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& 658.15(075.8) '' 65.290-93*73 78
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78
. ., . . $#% &. 2- .: . – : , 2009. – 520 #. ISBN 978-966-364-924-5
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ISBN 978-966-364-924-5
2
© 3. 4. , 4. 6. , 2009 © !!#/% # !, 2009 © , 2009
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8. L ('/# ! « !!'#»? 9. ?) * #/ )# ) . 10. / # # & 1 !!'#. 11. % " ) "*' "*' #!1 # !) 1. 12. ?) # & # 1. 13. / " # ) "# #%# !!'#. 14. N # "*' "# #%#? 15. ! ! (/# !!'#? 16. ! ! (/# !# !!'# )& #! # !? 17. / " #( #. 18. 4)% # !) #.
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E) "# )/ /# !!'# (' # #& : – ) & !) ) )% !% ! («)/% ) !) "# )/ ) )% !); – #& # ! !) ) («/% )» !)); – ) !) "# )/ ) !% ! («% )» !)). H/ "# )/ /# !!'# ' #% !, ")% ) & !#% "(: (5.31) "& = " ± " ± ", "& – #% ! ()); " – ! ()) )* !*; " – ! ()) 1 )*; " – )/ 1 !))*% !*%.
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(5.38) "1,0 – !, &% " ) !* * ) ##( )# . 144
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(5.39)
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, )! % " ! , ) ) #/# ! .
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= `1 `2 `3 `4,
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) #!1 #% !* ' ) «) ! !!'#». 4 !% /# !!'# #/ # #!(/ */ !. ! / &/: ! ! #" #' % *, )* #* ( !!'#.
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# & & 7 )1' ! , ) ' !!'# / # 1 ! #!# !# !*. 149
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*/ '/# " #' )* ) )% ! 1#/ ) !!% !. 150
P (!) 1 #('/# )* & ( ( #( 1 #( 1, " / #/ . # (!) 1 ! ) ! #'/# ": 'E H
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5.4.2. ;= +C = * /G
1 "# # !!'# #!&'/# «! » # !. !'# !#! ))/ , ) * !' % "# #%#/, "# )&#/. ) # & !!'# )’ '/# # "# #%# ( %# !. =%#/ )# ) ' !!#, + !!'# )&' #. @ ! * !!'# #/ & ) – ))! #% ! ). H/1 # * )&/ )# % !!'#, % . ! 151
## &% ) