 1$% &'()&*$% (60)N$% ()60342)% ?C"===%

3820$0&*%$83$1&*"%

/&%(20&D%

+b% X&5&)'28$)% &1% 8^'&)6% 'N82'6% 0&% 3820$0&*% e4$1@$06%

0&(6)5296b%73&%5&80)N$%73&%()60342)%1$%&'()&*$%($)$%g3*52Z24$)%

1$% 0&42*2;8% 0&% ()60342)% &11$% '2*'$% K% )&$12@$)% 1$% 289&)*2;8%

()6K&45$0$"% %

Ab% HI3J1% *&)N$% &1% ()&426% 'JQ2'6% 73&% 0&F&)N$% ($O$)% (6)% &1%

4$1@$06% 0&(6)5296% *2% *3*% 8&4&*20$0&*% 0&% ()603442;8% K% 9&85$%

*68%0&%!C"===%3820$0&*M%

Ib%U&()&*&85$)%O)JZ24$'&85&%1$*%06*%43&*5268&*%$85&)26)&*"%


11

P" -8$%&'()&*$%52&8&%38$*%4$)O$*%0&%&*5)3453)$%0&%B="===%>%K% 16*%46*5&*%9$)2$F1&*%6)2O28$06*%

(6)%1$%()603442;8%0&%?="===%3820$0&*%0&%()603456%$*42&80&8%$%i="===%>"%#$%9&85$%0&%!="===%

3820$0&*%0&%()603456%G$%O&8&)$06%38%28O)&*6%0&%iC"===%>"%I68%&*56*%0$56*.%*&%(20&D%%

$b%I$1431$)%K%46'&85$)%&1%-'F)$1%0&%)&85$F2120$0%6%_3856%W3&)56%0&%1$%&'()&*$"%%

Fb%A&8&Z2426%73&%6F5&80)N$%468%1$%9&85$%0&%P"===%3820$0&*%(6)%&842'$%0&%1$%()603442;8%0&%

(3856%'3&)56"%

!"#$%&'()"$*)+,-)"#$*)".!-,'#$-#(/0$)-#&-!("#$-0$%!'#-$

C" -8$%&'()&*$%()6034&%$1Z6'F)$*%73&%9&80&%$1%()&426%0&%B"C==%1$%3820$0"%#6*%46*5&*%3825$)26*%

9$)2$F1&*% *68% 0&% ?"C=="% /3(68O$'6*% 73&% 16*% 46*5&*% Z2g6*% 6% 4$)O$*% 0&% &*5)3453)$*% $83$1&*%

$*42&80&8%$%B%'21168&*"%H_$)$%73L%9613'&8%0&%$1Z6'F)$*%*&%$14$8@$)J%&1%(3856%'3&)56M%%

!"#$%&'()*@)788*+#L"04<+/*

B" _$)$%38$%0&5&)'28$0$%&'()&*$.%16*%46*5&*%Z2g6*%K%16*%46*5&*%9$)2$F1&*%($)$%Z$F)24$)%38%83&96%

()603456%$*42&80&8%$%!=="===%>%K%P==%>%(6)%3820$0.%)&*(&4529$'&85&"%:*&%83&96%()603456%

(60)N$% 46'()$)16% &8% &1% '&)4$06% $% B==% >% (6)% 3820$0"% HS3L% 1&% 46892&8&% $% 1$% &'()&*$.%

46'()$)16%6%Z$F)24$)16M%j%H(6)%73LM%U&()&*&85$%1$%*253$42;8%468%38%O)JZ246%&Q(124$5296"%%

!"#$%&'()*>.*&(1.<./+<M*L+4<&%+<*+*3+<1&<*B.*788*$(&B+B./*

]" -8$%*642&0$0%52&8&%386*%46*5&*% Z2g6*%0&%!=="===%>"%:Z&45^$%9&85$*%0&%<"C==%3820$0&*%$%38%

()&426%0&%C=%>[3820$0%K%52&8&%386*%46*5&*%9$)2$F1&*%0&%T=%>[3820$0"%I$1431$)D%%

$" X&Z28&%&1%(3856%'3&)56%6%3'F)$1%0&%)&85$F2120$0"%%

F" I$1431$)%024G6%(3856%'3&)56%&8%&*5$%*642&0$0"%

4" I$1431$%&1%F&8&Z2426%468%1$*%9&85$*%$453$1&*%e<"C==%3820$0&*b"%%0" U&()&*&85$)%O)JZ24$'&85&%&1%(3856%'3&)56"%%

!"#$%&'()*4,*7)888*$()9*%,*K8)888N*

<" -8$%*642&0$0%52&8&%386*%46*5&*% Z2g6*%0&%!=="===%>"%:Z&45^$%9&85$*%0&%C"===%3820$0&*%$%38%

()&426%0&%C=%>"%d2&8&%386*%46*5&*%9$)2$F1&*%0&%?=="===%>"%I$1431$)D%%

$" I$1431$)%&1%(3856%'3&)56%&8%&*5$%*642&0$0"%%

F" I$1431$%&1%)&*315$06%0&1%&g&)42426%468%1$*%9&85$*%$453$1&*"%%!"#$%&'()*+,*@8)888*$()9**4,*O78)888*N*

i" :1%(3856%'3&)56%6%3'F)$1%0&%)&85$F2120$0.%0&%38$%&'()&*$%73&%Z$F)24$%K%9&80&%38%()603456.%

&*%0&%P"]==%3820$0&*"%/$F2&806%73&%16*%46*5&*%9$)2$F1&*%*68%0&%?]%>[30"%j%&1%()&426%0&%9&85$%

0&1%()603456%&*%0&%T?%>[30.%H$%43$856%$*42&80&8%16*%46*5&*%Z2g6*M%/6F)&%38$%)&()&*&85$42;8%

O)JZ24$%&Q(124$%73L%*34&0&%*2%Z$F)24$%K%9&80&%'J*%0&%P"]==%3820$0&*"%%

!"#$%&'()*A6)788*

!=" -8$%&'()&*$%Z$F)24$%38%()603456%468%386*%46*5&*%Z2g6*%0&%?=="===%>%K%38%46*5&%9$)2$F1&%0&%

?=%>%(6)%3820$0.%K%*2%9&80&%!C"===%3820$0&*.%6F52&8&%38%F&8&Z2426%0&%!=="===%>"%I$1431&%&1%

()&426%3825$)26%0&%9&85$%0&1%()603456%K%&1%(3856%'3&)56"%

#12345678$*$9:;<=$*,$9$>;8;;;$378$?@$AB1?34C1$


12

!!" I$1431$)%&1%()&426%$1%73&%9&80&%38%()603456%38$%&'()&*$%73&%16%Z$F)24$%468%386*%46*5&*%Z2g6*%

0&%P<"===%>.%386*%46*5&*%9$)2$F1&*%0&%T=%>%(6)%3820$0.%K%$14$8@$%&1%3'F)$1%0&%)&85$F2120$0%

468% <==% 3820$0&*"% I$1431$)% &1% )&*315$06% 73&% 6F52&8&% *2% Z$F)24$% K% 9&80&% !"===% 3820$0&*"%

U&()&*&85$)%&8%38%O)JZ246%16*%46*5&*%&%28O)&*6*%0&%&*5$%&'()&*$"%%

#12345678$*$9$D;<=$)$9$>E8;;;<8$

!?" /2%38$%*642&0$0%52&8&%386*%46*5&*%Z2g6*%0&%C="==="===%0&%>"%K%386*%46*5&*%9$)2$F1&*%3825$)26*%0&%B"===%>.%K%&8%38%&g&)42426%&468;'246%G$%)&$12@$06%38$*%9&85$*%565$1&*%0&%?C="==="===%0&%

>".%73&%46))&*(680&8%$%?C"===%3"%ZN*24$*"%I$1431$)%&1%(3856%'3&)56%6%3'F)$1%0&%)&85$F2120$0%

&8%3820$0&*%ZN*24$*"%

#12345678$>E8F;;$378$

!T" -8$%&'()&*$%()&*&85$%16*%*2O32&85&*%46*5&*D%+17321&)%0&%164$1&*%i"===>\%I6'F3*52F1&%?"===>\%

/$1$)26*% !="===>\% W$5&)2$*% ()2'$*% !"C==>\% _3F12420$0% !"===>"% /3% ()603442;8% 565$1% G$%

$14$8@$06% 1$*%C==%3820$0&*%73&%46'&)42$12@$%$%38%()603456%3825$)26%0&%!?>"%X&5&)'28$)%&1%

3'F)$1%0&%)&85$F2120$0"%

#12345678$:8;;;$378$

!P" +%($)52)%0&%16*%0$56*%6F5&8206*%0&%1$%4685$F2120$0%0&%1$%/"+"%k%*&%*$F&%73&D%#6*%46*5&*%565$1&*%*&%&1&9$8%$%!]"C==%3"'"%

#6*%46*5&*%Z2g6*%0&%1$%&'()&*$%$*42&80&8%$%?"C==%3"'"%

#6*%28O)&*6*%(6)%9&85$*%$*42&80&8%$%!<"===%3"'"%

#$%&'()&*$%G$%9&80206%T==%3820$0&*%0&%()603456"%

/&%(20&%4$1431$)%&1%(3856%'3&)56"%

#12345678$EF;$378$

!C" -8$%&'()&*$%732&)&%&'(&@$)%$%Z$F)24$)%'&4G&)6*%0&%O$'$%$15$%($)$%)&O$16*%0&%&'()&*$"%:1%

()&426% 0&% 9&85$% 3825$)26% 0&420206% (6)% &1% 0&($)5$'&856% 0&% '$)l&528O% 5)$*% 38% &*53026% 0&%

'&)4$06% K% &1% $8J12*2*% 0&% ()&426*% 0&% 1$% 46'(&5&842$% &*% 0&% ?B% >"% #6*% 46*5&*% Z2g6*% 565$1&*%

)&73&)206*%(6)%&*5&%83&96%()603456%$*4&80&)J8%$%?!"?<=%>%K%16*%46*5&*%9$)2$F1&*%3825$)26*%$%

!=%>"%#$%()603442;8%$83$1%*&%&*52'$%&8%!"!==%3820$0&*"%

/&%(20&D%

$b%I$1431&%&1%(3856%'3&)56%K%)$@68&%*3%*2O82Z24$06"%

Fb%I$1431&%&1%)&*315$06%*3(682&806%73&%1$%&'()&*$%9&802&)$%560$%*3%()603442;8"%

!"#$%&'()*-P*2*@)668*0.%Q.<"/9*R*2*O6)=S8N)*

!B" -8$%&'()&*$%0&%'$5&)2$1%0&(6)5296%()&5&80&%1$8@$)%38$%83&9$%F24241&5$"%/&%1&%()&*&85$8%06*%

$15&)8$529$*D%

− f$F)24$)1$.% 16%73&%*3(68&%386*%465&*%Z2g6*%0&%?P?"===%>%K%386*%46*5&*%9$)2$F1&*%0&%!?C%

>[3820$0"%

− +0732)2)1$% $% 38$% Z$F)24$% K% 46'&)42$12@$)1$% 468% *3% '$)4$.% &*56% *3(68&% 38% 46*5&% 0&%

$0732*242;8%0&%!<=%>[38%

$" :Q(124$)%&8%73L%4$*6%1$%&'()&*$%Z$F)24$)J%K%43$806%46'()$)J"%

F" /2%1$%&'()&*$%0&420&%Z$F)24$)%&*5&%$h6%C"===%F24241&5$*.%H73L%6(42;8%&1&O2)JM%

!"#$%&'()*-P*2*?)?88*$()*


13

!]" #6*%$13'86*%0&%?m%0&1%I61&O26%#6*%_&h$*4$1&*.%468%6Fg&56%0&%)&4$F$)%Z6806*%($)$%*3%92$g&%Z28%

0&%&*53026*.%*&%(1$85&$%1$%(6*2F2120$0%0&%9&80&)%F64$02116*%&8%38%164$1%$0K$4&85&%$1%I&85)6"%

#6*%46*5&*%565$1&*%0&%&*5&%()6K&456%*68%16*%*2O32&85&*D%

+17321&)%0&1%164$1D%T==%>%

c'(3&*56%W38242($1D%C?%>%

I6*5&%9$)2$F1&%3825$)26%(6)%F64$02116D%="P=%>%%

_)&426%0&%9&85$%3825$)26D%!"C=%>%

I$1431$)%&1%(3856%'3&)56%6%3'F)$1%0&%)&85$F2120$0%K%46'&85$)%&1%)&*315$06"%

#12345678$GE;$378$

!<" -8%0&5&)'28$06%&'()&*$)26%0&*&$%$F)2)%38%)&*5$3)$85&%0&%46'20$*%&8%38$%@68$%0&%6Z2428$*%

0&%38$%O)$8%4230$0"% #6*%4J14316*%0&%46*5&*%($)$%!"===%46'20$*% *&)920$*% *68% 16*% *2O32&85&*%

e#6*%46*5&*%$83$1&*%0&%(&)*68$1%*68%()6(6)4268$1&*%4$0$%'&*bD%%

• /3&106*%K%*$1$)26*D%!"?=="===%>"%$83$1&*%%• +'6)52@$4268&*D%B=="===%>"%$83$1&*%(6)%0&()&42$42;8%0&%'$7328$)2$%&%28*5$1$4268&*"%%

• +17321&)%0&1%164$1D%C="===%>"%W&8*3$1&*%%

• ,&*56)N$%K%$*&*6)N$D%?="===%>"%W&8*3$1&*%%

• I$0$%46'20$%73&%&1$F6)$%52&8&%386*%46*5&*%(6)%16*%28O)&02&85&*%35212@$06*%0&%C=%>"%%

• :1%()&426%73&%Z2g$)$%0&%1$*%46'20$*%*&)J%0&%]=%>%4$0$%38$"%:*5&%()&426%16%Z2g$%&8%Z3842;8%0&%

1$% 46'(&5&842$% 0&% 16*% )&*5$3)$85&*% *2'21$)&*% 73&%G$K% &8% 1$% @68$% K% 0&% *3% &*5)3453)$% 0&%

46*5&*"%%

/&%(20&D%%

$" X&5&)'28$)% 43$856*% (1$56*% 5&80)J% 73&% *&)92)% $1% '&*% ($)$% $14$8@$)% *3% -'F)$1% 0&%

U&85$F2120$0%%

F" /2%03)$85&%&1%'&*%9&802&*&%!C"===%46'20$*%HI3J1%*&)N$%*3%F&8&Z2426M%%

!"#$%&'()*+,*@@)888*$()9*4,*S8)888N*

*

!


14

TEMA 7 - PROBLEMAS MODELO WILSON

Q5 \!#1B(912!#j$'#21#<1<)/!#!#+!#/0B(9!#X#=1-*!#<1#A9)@09UA)/02#)-<82*9)!+125#'!<!#!]0#/0B(9!#1-#K2)!#F#

=1-<1#1-#?890(!#V44#A9)@09UA)/025#?+#/02*1#<1#@12*)>-#<1#/!<!#(1<)<0#12#<1#QZ35PQ673#85B5#F#1+#/02*1#

<1#*1-19#8-#A9)@09UA)/0#!+B!/1-!<0#<89!-*1#8-#!]0#12#<1#6345444#85B5#'!+/8+!#1+#=0+8B1-#>(*)B0#<1#

(1<)<05#

!"#$%&'()*+,*-.&/".0-&%"12*

65 `-!# 1B(912!# -1/12)*!# !-8!+B1-*1# +!# /!-*)<!<# <1# 6635444# 8-)<!<12# <1# (90<8/*0# (!9!#

/0B19/)!+)_!9+05#?+#/02*1#<1#91!+)_!9#8-#(1<)<0#12#<1#I34#18902#F#1+#/02*1#<1#B!-*1-)B)1-*0#<1#/!<!#

8-)<!<#1-#1+#!+B!/R-#12#<1#473V#189025#E1#()<1C#

!" $0+8B1-#>(*)B0#<1#(1<)<02#!+#!]05#

:" ?+#-TB190#<1#(1<)<025#

/" \!#/!<1-/)!#>(*)B!#<1#(1<)<05#

!"#$%&'()*34*+,2555*$(&636718*94**:8*%4*;5*60312*

P5 \!#<1B!-<!#!-8!+#<1#8-#(90<8/*0#12#<1#Q645444#8-)<!<127#F#1+#(1<)<0#>(*)B0#12#<1#65444#8-)<!<125#

!5 a!++!#1+#(91/)0#2!:)1-<0#M81#+!#*!2!#<1#/02*1#<1#!+B!/R-#12#<1#8-#Q4#o#F#1+#/02*1#<1#91!+)_!9#8-#

(1<)<0#12#<1#6[764#S5##

:5 j1!+)_!#+!#91(9121-*!/)>-#@9NA)/!#<1+#(90:+1B!7#2!:)1-<0#M81#1+#2*0/d#<1#21@89)<!<#12#<1#644#8-5#

F#1+#(+!_0#<1#!(90=)2)0-!B)1-*0#12#<1#P#<U!25##GK]0#/0B19/)!+#&#PJ4#<U!25"#

!"#$%&'()*34**<=>:+?8**94**=5*@76&6"1*%363*=*60312*

V5 `-!#1B(912!#*)1-1#8-!#<1B!-<!#12*)B!<!#!-8!+#<1#8-#B!*19)!+#pmp#<1#6445444#d@5#E!:)1-<0#M81#1+#

=0+8B1-#>(*)B0#<1#(1<)<0#12#<1#645444#n@57#M81#1+#(+!_0#<1#!(90=)2)0-!B)1-*0#12#<1#Q4#<U!2#F#M81#1+#

2*0/d#<1#21@89)<!<#12#<1#P5I34#n@57#/!+/8+!C#

!" ?+#-TB190#<1#(1<)<02#M81#1A1/*8!9N#1-#8-#!]05#

:" ?+#*)1B(0#M81#*9!-2/8991#1-*91#(1<)<02#0#/!<1-/)!#>(*)B!#<1#(1<)<05#

/" ?+#(8-*0#<1#(1<)<05#!"#$%&'()*34*<5*@76&6"18**94*A=*60318**%4*:2A5=*$(&636712*

35 `-!# 1B(912!# M81# 21# <1<)/!# !# +!# A!:9)/!/)>-# <1# *9!-2A09B!/)0-12# /!8/L19!2# /0B(9!# 8-!# ()1_!# <1#

B1*!+# M81# )-/09(09!# !# 282# (90<8/*02# *9!-2A09B!<025# '!<!# <U!# 21# /0-28B1-#Q[I#()1_!25# ?+# (1<)<0#

*!9<!#Z#<U!2#1-#++1@!9#G<12<1#M81#21#91!+)_!#1+#(1<)<0"#F#282#/02*12#<1#1B)2)>-#20-#<1#J44#189025#?+#

/02*1#8-)*!9)0#<1#B!-*1-)B)1-*0#12#<1#673#18902#(09#8-)<!<#F#!]05#'!+/8+!C#

!" ?+#*!B!]0#<1+#+0*1#M81#B)-)B)/1#+02#/02*12#*0*!+12#<1#+!#@12*)>-#<1#2*0/d25#

:" %TB190#<1#(1<)<02#!+#!]05#

/" '!<1-/)!#>(*)B!#<1#(1<)<05#

<" D8-*0#<1#(1<)<0#2!:)1-<0#M81#1+#2*0/d#<1#21@89)<!<#12#Q5444#8-)<!<125#!"#$%&'()*34*,2=B,*$(&636718*94*<+*60318*%4*A5*60318*64*+2=BA2*


15

TEMA 9 – SELECCIÓN DE INVERSIONES HOJA 1

Q5 `-# A!:9)/!-*1# <1# /!B)21*!2# <1# !+@0<>-# <121!# !:9)9# 8-!# -81=!# AN:9)/!# F# *)1-1# <02# 0(/)0-12# <1#

+0/!+)_!/)>-C#Q"#;!99!2!5#?+#<121B:0+20#)-)/)!+#219U!#<1#8-#B)++>-#<1#189027#@1-19N-<021#8-02#A+8^02#<1#

/!^!# 12*)B!<02# <1# 3345444# 18902# F# <1# J635444# 1-# 1+# (9)B19# F# 21@8-<0# !]07# 912(1/*)=!B1-*15# 6"#

eR9)<!5#?+#<121B:0+20#)-)/)!+#219U!#<1#[445444#189027#@1-19N-<021#8-02#A+8^02#<1#/!^!#12*)B!<02#<1#

6345444#18902#F#<1#I445444#18902#1-#1+#(9)B19#F#21@8-<0#!]07#912(1/*)=!B1-*15#?+#/02*1#<1#/!()*!+#

12#<1+#Q4o5#

!5 h'8N+#12#1+#=!+09#!/*8!+#-1*0#G$K%"#<1#/!<!#)-=192)>-i#:5 hf8R#/)8<!<#1+1@)9N#1+#A!:9)/!-*1#(!9!#)-2*!+!9#+!#AN:9)/!#F#(09#M8Ri#

!"#$%&'(2*34*CDE!"F*<=2,+B>:A8*CDE

#"F*,2GB,><+;*

65 `-!#1B(912!#21#(+!-*1!#<02#(90F1/*02#<1#)-=192)>-5#?+#(9)B190#)B(+)/!#8-#<121B:0+20#<1#3#B)++0-12#

<1# 189025# ?+# 12*8<)0# (91=)0# (91=R# M81# @1-191# 8-02# A+8^02# <1# /!^!# <1# 6#B)++0-12# 1+# (9)B19# !]07# V#

B)++0-12#1+#21@8-<05#?+#21@8-<0#(90F1/*0#12#*!B:)R-#<1#3#B)++0-12#<1#189025#\!#)-=192)>-#(!9!#12*1#

21@8-<0#(90F1/*0#@1-19!9N#8-02#A+8^02#<1#/!^!#!#+0#+!9@0#<1#<02#!]02#<1#V#B)++0-12#1+#(9)B190#F#<1#6#

B)++0-12#1+#21@8-<05#?+#=!+09#912)<8!+#21#12*)B!#)-1O)2*1-*15#W1*19B)-1#/8N+#<1#+02#<02#(90F1/*02#<1#

)-=192)>-7#28(0-)1-<0#8-#*)(0#<1#)-*19R2#<1#B19/!<0#<1+#3o#!-8!+7#12#B1^09C#

!5 K(+)/!-<0#1+#BR*0<0#<1+#(+!_0#<1#91/8(19!/)>-5#

:5 K(+)/!-<0#1+#BR*0<0#<1+#$K%5#j!_0-1#!B:!2#912(812*!2#

!"#$%&'(2*34*HI!*F*<*3J"*K*:*L71718*HI

#"F*<*DJ"*K*=*L71718*94*CDE

!*F*,A+2BG:>B8*CDE

#*F*=+A2,B+>B*

P5 `-!#1B(912!#<1:1#<1/)<)9#1-*91#<02#(90F1/*02#<1#)-=192)>-5#?+#(90F1/*0#k#91M8)191#8-#<121B:0+20#

)-)/)!+#<1#P45444#18902#F#21#12(19!#M81#91(09*1#8-02# A+8^02#<1#/!^!#<1#Q[5444#18902#1+#(9)B19#!]07#

[5444#18902#1+#21@8-<07#V5444#18902#1+#*19/19#!]07#645444#18902#1+#/8!9*0#F#P5444#18902#1+#M8)-*0#F#

T+*)B0#!]05#D09#28#(!9*17#1+#(90F1/*0#m#*!B:)R-#-1/12)*!#8-#<121B:0+20#)-)/)!+#<1#P45444#18902#F#21#

12(19!# M81# (90<8_/!# 8-02# A+8^02# <1# /!^!# <1# V5444# 18902# 1+# (9)B19# !]07# [5444# 18902# 1+# 21@8-<07#

QV5444#18902#1+#*19/19#!]07#PJ5444#18902#1+#/8!9*0#F#665444#18902#1+#M8)-*0#F#T+*)B0#!]05#E1#()<1C#

!5 h'8N+#219U!#(91A19):+1#2)#21#8*)+)_!9!#1+#/9)*19)0#<1+#(+!_0#<1#91/8(19!/)>-#0#(!FX:!/di#:5 hK#28#1-*1-<197#219U!#+>@)/!#<)/L!#1+1//)>-i#/5 D+!-*11#+!#1O(912)>-#<1+#$!+09#K/*8!+#%1*0#<1+#(90F1/*0#k#

!"#$%&'(2*34*HI$"F*A*3J"18*HI

%*F*A*3J"1*K*;5*6031*

V5 `-#1B(912!9)0#*)1-1#+!#(02):)+)<!<#<1#)-=19*)9#1-#<02#(90F1/*02C#

!5 '0B(9!#<1#8-#:!9/0#1-#/0-2*98//)>-#/0-#8-!#)-=192)>-#<1#Q445444#189025#'0-#+!#=1-*!#<1+#B)2B07#

*9!-2/899)<02#<02#!]027#0:*1-<9U!#QP45444#189025#

:5 \!#(812*!#1-#B!9/L!#<1#8-!#AN:9)/!#<1#/!9!B1+02#/0-#8-!#)-=192)>-#<1#P445444#18902#F#8-02#A+8^02#

<1#/!^!#<1#Q345444#F#QJ45444#189027#<89!-*1#1+#(9)B19#F#21@8-<0#!]07#912(1/*)=!B1-*15#E1#M8)191#

2!:19#1-#M8R#0(/)>-#<1:19U!#)-=19*)9#1+#1B(912!9)0#F#(09#M8R5#

!"#$%&'(2*34*MNI&*F*<;>5+O8*MNI

'"F*+><:O*

35 '!+/8+!#+!#91-*!:)+)<!<#M81#/0-2)@81#8-#!//)0-)2*!#M81#/0B(9!#8-!#!//)>-#(09#644#85B#F#+!#=1-<1#(09#

P44#85B5#a!:)1-<0#/0:9!<0#64#85B5#/!<!#!]0#1-#/0-/1(*0#<1#<)=)<1-<025#?-/81-*9!#+!#91-*!:)+)<!<#

<1+#(90F1/*0#(!9!#1+#!//)0-)2*!#2)#+!#<89!/)>-#<1#+!#)-=192)>-#12#<1#6#!]025#

!"#$%&'(2**MNI*F*A<>,:O*


16

J5 `2*1<#A09B!#(!9*1#<1+#<1(!9*!B1-*0#<1# )-=192)0-12#<1# +!#1B(912!#qge?jEK#F#*)1-1#20:91# +!#B12!#

<02#(90F1/*02#<1#)-=192)>-#/0-#+!2#2)@8)1-*12#/!9!/*19U2*)/!2#G1-#B)+12#<1#18902"C#

Djbm?';bE#W?#g%$?jEgr%#

D90F1/*0# W121B:0+20#

)-)/)!+#

q+8^02#<1#/!^!#

# # #

K# 63# Q[# QQ#

c# 34# 63# P4#

E1#()<1#/!+/8+!9#+!#*!2!#)-*19-!#<1#91-*!:)+)<!<#<1#/!<!#(90F1/*0#F#9!_0-!97#21@T-#12*1#/9)*19)07#/8N+#12#

1+#(90F1/*0#BN2#/0-=1-)1-*15#

!"#$%&'(2*34*MNI&*F*<<>;GO8*MNI

'*F*=>A:O*

I5 `-!# 1B(912!# <121!# ++1=!9# !# /!:0# 8-# -81=0# (90F1/*0# <1# )-=192)>-# =!+09!<0# 1-# 6345444# 189025# ?+#

(90F1/*0#*)1-1#8-!#<89!/)>-#<1#<02#!]025#\02#A+8^02#<1#/!^!#M81#12(19!#0:*1-19#(09#+!#91!+)_!/)>-#<1+#

(90F1/*0# 20-# <1# Q345444# 18902# 1+# (9)B19# !]0# F# <1# QJ45444# 18902# 1+# 21@8-<0# !]05# E)# 1+# /02*1# <1+#

<)-190#12#<1+#Q4o#!-8!+7#21#()<1C#

!5 W1*19B)-!9#1+#(+!_0#<1#91/8(19!/)>-#G(!FX:!/d"#<1#12*!#)-=192)>-7#1O(912!<0#1-#!]02#

:5 '!+/8+!9#1+#$!+09#K/*8!+#%1*0# G$K%"#<1#12*!# )-=192)>-5# hj1/0B1-<!9U!# !# +!# 1B(912!#!/1(*!9#1+#

(90F1/*0i#hD09#M8Ri#

/5 '!+/8+!9#1+#;gj#<1#12*!#)-=192)>-5#!"#$%&'(2*34*HI*F*<>=+,*3J"18*94*CDE*F*<B2,:,>5;8*%4*MNI*F*<,>;;O*

[5 '0-2)<19!#+!2#<02#)-=192)0-12#2)@8)1-*12C#- g-=192)>-#KC#K<M8)2)/)>-#<1#Q5444#0:+)@!/)0-12#<1#=!+09#-0B)-!+#J#S5#/8F0#=!+09#<1#911B:0+20#12#<1+#

QQ4o#M81#0A91/1#8-#*)(0#<1#)-*19R2#!-8!+#<1+#Q4o#F#/8F!#!B09*)_!/)>-#21#L!9N#<1-*90#<1#<02#!]025#

- g-=192)>-#cC#K<M8)2)/)>-#<1#8-!#BNM8)-!#M81#/812*!#J5444#S#F#@1-19!#A+8^02#<1#/!^!#<1#Q5[44#S5#1+#

(9)B19#!]0#F#35644#S#1+#21@8-<05#

!" ?+1@)9#+!#B1^09#)-=192)>-#21@T-#1+#/9)*19)0#<1+#$K%#2!:)1-<0#M81#1+#/02*1#<1+#<)-190#12#<1+#Io5#

:" '!+/8+!9#1+#;gj#<1#!B:!2#)-=192)0-12#F#1O*9!19#+!2#/0-21/81-/)!2#0(09*8-!25#

!"#$%&'(2*34*CDE&*F*B;:>,8*CDE

'*F*++;><+8*MNI

&*F*<;>==O8*MNI

'*F*:>AO*

Z5 `-!#1B(912!#12*8<)!#8-#(90F1/*0#<1#)-=192)>-#M81#(9121-*!#+!2#2)@8)1-*12#/!9!/*19U2*)/!2C#

- W121B:0+20#)-)/)!+C#[45444#85B5#

- q+8^0#<1#/!^!#Q19#!]0C#P45444#85B5#

- D!9!#1+#912*0#<1#+02#!]02#21#12(19!#M81#A+8^0#<1#/!^!#21!#8-#Q4o#28(19)09#!+#<1+#!]0#!-*19)095#

- W89!/)>-#*1B(09!+C#3#!]02#

- $!+09#912)<8!+C#645444#85B5#

- '02*1#B1<)0#/!()*!+C###Jo##

E1@T-#1+#/9)*19)0#<1+#$K%7#h21#(81<1#++1=!9#!#*R9B)-0#12*!#)-=192)>-i#

!"#$%&'(2**CDE*F*BG2,;,>+A*

Q45 \!#1B(912!#KEeKj#12*N#12*8<)!-<0#<02#(02):+12#)-=192)0-12C#

g-=#KC# XQ445444#,#J45444#,#I45444#

g-=#cC# XQ645444#,#[45444#,#J45444#

'02*1#<1+#/!()*!+#12#Jo5#

!" a!++!#1+#$K%#<1#/!<!#)-=192)>-#F#<)#2)#)-*1912!5#:" a!++!#1+#;gj#<1#/!<!#)-=192)>-#F#<)#2)#)-*1912!5#

!"#$%&'(2*34*CDE&"F*<B2:5A>,+8*CDE

'"F*B2BG<>;B8*MNI

&*F*<B>BBO8*MNI

'"F*<<>,<O*


17

SELECCIÓN DE INVERSIONES HOJA 2

Q5 `-!#1B(912!#*)1-1#M81#<1/)<)9#1-*91#<02#(90F1/*02#<1#)-=192)>-#!#(!9*)9#<1#+02#<!*02#2)@8)1-*12C#

-<"T.%1"*;U*

- W121B:0+20#)-)/)!+C#Q65444#S#

- D!@02#!#91!+)_!9#<89!-*1#1+#(9)B19#!]0C#V5444#S#

- D!@02#!#1A1/*8!9#1+#21@8-<0#!]0C#J5444#S#- '0:902#0:*1-)<02#1+#(9)B19#!]0C#QJ5444#S#

- '0:902#0:*1-)<02#1+#21@8-<0#!]0C#Q[5444#S#

-<"T.%1"*IU*

- W121B:0+20#)-)/)!+C#QV5444#S#

- D!@02#!#91!+)_!9#<89!-*1#1+#(9)B19#!]0C#[5444#S#

- D!@02#!#1A1/*8!9#1+#21@8-<0#!]0C#Q45444#S#- '0:902#0:*1-)<02#1+#(9)B19#!]0C#645444#S#

- '0:902#0:*1-)<02#1+#21@8-<0#!]0C#6V5444#S#

W1*19B)-!9C#!"#'8N+#<1#+!2#<02#)-=192)0-12#12#BN2#/0-=1-)1-*1#(!9!#+!#1B(912!7#28(0-)1-<0#8-#*)(0#

<1# )-*19R2#<1+# 3o#(!9!# +02#<02#!]025#:"#'8N+#<1# +!2# <02# )-=192)0-12# 219U!#BN2#/0-=1-)1-*1#(!9!# +!#

1B(912!7#2)#1+#*)(0#<1#)-*19R2#A819!#<1+#3o#(!9!#1+#(9)B19#!]0#F#<1+#[o#(!9!#1+#21@8-<05#

!"#$%&'(2*34*CDE&*F*<52A<+>*CDE

'*F*<52<+=8*94*CDE

"&*F*:2G<=>*CDE

'*F*:2;A52*

65 `-#:!-/0#L!#/0-/1<)<0#8-#(9R2*!B0#<1#[445444#18902#!#+!#1B(912!#WKW?#(09#1+#M817#1-#/!<!#8-0#<1#

+02# <02# !]02# <1# 28# <89!/)>-7# +1# /0:9!9N# 8-# )-*19R2# <1+# Q6# o5# ?+# T+*)B0# !]07# +!# 1B(912!# <1:19N#

<1=0+=19#!+#:!-/0#1+#(9)-/)(!+#<1+#(9R2*!B0#F#+02#)-*191212#<1+#T+*)B0#!]05#E1#()<1#

!5#h'8N+#12#1+#<121B:0+20#)-)/)!+#F#+02#<)2*)-*02#A+8^02#<1#/!^!#<1#+!#)-=192)>-i#

:5#h'8N+#12#1+#;gj#<1#+!#)-=192)>-i#

!"#$%&'(2*34*PB552555Q:=2555QB:=25558*94*MNIF*<+O*

P5 E8(0-@!B02#M81#1912#1+#@191-*1#<1#8-!#1B(912!#F#<1:12#)-=19*)9#J45444#S#<1+#B0<0#BN2#A!=09!:+1#

<89!-*1#+02#(9>O)B02#/8!*90#!]025##E82#!+*19-!*)=!2#20-#+!2#2)@8)1-*12C#

- '0-2*98)9#8-!#-81=!#(+!-*!#(90<8/*)=!#(09#1+#B1-/)0-!<0# )B(09*15#?2*!#(+!-*!#-0# +1# 91(09*!9N#

-)-@T-#:1-1A)/)0#G-)#(R9<)<!"#<89!-*1# +02#<02#(9)B1902#!]027#0:*1-)1-<0#V65444#S#/!<!#8-0#<1#

+02#<02#!]02#2)@8)1-*12l#+!#(+!-*!#(19<19N#/0B(+1*!B1-*1#28#=!+09#!+#/!:0#<1#+02#/8!*90#!]025#

- K<M8)9)9#<18<!#(T:+)/!#!#<02#!]02#!#8-#*)(0#<1#)-*19R2#<1+#3#(09#/)1-*05#- '0B(9!9#8-# +0/!+#/0B19/)!+7#(09#1+#M81#/0:9!9U!#8-#!+M8)+19#!-8!+#<1#P5J44#S7#=1-<)1-<0#<)/L0#

+0/!+#!+#A)-!+#<1+#/8!9*0#!]0#(09#JJ5P44#S5#

!5#b9<1-!#+!2#*912# )-=192)0-12#(09#09<1-#<1#(91A191-/)!#21@T-#1+#/9)*19)0#<1+#=!+09#!/*8!+#-1*07#2)# +!#

*!2!#<1#<12/81-*0#(!9!#+!#1B(912!#12#<1+#3#(09#/)1-*05#

:5#W1*19B)-!#1+#(+!_0#<1#91/8(19!/)>-#<1#/!<!#8-!#<1#+!2#*912#)-=192)0-12#!-*19)09127#/+!2)A)/N-<0+!2#

(09#09<1-#<1#(91A191-/)!5#

/5#'!+/8+!#1+#;gj#<1#+!#6s#)-=192)>-#

!"#$%&'(2*34*CDE&*F*<52BA;>*CDE

'*F*5>**CDE

(*FG2A+58*94*HR

&FA3*K*<,;*68*HR

'F*<3*K*A+,6>*HR

(F*A3*K*A5;68*%4*,O2*


18

TEMA 9 - PERIODO MEDIO MADURACIÓN HOJA 1

Q5 '!+/8+!# 1+# (19)0<0#B1<)0# <1#B!<89!/)>-# <1# 8-!# 1B(912!# 1-/!9@!<!# <1# A!:9)/!/)>-# <1# (90<8/*02#

*1/-0+>@)/02#M81#(9121-*!#+02#2)@8)1-*12#<!*02C##

D19U0<0#B1<)0#<1#!(90=)2)0-!B)1-*0C#Q3#<U!2##

D19U0<0#B1<)0#<1#A!:9)/!/)>-C#66#<U!2##

D19U0<0#B1<)0#<1#=1-*!C#P4#<U!2##

%TB190#<1#=1/12#M817#1-#1+#!]07#21#91-0=>#+!#<18<!#B1<)!#<1#+02#/+)1-*12C#Q4#

%TB190#<1#=1/12#M817#1-#1+#!]07#21#91-0=>#+!#<18<!#B1<)!#<1#+02#(90=11<0912C#J##

!"#$%&'(2*HSS*F*;A*6031*

65 \!# 1B(912!# Eb'g?WKW7# EK7# L!# 1A1/*8!<0# =1-*!2# !# /9R<)*0# (09# Q665V44S# <89!-*1# 1+# 1^19/)/)07#

B!-*1-)1-<0# 8-# 2!+<0#B1<)0# <1# /+)1-*12# <1# Q45644S5# K2)B)2B0# L!# 91!+)_!<0# /0B(9!2# !# /9R<)*0# !#

(90=11<0912#(09#6P5V44S7#B!-*1-)1-<0#8-#2!+<0#B1<)0#<1#65J44S5#E1#()<1C#

! '!+/8+1#1+#D19)0<0#e1<)0#<1#e!<89!/)>-#<1#/+)1-*12#F#(90=11<09125#

! b()-1#20:91#+!#(0+U*)/!#<1#/0:902#F#(!@02#<1#+!#1B(912!5#

!"#$%&'(2*HS*@3/"*F*;5*6031*K*HS*%"9."*F*A5*6031*

P5 `-!#1B(912!#<1<)/!<!#!# +!# /0B19/)!+)_!/)>-#<1#1+1/*90<0BR2*)/02# 21#(90(0-1#B1^09!9# 28# /)/+0#<1#

1O(+0*!/)>-#<)2B)-8F1-<0#1+#(19)0<0#B1<)0#<1#B!<89!/)>-5#K+# A)-!+)_!9#1+#1^19/)/)0#1/0->B)/0#-02#

(9121-*!#+!#2)@8)1-*1#)-A09B!/)>-C#

! E!+<0#B1<)0#<1#/+)1-*12# P5644#18902#

! E!+<0#B1<)0#D90=11<0912# V5344#18902#

! E!+<0#B1<)0#<1#!+B!/R-# Q5J44#18902#

! $1-*!2#!#/9R<)*0# # 635J44#18902#

! '0B(9!2#!#/9R<)*0# # VZ5344#18902#

! '02*1#<1#=1-*!2#!-8!+12# 6P5644#18902#

'0-#+!#)-A09B!/)>-#!-*19)09#21#()<1C#

!5 '!+/8+!9#1+#-TB190#<1#<U!2#M81#*!9<!#1-#/0:9!9#!#+02#/+)1-*125#

:5 '!+/8+!9#1+#-TB190#<1#<U!2#M81#*!9<!#1-#(!@!9#!#+02#(90=11<09125#

/5 '!+/8+!9#1+#-TB190#<1#<U!2#M81#(19B!-1/1-#1-#28#!+B!/R-#+!2#1O)2*1-/)!25#

<5 '!+/8+!#1+#(19)0<0#B1<)0#<1#B!<89!/)>-5#

!"#$%&'(2*34*HS*%"9."*F*;,*6031*94*HS@*F*A+>G+*6>*%4*HS*T7(U3*F*+;>B+*6031>*64*HSS*F*AG><*6031*

V5 ?-#8-!#1B(912!#<1# A!:9)/!/)>-#<1#1+1/*90<0BR2*)/02# 21#B!-1^!-#(!9!# +!#(+!-)A)/!/)>-#<1+#(9>O)B0#

1^19/)/)0#1/0->B)/0#+02#2)@8)1-*12#<!*02C#

!5 ?+#(19)0<0#B1<)0#<1#/0:90#1-#1+#1^19/)/)0#!-*19)09#12#<1#6673#<U!25#

:5 ?+#(19)0<0#B1<)0#<1#A!:9)/!/)>-#1-#1+#1^19/)/)0#!-*19)09#12#<1#PP#<U!25#

/5 ?+#(19)0<0#B1<)0#<1#=1-*!#1-#1+#1^19/)/)0#!-*19)09#12#<1#V4#<U!25#

<5 ?+#(19)0<0#B1<)0#<1#B!<89!/)>-#L!#2)<0#<1#Q64#<U!25#

'!+/8+!#1+#(19)0<0#B1<)0#<1#!(90=)2)0-!B)1-*0#F#1O(+)M81#1+#2)@-)A)/!<0#<1#<)/L02#<!*025#

!"#$%&'(2*HS*[email protected]*F*+;>,*6031*

35 ?-# +!#1B(912!#<0-<1#82*1<# *9!:!^!# 21#L!-# 91!+)_!<0#=1-*!2# !# /9R<)*0#(09#8-# )B(09*1#<1#ZJ45444S#

<89!-*1#8-#!]07#B!-*1-)R-<021#8-#2!+<0#B1<)0#<1#/+)1-*12#<1#P65444S5#

E1#()<1C#

! '!+/8+1#1+#D19)0<0#e1<)0#<1#e!<89!/)>-#<1#/+)1-*125#

! E)#+!2#1B(912!2#<1#+!#/0B(1*1-/)!#/0:9!21-#!#282#/+)1-*12#!#+02#Q3#<U!2#h<1:19N#+!#1B(912!#21@8)9#

/0-#28#(0+U*)/!#!/*8!+#<1#/0:90#!#/+)1-*12i#hD09#M8Ri#

!"#$%&'(2*HS*%"9."*F*<+*6031*


19

J5 E)#+02#D19U0<02#e1<)02#<1#+!#1B(912!#\btg7#E5#K57#20-C#

X#D19U0<0#e1<)0#?O)2*1-/)!2C#P4#<U!25#

X#D19U0<0#e1<)0#<1#'0:90C#P4#<U!25#

X#D19U0<0#e1<)0#<1#D!@0C#I3#<U!25#

h'8N+#12#1+#D19U0<0#e1<)0#<1#e!<89!/)>-i#

!"#$%&'(2*HSS*F*P<,*60312*

I5 `-!#1B(912!# /0B(9># F# /0-28B)># 1+# (!2!<0# !]07# (!9!# +!# A!:9)/!/)>-# <1# 28# (90<8/*07# 645444# S# <1#

B!*19)!2#(9)B!2#F7#(09#*R9B)-0#B1<)07#B!-*8=0#8-#-)=1+#<1#1O)2*1-/)!2#<1#+!2#B)2B!2#1-#!+B!/R-#<1#

65444#S#h'8N+#12#28#(19U0<0#B1<)0#<1#!+B!/1-!B)1-*0i#

!"#$%&'(2*HSD*FA=*60312*

[5 `-!#1B(912!# L!# 91!+)_!<0# 1-# 1+# 1^19/)/)0# /0B(9!2# !# /9R<)*0# !# (90=11<0912# (09# =!+09# <1# Q45[44# S7#

B!-*1-)1-<0# 8-# 2!+<0# B1<)0# <1# Q5[44# S5# \!# B)2B!# 1B(912!# L!# 1A1/*8!<0# =1-*!2# !# /9R<)*0# (09#

Q3P5444#S#/0-#8-#2!+<0#B1<)0#<1#Q65I34#S5#;1-)1-<0#1-#/81-*!#+02#<!*02#!-*19)09127#21#()<1C#'!+/8+!9#

1+#(19)0<0#B1<)0#<1#B!<89!/)>-#<1#/+)1-*12#F#(90=11<0912#

!"#$%&'(2*HSV*FA5*6038*HSH*F*=5*60312*

Z5 `-!# 1B(912!# 91!+)_># 1-# 1+# 1^19/)/)0# /0B(9!2# !+# /0-*!<0# (09# =!+09# <1# Q445444# S7#B!-*1-)1-<0# 8-#

2!+<0#B1<)0#<1#Q45444#S5#?+#/02*1#*0*!+#<1#+!#A!:9)/!/)>-#91!+)_!<!#1-#121#!]0#A81#<1#P445444#S#F#+!#

B1<)!#<1+#2*0/d#<1#(90<8/*02#1-#/8920#<1#A!:9)/!/)>-#A81#<1#Q35444#S5#W89!-*1#121#!]0#=1-<)>#*0<!#

+!#(90<8//)>-#M81#A!:9)/>#F#1+#-)=1+#B1<)0#<1#1O)2*1-/)!2#M81#B!-*8=0#A81#<1#Q45444#S5#\02#)-@91202#

*0*!+12#(09# =1-*!2#M81#0:*8=0# A8190-#3445444#S# F#1+# 2!+<0#<1# /+)1-*12#<1#Q635444#S5# ;1-)1-<0#1-#

/81-*!#+02#<!*02#!-*19)09127#21#()<1C#'!+/8+!9#1+#(19)0<0#B1<)0#<1#B!<89!/)>-#<1#+!#1B(912!5#F#2)#+!#

(0+U*)/!#<1#+!#1B(912!#19!#/0-/1<19#!#282#/+)1-*12#8-#(+!_0#B1<)0#<1#(!@0#<1#J4#<U!27#1O(+)/!9#2)#+!#L!#

B!-*1-)<05#

!"#$%&'(2*HSS*F*<,=*60312*

Q45 ?+#@191-*1#<1#e!-8A!/*89!2#<1# +!#c!LU!7#E5K5#<121!#B1^09!9# +!#(90<8/*)=)<!<#<1#28#1B(912!7#(09# +0#

M81#!-*12#<1#)-)/)!9#1+#(90@9!B!#<1#B1^09!#M8)191#/0-0/19#1+#u(19)0<0#B1<)0#<1#B!<89!/)>-v#<1#+!#

1B(912!5#\02#<!*02#A!/)+)*!<02#20-C##

X#?O)2*1-/)!2#B1<)!2#<1#B!*19)!2#(9)B!2C#JP5444#S#

X#'0B(9!2#<1#B!*19)!+12C#ZII5444#S#

X#'02*1#*0*!+#<1#+!#(90<8//)>-C#65Q4V5444#S#

X#?O)2*1-/)!2#B1<)!2#<1#(90<8/*02#1-#/8920C#V[5444#S#

X#'02*1#<1#+!2#=1-*!2C#654Q65444#S#

X#?O)2*1-/)!2#B1<)!2#<1#(90<8/*02#*19B)-!<02C#QQ35444#S#

X#$1-*!2#*0*!+12C#65VQ35444#S#

X#E!+<0#B1<)0#<1#/+)1-*12C#QP[5444#S#

'!+/8+!#+!#)-A09B!/)>-#M81#-1/12)*!#1+#@191-*17#91+!*)=!#!+#(19U0<0#B1<)0#<1#B!<89!/)>-5#

!"#$%&'(2*HSS*F*G+>,G*60312*

QQ5 \!#1B(912!#'agDE7#EK7#L!#1A1/*8!<0#=1-*!2#!#/9R<)*0#(09#Q465444#S#<89!-*1#1+#1^19/)/)07#B!-*1-)1-<0#

8-#2!+<0#B1<)0#<1#/+)1-*12#<1#[5344#S5#K2)B)2B0#L!#91!+)_!<0#/0B(9!2#!#/9R<)*0#!#(90=11<0912#(09#

I5644#S7#B!-*1-)1-<0#8-#2!+<0#B1<)0#<1#Q5644#S5#E1#()<1C#

!5 '!+/8+1#1+#D19)0<0#e1<)0#<1#e!<89!/)>-#<1#/+)1-*12#F#(90=11<09125#

:5 b()-1#20:91#+!#(0+U*)/!#<1#/0:902#F#(!@02#<1#+!#1B(912!5#

!"#$%&'(2*HSH*F*=5*60318*HSV*F*A5*6031!


20

TEMA 10 - EJERCICIOS DE BALANCES

HVHRJWJW:*@*

'0-A1//)0-!#1+#:!+!-/1#<1#2)*8!/)>-#<1#+!#1B(912!#\KjK7#EK7#!#PQ#<1#<)/)1B:91#<1#64Q65#a!++!#+!#/)A9!#

<1+#/!()*!+#20/)!+C#

D90=11<0912# # Q4# # # '9R<)*02#!#/,(# # # 3#

c!-/02# # # J# # # '!^!# # # # P#

j1219=!2# # # Q6# # # K/911<0912# # # 3#

aD7#!/911<09# # V# # # ;1991-02# # # I#

'+)1-*12# # # J# # # '+)1-*12#1A1/5#/0B#/0:9!9# V#

e0:)+)!9)0# # # I# # # '0-2*98//)0-12## # Q[#

e19/!<19U!2# # 3# # # W18<!2#!#+,(# # # Z#

!"#$%&'(2*V3@&U3#*!"%&3#*+<*

HVHRJWJW:*A*

'0-A1//)0-!#1+#:!+!-/1#<1#2)*8!/)>-#<1#+!#1B(912!#WKgeg?\7#EK7#!#PQ#<1#<)/)1B:91#<1#64Q6#F#L!++!#+!#

/)A9!#<1+#/!()*!+#20/)!+C#

'!^!# # # # 6# # c!-/02# # # # Q6#

KB09*)_5#!/8B5#)-B5#B!*# # Q# # $1-*!#B19/!<19U!2# # Q[#

E8B)-)2*902# # # J# # D90=11<0912# # # 63#

'0-2*98//)0-12# # # QJ# # '+)1-*127#1A#/0B#/0:9!9## QP#

?M8)(02#(90/120#)-A09B!/)>-# P# # e19/!<19U!2# # # Q6#

W18<0912#/,(# # # J# # W18<!2#!#/,(# # # J#

j1219=!#=0+8-*!9)!## # P# # b9@!-)2B0#EE7#!/911<09# Q#

g-@9120#(09#/0B)2)0-12# # P## # D90=7#1A5#'0B5#!#(!@!9# # 3#

K/911<0912# # # 3# # '+)1-*12# # # J#

j1219=!#+1@!+# # # 3# # '0B(9!#B19/!<19U!2# # Q4#

D90()1<!<#)-<82*9)!+# # 6# # ;1991-02# # # [#

!"#$%&'(2*V3@&U3#*!"%&3#*+;*

HVHRJWJW:*6*

b9<1-!#1+#:!+!-/1#<1#2)*8!/)>-#<1#+!#1B(912!#'Ke?\b;7#EK#1+#<U!#PQ#<1#<)/)1B:91#<1#64Q6#F#L!++!#28#

/)A9!#<1#DR9<)<!2#F#t!-!-/)!2#

#

D90=11<0912#1A1/*02#!#(!@!9# [#

W18<!2#!#/,(# Z#

'0-2*98//)0-12# 66#

b9@5#E1@5#E0/)!+7#!/911<09# P#

g-=1925#(19B!-1-*12#/!()*!+# I#

e19/!<19U!2# Q6#

'+)1-*12#1A1/*02#!#/0:9!9# V#

e0:)+)!9)0# [#

W18<0912# 6#

?+1B1-*02#<1#*9!-2(09*1# 3#

D90=11<0912#)-B0=#+,(# [#

'9R<)*02#!#/,(# 3#

a!/5#DT:+)/!7#<18<09# P#

'!^!# V#

;1991-02# V6#

'!()*!+#E0/)!+# 63#

'+)1-*12# [#

e!M8)-!9)!# V#

W18<!2#!#+,(# Q[#

KB09*)_5#K/8B5#g-B0=#e!*5# Q4#

D90=11<0912# 64#

c!-/02# Q4#

j1219=!2# 64#

K/911<0912# QJ#

!"#$%&'(2*HW.6&631*K*/3(3(%&31*XP<4*


21

HVHRJWJW:*?*

;1-)1-<0# +!# 2)@8)1-*1# )-A09B!/)>-#<1# +!#1B(912!#K\?tjgK7#EK7#1+#<U!#PQ#<1#W)/)1B:91#<1#64Q67# 21#

()<1#1+#:!+!-/1#09<1-!<0#1-#B!2!2#(!*9)B0-)!+12#F#L!++!9#+!#/)A9!#<1#/!()*!+#20/)!+5#

#

'+)1-*12# # # # ##I5444#

'0B(9!#<1#B19/!<19U!2# # V45444#

E81+<02#F#2!+!9)02# # # Q65444#

e!M8)-!9)!# # # # ##[5444#

W18<0912# # # # ##V5444#

KB09*5#!/8B5#g-B0=5#e!*19)!+# # Q45444#

e19/!<19U!2## # # # ##Z5444#

E8B)-)2*902# # # # ##P5444#

a!/)1-<!#D8:+5#W18<09# # # ##P5444#

D90=#1A#/0B19/#!#(!@!9## # ##J5444#

'!^!# # # # # ##65444#

'!()*!+#E0/)!+# # # # #iiiii#

g-@91202#(09#!+M8)+19# # # ##P5444#

j1219=!2# # # # 635444#

b9@#E1@#E0/)!+7#!/911<09# # ##P5444#

'+)1-*127#1A#/0B19/#!#/0:9!9# # ##35444#

D90=11<0912# # # # ##Z5444#

g-=1925#q)-!-/5#D19B!-1-*12# # ##35444#

W18<!2#!#+!9@0#(+!_0# # # Q[5444#

K/911<0912# # # # ##35444#

?M8)(02#(90/120#)-A09B!/)>-# # ##65444#

D90=5#g-B0=5#+,(+!_0# # # QQ5444#

'9R<)*0#+,(+!_0# # # # ##P5444#

$1-*!#<1#B19/!<19U!2# # # J45444#

c!-/02# # # # # ##Z5444#

;1991-02# # # # 645444#

KB09*)_5#g-B0=#e!*19)!+# # ##35444#

'0-2*98//)0-12## # # P45444#

!"#$%&'(2*V3@&U3#*!"%&3#*<G*

HVHRJWJW:*7*

b9<1-!#1+#:!+!-/1#<1#2)*8!/)>-#<1#+!#1B(912!#q`?%\K7#EK#1+#<U!#PQ#<1#<)/)1B:91#<1#64Q6#F#L!++!#28#

/)A9!#<1#/+)1-*125#

K/911<0912# QP#

j1219=!2# P4#

D90=11<0912#1A1/*02#!#(!@!9# 3#

g-=1925#(19B!-1-*12#/!()*!+# 3#

E8B)-)2*902# 6#

'!^!# 3#

D90=11<0912# Q6#

D9R2*!B02#!#+,(# [#

e19/!<19U!2# Q4#

'9R<)*02#!#/,(# [#

W18<0912# V#

$1-*!#<1#B19/!<19U!2# P3#

b9@5#E1@5#E0/)!+7#<18<09# 6#

'!()*!+#E0/)!+# 34#

'0B(9!#<1#e19/!<19U!2# Q3#

'0-2*98//)0-12# 6J#

'+)1-*12#1A1/*02#!#/0:9!9# 3#

;1991-02# 3J#

D90=11<0912#)-B0=#+,(# Q3#

c!-/02# Q6#

KB09*)_5#g-B0=#e!*19)!+# 3#

W18<!2#!#+,(# 3#

KB09*)_5#K/8B5#g-B0=#e!*5# J#

e!M8)-!9)!# [#

a!/5#DT:+)/!7#!/911<09# P#

g-@91202#(09#)-*191212# V#

e0:)+)!9)0# J#

E81+<02#F#2!+!9)02# J#

!"#$%&'(2*V#&7(U71*<<*


22

TEMA 11 - EJERCICIOS DE FONDO DE MANIOBRA

Q5 '0-A1//)0-!#1+#:!+!-/1#<1#2)*8!/)>-#!#PQ#<1#<)/)1B:917#<1:)<!B1-*1#09<1-!<0#F#/+!2)A)/!<0#(09#B!2!2#

(!*9)B0-)!+12C#

D90=11<09127#1A1/*02#/0B19/)!+12#!#(!@!97#65[44l#'!()*!+#20/)!+7#J45444l#KB09*)_!/)>-#!/8B8+!<!#<1+#

)-B0=)+)_!<0# B!*19)!+7# ZP64l# '!^!7# 3J4l# W18<!2# !# +!9@0# (+!_0# /0-# 1-*)<!<12# <1# /9R<)*07# QI53V4l#

'0-2*98//)0-127# J45344l# '+)1-*127# 1A1/*02# /0B19/)!+12# !# /0:9!97# P5644l# W18<!2# /0-# 1-*)<!<12# <1#

/9R<)*0# !# /09*0# (+!_07# 35QI4l# j1219=!2# =0+8-*!9)!27# V5444l# ?+1B1-*02# <1# *9!-2(09*17# Q[5P44l#

b9@!-)2B02# <1# +!# E1@89)<!<# E0/)!+7# !/911<09127# PJ4l# e!*19)!2# (9)B!27# P444l# W18<09127# 1A1/*02#

/0B19/)!+12# !# /0:9!97# Q[6l# D90=11<0912# <1# )-B0=)+)_!<0# !# +!9@0# (+!_07# QZ5JI4l# e0:)+)!9)07# J5344l#

D90<8/*02# *19B)-!<027# QZ5[Q4l# K/911<09127# 1A1/*02# /0B19/)!+12# !# (!@!97# Q5P34l# j128+*!<0# <1+#

1^19/)/)0# GDR9<)<!2# F# t!-!-/)!2"7# hil# j1219=!# +1@!+7# Q35444l# '+)1-*127# 6V5[34l# a!/)1-<!# DT:+)/!7#

!/911<09!#(09#/0-/1(*02#A)2/!+127#Q5644l#c!-/02#/,/7#V56P[l#D90=11<09127#QP5346l#;1991-02#F#:)1-12#

-!*89!+127#P45444l#K/911<09127#Q5444l#D90<8/*02#21B)*19B)-!<027#I56P4l#j1219=!#12*!*8*!9)!7#Q5444l#

W18<09127#J5[Z4l#K/911<0912#!#+!9@0#(+!_07#Q65PV[5#

'!+/8+!#1+#A0-<0#<1#B!-)0:9!#0#/!()*!+#/)9/8+!-*1#(09#*0<!2#+!2#=U!2#M81#/0-0_/!25#'0B1-*!#1+#9128+*!<0#

1-#*0<!2#+!2#0(/)0-125#

YS*F*;;2,GB*

65 b9<1-!#1+#:!+!-/1#<1#2)*8!/)>-#<1#+!#1B(912!#'KE'Kjb%7#EK#1+#<U!#PQ#<1#<)/)1B:91#<1#64Q4#F#L!++!#28#

/)A9!#<1#'!()*!+#E0/)!+#F#1+#A0-<0#<1#B!-)0:9!5#

'+)1-*12#1A1/*02#!#/0:9!9# J#

D90=11<0912#1A1/*02#!#(!@!9# Q6#

e!M8)-!9)!# Q3#

?+1B1-*02#<1#*9!-2(09*1# J#

KB09*)_5#K/8B5#g-B0=#e!*5# P#

'0B(9!#<1#e19/!<19U!2# 63#

$1-*!#<1#B19/!<19U!2# V4#

E81+<02#F#2!+!9)02# Q6#

'0-2*98//)0-12# PP#

a!/5#DT:+)/!7#<18<09# 6#

'!^!# [#

;1991-02# P3#

'!()*!+#E0/)!+# hi#

j1219=!2# Q3#

W18<!2#!#+,(# Z#

KB09*)_5#g-B0=#e!*19)!+# P#

e0:)+)!9)0# QQ#

g-=1925#(19B!-1-*12#/!()*!+# 3#

'+)1-*12# 6#

'9R<)*02#!#/,(# P#

b9@5#E1@5#E0/)!+7#!/911<09# 6#

D90=11<0912#)-B0=#+,(# Q3#

e19/!<19U!2# P#

c!-/02# Q[#

D90=11<0912# V#

W18<!2#!#/,(# QV#

g-@91202#(09#/0B)2)0-12# Q#

E8B)-)2*902# V#

K/911<0912# 3#

W18<0912# I#

V!*F*GB8*YS*F*<+*


23

P5 \!#1B(912!#'Kjgc?EK#(9121-*!#!#PQ,kgg#<1+#1^19/)/)0#M81#*19B)-!#+!#2)@8)1-*1#)-A09B!/)>-#(!*9)B0-)!+C#

'!^!#344# # # # # K/911<0912#!#/09*0#(+!_0#6644#

;1991-02#6J44# # # # j1219=!2#PP44#

'+)1-*12#J44# # # # # g-2*!+!/)0-12#3444#

?<)A)/)02#[344## # # # KB09*)_!/)>-#!/8B8+!<!#6444#

D90=11<0912#P344# # # # W18<!2#!#+!9@0#(+!_0#P444#

c!-/02#/,/#Q644# # # # DR9<)<!2#F#t!-!-/)!2#hi#

'!()*!+#20/)!+#3444# # # # e19/!<19U!2#QV44#

D!9*)1-<0#<1#+!#)-A09B!/)>-#!-*19)09#21#()<1C##

X#W1*19B)-1#1+#9128+*!<0#<1#1^19/)/)07#1O(+)/!-<0#2)#21#L!#0:*1-)<0#:1-1A)/)0#0#(R9<)<!#

X#D9121-*1#1+#:!+!-/1#09<1-!<0#1-#B!2!2#(!*9)B0-)!+12#

X#'!+/8+1#1+#/!()*!+#/)9/8+!-*1#0#A0-<0#<1#B!-)0:9!#F#'0B1-*1#+!#2)*8!/)>-#A)-!-/)19!#<1#+!#1B(912!5#

!"#$%&'(2*I71$#U36"*7Z7.%&%&"*F*B558*Y2*S3(&"9.3F*P+555*

V5 b9<1-!#1+#:!+!-/1#<1#2)*8!/)>-#<1# +!#1B(912!#q\bjgWK7#EK#1+#<U!#PQ#<1#<)/)1B:91#<1#64Q4#F#L!++!#28#

/)A9!#<1#/+)1-*12C#

'+)1-*12# # # # iiiiii#

'0B(9!#<1#B19/!<19U!2# # V45444#

E81+<02#F#2!+!9)02# # # Q65444#

e!M8)-!9)!# # # # ##[5444#

W18<0912# # # # ##V5444#

KB09*5#!/8B5#g-B0=5#e!*19)!+# Q45444#

e19/!<19U!2## # # # ##Z5444#

E8B)-)2*902# # # # ##P5444#

a!/)1-<!#D8:+5#W18<09# # # ##P5444#

D90=#1A#/0B19/#!#(!@!9## # ##J5444#

'!^!# # # # # ##65444#

'!()*!+#E0/)!+# # # # 635444#

g-@91202#(09#!+M8)+19# # # ##P5444#

j1219=!2# # # # 635444#

b9@#E1@#E0/)!+7#!/911<09# # ##P5444#

'+)1-*127#1A#/0B19/#!#/0:9!9# # ##35444#

D90=11<0912# # # # ##Z5444#

g-=1925#q)-!-/5#D19B!-1-*12# # ##35444#

W18<!2#!#+!9@0#(+!_0# # # Q[5444#

K/911<0912# # # # ##35444#

?M8)(02#(90/120#)-A09B!/)>-## ##65444#

D90=5#g-B0=5#+,(+!_0# # # QQ5444#

'9R<)*0#+,(+!_0# # # ##P5444#

$1-*!#<1#B19/!<19U!2# # J45444#

c!-/02# # # # ##Z5444#

;1991-02# # # # 645444#

KB09*)_5#g-B0=#e!*19)!+# # ##35444#

'0-2*98//)0-12# # # P45444#

!"#$%&'(2*V#&7(U71*F<A*

35 \!# 1B(912!# E?t`%WK7# E5K5# (9121-*!# <1*19B)-!<!# )-A09B!/)>-# /0-*!:+17# (09#B1<)0# <1# +!2# 2)@8)1-*12#

/81-*!2#=!+09!<!2#1-#18902C#

W)-190#1-#/!^!# [44#

W1:1#!#+02#(90=11<0912# [5J44#

e!M8)-!9)!# J5444#

D9R2*!B0#91/):)<0#<1#8-#:!-/0#!#\,D# 665V44#

?<)A)/)0#<1+#!+B!/R-#F#0A)/)-!2# 6[5644#

e19/!<19U!2#1-#1O)2*1-/)!2# V44#

b9<1-!<09# Q5J44#

W191/L02#<1#/0:90#20:91#+02#/+)1-*12# Q45444#

'!()*!+#20/)!+#F#91219=!2# !#<1*19B)-!9#

!5#j1(9121-*1#1+#:!+!-/1#<1#2)*8!/)>-#09<1-!<0#1-#B!2!2#(!*9)B0-)!+125#

:5#'!+/8+1#1+#A0-<0#<1#B!-)0:9!#0#/!()*!+#/)9/8+!-*1#1#)-*19(91*1#28#2)@-)A)/!<05#

Y"(6"1*H."@&"1*F*<=25558*Y2*S3(&"9.3F*+2=55*


24

J5 D!9*)1-<0#<1#+!#2)@8)1-*1#)-A09B!/)>-#(90(09/)0-!<!#(09#+!#1B(912!#w`?tbE$gj%?;7#1-#18902C#

'+)1-*12# 644#

KB09*)_!/)>-#!/8B8+!<!#)-B0=)+)_!<0#B!*19)!+# Z5I44#

K/911<0912#!#/09*0#(+!_0# 65344#

?+1B1-*02#<1#*9!-2(09*1# QQ5444#

?O)2*1-/)!2#<1#B19/!<19U!2# Q5444#

j1219=!2# 65V44#

e0:)+)!9)0# P5444#

W18<!2#!#/09*0#(+!_0# 65444#

?M8)(02#)-A09BN*)/02# P5J44#

DR9<)<!2#F#@!-!-/)!2# V5444#

c!-/02# I5444#

'!()*!+#E0/)!+# hi#

E1#()<1C#!"#'!+/8+1#+!#/)A9!#<1#+!#/81-*!#<1#'!()*!+#E0/)!+7#:"#?+!:091#1+#c!+!-/1#<1#E)*8!/)>-7#09<1-N-<0+0#

1-#B!2!2#F#28:B!2!2#(!*9)B0-)!+127#/"#'!+/8+1#1+#q0-<0#<1#e!-)0:9!#0#'!()*!+#')9/8+!-*17#<"#'0B1-*1#+!#

2)*8!/)>-#A)-!-/)19!#<1#+!#1B(912!7#:!2N-<021#1-#+02#<!*02#0:*1-)<025#

V3@&U3#*!"%&3#F*,2+558*Y2*S3(&"9.3F*A2G55*

I5 \!#20/)1<!<#bjg?%;?#E5\57#M81#A81#/0-2*)*8)<!#L!/1#Q3#!]027#(9121-*!#+!#2)@8)1-*1#)-A09B!/)>-#/0-*!:+17#

/09912(0-<)1-*1#!+#:!+!-/1#A)-!+#<1#2)*8!/)>-C##

X#e!-*)1-1#+!#/)A9!#<1#/!()*!+#282/9)*0#1-#+!#/0-2*)*8/)>-#<1#+!#20/)1<!<#(09#8-#=!+09#<1#665444#189025##

X#?+#1<)A)/)0#M81#0/8(!7#=!+09!<0#1-#645444#189027#12#<1#28#(90()1<!<5#?+#*1991-0#21#=!+09!#1-#Z5444#S5##

X#;)1-1#8-!#<18<!#!#+!9@0#(+!_0#(09#8-#B0-*!-*1#<1#Q45444#189025##

X#?+#B0:)+)!9)0#<1+#+0/!+#+0#*)1-1#=!+09!<0#1-#Q5444#189025##

X#\!2#1O)2*1-/)!2#<1#+02#(90<8/*02#(!9!#+!#=1-*!#)B(09*!-#P5J44#189025##

X#\!2#0:+)@!/)0-12#<1#(!@0#/0-#+02#(90=11<0912#!2/)1-<1-#!#344#189025##

X#e!-*)1-1#8-!2#91219=!2#<1#65444#189025##

X#W)2(0-1#<1#65444#18902#1-#+!#/81-*!#/099)1-*1#<1+#:!-/05##

'0-#+!#)-A09B!/)>-#!-*19)09#21#()<1C##

!"#?+#:1-1A)/)0#-1*0#<1+#1^19/)/)07#<1#!/819<0#/0-#+02#<!*02#A!/)+)*!<02#!-*19)09B1-*15##

:"#W12/9):!#1+#)B(09*1#<1#+!2#B!2!2#(!*9)B0-)!+12#<1C#!/*)=0#-0#/099)1-*1#G!/*)=0#A)^0"l#!/*)=0#/099)1-*1#

G!/*)=0#/)9/8+!-*1"l#A0-<02#(90()02l#(!2)=0#-0#/099)1-*1#G(!2)=0#1O)@):+1#!#+!9@0#(+!_0"#F#(!2)=0#/099)1-*1#

G(!2)=0#1O)@):+1#!#/09*0#(+!_0"5##

/"# '0B1-*1# +!# (02)/)>-# A)-!-/)19!7# 8*)+)_!-<0# 1+# A0-<0# <1# B!-)0:9!# 0# /!()*!+# /)9/8+!-*1# G1M8)+):9)0#

A)-!-/)190"##

34*R7(7-&%&"*E7U"*F*<2<558*94*YS*F*,2<55*

[5 \!#1B(912!#eg\\b#(9121-*!#+!#2)@8)1-*1#)-A09B!/)>-#/0-*!:+1#G1-#18902"C#

'0-/1(*0# gB(09*1# '0-/1(*0# gB(09*1#

j128+*!<0#1^19/5# XQ56I4# c!-/02#/,/# 35I34#

W18<!2#!#+,(#/0-#1-*)<!<12#<1#/9R<)*0 V5IV4# j1219=!2# 3V4#

D90=11<0912# Z[3# '!()*!+#20/)!+# P45444#

?+1B1-*02#<1#*9!-2(09*1# 635V44#KB09*5#K/8B5#1+1B5#

<1#*9!-2(09*1#I5J64#

g-=192)0-12#A)-!-/)19!2#*1B(57#

!//)0-12#/0-#/0*)_!/)>-#0A)/)!+#[5V34# '+)1-*12# kkk#

E1#()<1C##

!"#W1*19B)-!9#+!#/)A9!#<1#/+)1-*125##

:"#?+!:09!9#1+#:!+!-/1#<1#2)*8!/)>-7#09<1-!<0#F#!@98(!<0#1-#B!2!2#F#28:B!2!2#(!*9)B0-)!+125#

/"#'!+/8+!9#1+#A0-<0#<1#B!-)0:9!5#

<"#'0B1-*!9#+!#2)*8!/)>-#A)-!-/)19!#<1#+!#1B(912!#eg\\b#G1M8)+):9)0#A)-!-/)190"5#

34*V#&7(U71*F*A25+,8*%4*YS*F*<=2+A5*


25

TEMA 11 - FONDO DE MANIOBRA Y RATIOS HOJA 1

b9<1-!#+02#2)@8)1-*12#:!+!-/125#'!+/8+!#1+# A0-<0#<1#B!-)0:9!#F#L!++!# +02#9!*)02#<1# +)M8)<1_7#*120919U!#F#

@!9!-*U!5#W12(8R2#)-*19(91*!#*0<02#+02#9128+*!<02#0:*1-)<02#1O(+)/!-<0#1+#2)@-)A)/!<0#<1#+02#B)2B025#

;1991-02# # # # Q3# # K/911<09#+,(# # # # V#

W18<!2#!#+,(## # # [# # c!-/02# # # # # [#

j1219=!#+1@!+# # # J# # e19/!<19U!2# # # # J#

'+)1-*12# # # # Q4# # '!()*!+#20/)!+# # # # Q4#

'!^!## # # # P# # D90=11<0912# # # # Q4#

aD7#!/911<09# # # Q# # W18<0912#/,(# # # # V#

KB09*5#K/8B5#)-B0=5#B!*19)!+# 3# # j1219=!#=0+8-*!9)!# # # 3#

'9R<)*0#!#/,(# # # P# # D90=#1A1/*#/0B19/#(!@!9# # 3#

j1219=!#12*!*8*!9)!# # # V# # ?M8)(02#(90/120#)-A09B!/)>-# # P#

e!M8)-!9)!# # # # J# #

!"#$"%&'#(")*'%+!,% -.///%

*0123%456"*5*('% .78%

*0123%9(:;($5<% .7=%

*0123%>'*'#4?'% .7@=%

#

e!M8)-!9)!# Z5444#

#

'!()*!+#E0/)!+# V5444#

KB09*)_5#K/8B5#g-B0=#e!*5# Q5444#

#

j1219=!2# Q5444#

e19/!<19U!2# Q5444#

#

D9R2*!B02#!#/,(# 6444#

W18<!2#!#/,(# Q5444#

#

D90=11<0912# 65444#

DR9<)<!2#F#t!-!-/)!2# 65444#

#

'+)1-*12# Q5444#

# # # # #!"#$"%&'#(")*'%+!,% -.///%

*0123%456"*5*('% /7A%

*0123%9(:;($5<% /7B%

*0123%>'*'#4?'% C7C%

% %#

;1991-02# 34#

#

'!()*!+#E0/)!+# P[#

j1219=!2# 66#

#

e!M8)-!9)!# 6#

e0:)+)!9)0# 3#

#

c!-/02# Z#

D90=11<0912# QI#

#

'0-2*98//)0-12# PP#

a!/5#DT:+)/!7#!/911<09# I#

#

D90=11<0912#)-B0=#+,(# Q3#

KB09*)_5#K/8B5#g-B0=#e!*5# X3#

#

'+)1-*12# J#

g-=192)0-12#(19B!-1-*12#/!()*!+# Q4#

#

D90=11<0912#1A1/*02##(!@!9# Q3#

e19/!<19U!2# 3#

#

K/911<0912# Q[#

W18<!2#!#+,(# Q6#

#

W18<0912# [#

'+)1-*12#1A1/*02#!#/0:9!9# I#

#

b9@5#E1@5#E0/)!+7#!/911<09# 6#

DR9<)<!2#F#t!-!/)!2# GI"#

#

'!^!# J#

# # #

'9R<)*02#!#+,(# P#

!"#$"%&'#(")*'%+!,% -.B%

*0123%456"*5*('% /7A%

*0123%9(:;($5<% /7=%

*0123%>'*'#4?'% .7A%


26

TEMA 11 - FONDO DE MANIOBRA Y RATIOS HOJA 2

Q5 ;1-)1-<0#1-#/81-*!#1+#:!+!-/1#M81#(9121-*!#!#A)-!+#<1#!]0#8-!#1B(912!C#

;1991-02#[45444#'!()*!+#Q445444#'0-2*98//)0-12#Q645444#j1219=!2#Q645444#e!M8)-!9)!#Q65444#?O)@):+1#!#

+!9@0# (+!_0# Q645444#e0:)+)!9)0# [5444#W18<!2# !# +!9@0# (+!_0# Q645444# ?O)2*1-/)!2# [45444# ?O)@):+1# !# /09*0#

(+!_0# 6V5444# e19/!<19U!2# [45444# W18<!2# 1-*5# /<*057# /09*0# (+!_0# [5444# * D90=11<0912# QJ5444# '+)1-*12#

V45444#c!-/02#6V54445#

E1#()<1C#

!" '!+/8+!9# 1+# A0-<0# <1# B!-)0:9!# G/!()*!+# /)9/8+!-*1"# <1# 12*!# 1B(912!# 1# )-*19(91*!9# 1+# 9128+*!<0#

0:*1-)<05#

:" '!+/8+!9#+02#9!*)02#<1#*120919U!7#+)M8)<1_#F#@!9!-*U!5#$!+09!9#+02#9128+*!<02#0:*1-)<025#/" W1*19B)-!9#+!#91-*!:)+)<!<#1/0->B)/!#F#A)-!-/)19!#0:*1-)<!#(09#+!#1B(912!7#*1-)1-<0#1-#/81-*!#M81#

1-#1+#T+*)B0#1^19/)/)0#0:*8=0#8-#:1-1A)/)0#!-*12#<1# )-*191212#1# )B(812*02#<1#Q65444#189027#M81# +02#

(!@02#91!+)_!<02#1-#/0-/1(*0#<1#)-*191212#!2/1-<)190-#!#I5[44#18902#F#+02#)B(812*02#L!-#28(812*0#

Q5644#189025#?=!+8!9#<)/L02#9!*)025#

65 E1#M8)191#91!+)_!9#8-#!-N+)2)2#A)-!-/)190#<1#8-!#1B(912!#!#(!9*)9#<1#+!#)-A09B!/)>-#M81#-02#28B)-)2*9!#1+#

:!+!-/1#<1#2)*8!/)>-5##

I+#+(%.*B.*/&1$+%&'(*5.X3<./+B"*.(*0&#./*B.*.$<"/,*

# K';g$b## # # DKEg$b# # # *

e!*19)!2#(9)B!2# JI4# D9R2*!B02#!#+!9@0#(+!_0# P65444#

'!^!## 35444# D90=11<0912# QP5344#

'+)1-*127#1A1/*02#/0B19/)!+12#!#/0:9!9#Q356V4# D9R2*!B02#!#/09*0#(+!_0# 635VP4#

e!M8)-!9)!# PV5J44# j1219=!2# 65444#

D90<8/*02#1-#/8920# Z44# '!()*!+# P45444#

c!-/0## V45444#

D90<8/*02#*19B)-!<02# Q5Q44#

e0:)+)!9)0# V5444#

KB09*)_!/)>-#!/8B8+!<!# G[53[4"#

ÇhÇ![ !/ÇLëh � � � � � � � ÇhÇ![ t!{Lëh � � � � � � �

\02#=!+0912#B1<)02#<1#+!2#1B(912!2#<1+#21/*09#M81#21#/0-2)<19!-#!/1(*!:+12#20-#1-*91#Q#F#6#(!9!#1+#

(9)B1907#F#B!F09#M81#Q#(!9!#1+#21@8-<05#

!" '!+/8+1#+!2#9!*)02#!-*19)09B1-*1#1O(912!<02#1#)-*19(91*1#+02#9128+*!<02#0:*1-)<025#

:" W1*19B)-1#1+#=!+09#<1+#q0-<0#<1#e!-)0:9!#F#1O(9121#+0#M81#91(9121-*!#1+#B)2B05#


27

P5 '!+/8+!9#(!9!#1+#2)@8)1-*1#c!+!-/1#+!2#9!*)02#<1#*120919U!#F#+)M8)<1_7#)-<)/!-<0#28#2)@-)A)/!<05#

?<)A)/)02# IPVZ4# D90=11<0912# Q[6[4#

e!*19)!2#(9)B!2# V644# '!()*!+# IZ444#

c!-/02# P444# W18<!2#!#/,(# [V4#

'+)1-*12# 6J444# j1219=!2# Q3644#

e!M8)-!9)!# [36Q3# W18<!2#!#g,(# 6[644#

e0:)+)!9)0# JQ63# D9R2*!B02#!#/,(# QJI64#

'!^!## Q44# #

W18<0912#!#/,(## 644# #

D90<8/*02#1-#/8920## ZP64# #

D90<8/*02#*19B)-!<02## [6[4# #

KB09*)_!/)0-12## G3IJZ4"# # #

C"B+#** <8G;2/* C"B+#* <8G;2/*

V5 K-N+)2)2#<1#+!#A)-!-/)!/)>-#<1#8-!#1B(912!5#K#(!9*)9#<1#+!#)-A09B!/)>-#M81#(9121-*!#1+#2)@8)1-*1#:!+!-/1#<1#

2)*8!/)>-#!#PQ#<1#<)/)1B:91#<1#6444#1-#189025#

;1991-02## 6445444## '!()*!+# #Q54445444#

'0-2*98//)0-12## Q54445444## j1219=!2#+1@!+12# #P345444#

e!M8)-!9)!# +54445444## DR9<)<!2#F#t!-!-/)!2## #QI45444#

KB09*5#K/8B5#g5#e!*19)!+# #G3345444"## D9R2*!B02#!#+!9@0#(+!_0## V445444#

e!*19)!2#(9)B!2## [45444## D90=11<0912## 6[45444#

'+)1-*12## P345444## K/911<0912## #Q345444#

W18<0912# 345444## D9R2*!B02#!#/09*0#(+!_0## #P45444#

c!-/0# 6445444#

'!^!# 345444#

;b;K\#K';g$b## 65P[45444## ;b;K\#DKEg$b## 65P[45444#

j1!+)/1#+02#2)@8)1-*12#*9!:!^02C##

G � � D9121-*1#1+#:!+!-/1#<1#2)*8!/)>-#<1#+!#1B(912!#1-#� � � � � � � � � � � � � � � � � � � #

G � "# W1*19B)-1# 1+# � � � � � � � � � � � � � � � M81# 21# <1<8/1# <1# 12*!# 2)*8!/)>-# (!*9)B0-)!+# F# L!@!# 8-!#

)-*19(91*!/)>-#<1+#9128+*!<0#0:*1-)<05##

� � � '!+/8+1#+02#9!*)02#<1#20+=1-/)!#!#+!9@0#*!B:)R-#/0-0/)<0#/0B0#9!*)0#<1#@!9!-*U!7#F#1+#<1#20+=1-/)!#!#

/09*0#(+!_07#/0-0/)<0#*!B:)R-#/0B0#+)M8)<1_7#F#1O(+)M81#28#2)@-)A)/!<05#

35 ;1-1B02#1+#2)@8)1-*1#:!+!-/1#<1#2)*8!/)>-C#

* ;JYWZ:* * * -;!WZ:*

'!^!# # QJ5444# '!()*!+#E0/)!+# # hiiiii#

'+)1-*12# # Q45444# W18<0912# # Q45444#

e!M8)-!9)!# # V45444# j1219=!#+1@!+# # QJ5444#

c!-/07#/,/# # Q45444# D90=11<0912# # I5444#

;1991-02# # [5444# ?O)2*1-/)!2# # V5444#

D9R2*!B02#!#/,(# # P5444# D#F#t#Gc1-1A)/)0"# # Q35444#

!" g<1-*)A)M81#+02#1990912#M81#21#L!-#/0B1*)<0#!+#09<1-!9#1+#:!+!-/15#

:" '!+/8+1#1+#/!()*!+#20/)!+#F#09<1-1#(09#B!2!2#(!*9)B0-)!+125#

/" ?O(+)M81#B1<)!-*1# +02# 9!*)02#M81#/0-2)<191#0(09*8-02# +!# 2)*8!/)>-#1/0->B)/!#F# A)-!-/)19!#<1# +!#

1B(912!#1#)-*19(91*1#1+#9128+*!<0#0:*1-)<05#


28

J5 K#(!9*)9#<1+#2)@8)1-*1#:!+!-/1#<1#2)*8!/)>-#21#()<1#G*0<!2#+!2#/)A9!2#21#1O(912!-#1-#18902"#

#

!" '!+/8+1# 1+# A0-<0# <1# B!-)0:9!# G/!()*!+# /)9/8+!-*1"# <1# 12*!# 1B(912!# 1# )-*19(91*1# 1+# 9128+*!<0#

0:*1-)<05#

:" '!+/8+1#+02#9!*)02#<1#*120919U!7#+)M8)<1_7#1-<18<!B)1-*0#*0*!+#1#)-B0=)+)_!/)>-5#$!+091#+02#9128+*!<02#

0:*1-)<025#

/" W1*19B)-1#+!#91-*!:)+)<!<#1/0->B)/!#F#A)-!-/)19!#0:*1-)<!#(09#+!#1B(912!7#*1-)1-<0#1-#/81-*!#M81#

1-#1+#T+*)B0#1^19/)/)0#0:*8=0#8-#:1-1A)/)0#!-*12#<1#)-*191212#F#<1#)B(812*02#<1#Q65444#189027#M81#

+02# (!@02# 91!+)_!<02# 1-# /0-/1(*0# <1# )-*191212# !2/1-<)190-# !# I5[44# 18902# F# +02# )B(812*02# L!-#

28(812*0#Q5644#189025#?=!+T1#<)/L02#9!*)025#

#

;JYWZ:* -;!WZ:*

;1991-0# [45444# '!()*!+# Q445444#

'0-2*98//)0-12# Q645444# j1219=!2# Q645444#

e!M8)-!9)!# Q65444# W18<!2#!#+!9@0#(+!_0# Q645444#

e0:)+)!9)0# [5444# W18<!2#/0-#1-*)<!<12#/<*07#/09*0#

(+!_0#

[5444#

e19/!<19U!2# [45444# D90=11<0912# QJ5444#

'+)1-*12# V45444# # #

c!-/027#/,/# 6V5444# # #

Y:Y;>*;JYWZ:* 6=?)888* Y:Y;>*-;!WZ:* 6=?)888*


29

TEMA 12 - ANÁLISIS ECONÓMICO

Q5 W1# +!2# /81-*!2# !-8!+12# <1# +!# 20/)1<!<# u'!B:)!_0# E5K5v7# 91A19)<!2# !+# 1^19/)/)0# 6544Z# 21# <12(91-<1# +!#

2)@8)1-*1#)-A09B!/)>-#1/0->B)/0XA)-!-/)19!#1O(912!<!#1-#18902C#

.� � � � � � � � � � � � � � � � �

g-B0=)+)_!<0#J544454447#1O)2*1-/)!2#Q544454447#91!+)_!:+1#Q534454447#<)2(0-):+1#34454447#A0-<02#(90()02#

35Z4454447#1O)@):+1#!#+!9@0#(+!_0#Q5I4454447#1O)@):+1#!#/09*0#(+!_0#Q5V445444#

/� � � � � � � � � � � � � � � � � � � � � � � � �

g-@91202#1O(+0*!/)>-#Q5J4454447#@!2*02#<1#1O(+0*!/)>-#I4454447#@!2*02#A)-!-/)1902#Q[454447#)B(812*02#

20:91#:1-1A)/)0#63654445#

W1-*90#<1# +!#B!2!#(!*9)B0-)!+#<1# +02#(90()02#12*N# )-/+8)<0#1+#:1-1A)/)0#-1*0#<1# +!#1B(912!#<1+#1^19/)/)0#

M81#!2/)1-<1#V[454445#

E1#()<1C#

!" '!+/8+!9#+!#j1-*!:)+)<!<#?/0->B)/!#0:*1-)<!#(09#+!#1B(912!#1-#1+#1^19/)/)0#6544Z#

:" '!+/8+!9#+!#j1-*!:)+)<!<#q)-!-/)19!#0:*1-)<!#(09#+!#1B(912!#1-#1+#1^19/)/)0#6544Z#

/" ?O(+)/!9#1+#2)@-)A)/!<0#<1#/!<!#8-!#<1#12*!2#91-*!:)+)<!<125#!"#$%&'()*+,-*./0.1**+2-./.3*

65 \!#1B(912!#'Kjjb#0:*8=0#1+#(!2!<0#1^19/)/)0#8-#:1-1A)/)0#!-*12#)B(812*02#<1#Q445444#189025#?+#=!+09#<1#

282#!/*)=02#*0*!+12#12#<1#3445444#189025#?+#[4o#<1#12*1#=!+09#12*!:!#A)-!-/)!<0#B1<)!-*1#91/89202#!^1-02#

91B8-19!<02#!+#Q4o#<1#)-*19R2#!-8!+5#E!:)1-<0#M81#+02#)B(812*02#28(0-1-#1+#P3o#<1+#:1-1A)/)07#/!+/8+1#+!#

91-*!:)+)<!<#1/0->B)/!#F#A)-!-/)19!#M81#0:*8=0#+!#1B(912!5#

!"#$%&'()*+,-*./451**+2-./67*

P5 ̀ -!#1B(912!#(9121-*>#+02#2)@8)1-*12#<!*02#1-#18902#(!9!#1+#(!2!<0#(19)0<0C#

g-@91202#(09#=1-*!2#Q445444#

t!2*02#<1#1O(+0*!/)>-#[45444#

t!2*02#A)-!-/)1902#35444#

gB(812*02#35634#

E!:)1-<0#M81#+02#!/*)=02#*0*!+12#<1#+!#1B(912!#12*N-#=!+09!<02#1-#I35444#

E1#()<1C#

!5X#/!+/8+!9#+!#91-*!:)+)<!<#1/0->B)/!#<1#+!#1B(912!#

:5X#1+#B!9@1-#20:91#=1-*!2#

/5X#/0B1-*!9#1+#2)@-)A)/!<0#<1#!B:02#/N+/8+02#

!"#$%&'()**+,-./481*9:;<,(-*./4*

V5 \!# 1B(912!# j?%;Kc\?EK# (9121-*!# +!# 2)@8)1-*1# )-A09B!/)>-# G1-# 18902"# /09912(0-<)1-*12# !+# (!2!<0#

1^19/)/)0C#/!()*!+#Q3454447#91219=!2#QP454447# A0-<02#!^1-02#66454447#!/*)=0# A)^0#P4454447#!/*)=0#/)9/8+!-*1#

64454447# )-@91202# <1# 1O(+0*!/)>-# 63454447# @!2*02# <1# 1O(+0*!/)>-# Q3454447# )-*191212# <1# <18<!2# 654447#

)B(812*02#6[5444#

E1#()<1C#W1*19B)-1#+!#91-*!:)+)<!<#1/0->B)/!#F#A)-!-/)19!#<1#+!#1B(912!5#

!"#$%&'()*+,-*./41**+2-./47*

35 e!-)++!9#E5K5#12#8-!#1B(912!#M81#21#<1<)/!#!#+!#A!:9)/!/)>-#<1#/0B(0-1-*12#(!9!#:)/)/+1*!2#F#/)/+0B0*09125#

'81-*!#/0-#8-!#)-=192)>-#0#!/*)=0#*0*!+#-1*0#<1#P4#B)++0-12#<1#189025#\02#:1-1A)/)02#0:*1-)<02#1-#1+#T+*)B0#

1^19/)/)0#L!-#2)<0#37V#B)++0-12#<1#18902#!-*12#<1#)-*191212#1#)B(812*025#?+#*)(0#)B(02)*)=0#12#<1+#P4o5#E1#

<121!#2!:19C#

!5X#\!#91-*!:)+)<!<#1/0->B)/!#<1#+!#1B(912!#

:5X#+!#91-*!:)+)<!<#A)-!-/)19!7#1-#1+#/!20#<1#M81#2>+0#21#A)-!-/)1#/0-#/!()*!+#(90()0#

/5X# +!# 91-*!:)+)<!<# A)-!-/)19!# 28(0-)1-<0#M81# 21# A)-!-/)!# /0-#8-# J4o#<1# /!()*!+# (90()0# F# 8-# V4o# /0-#

<18<!#0#/!()*!+#!^1-05#?2*!#<18<!#*)1-1#8-#/02*1#0#)-*19R2#B1<)0#<1+#QVo5#

!"#$%&'()*:=*+,-*./051*>=*+2-./051*%=*./40*


30


31


32

#

cuaderno de ejercicios - ramaeco.files.wordpress.com€¦ · Índice de ejercicios pÁg. tema 3 –...

Documents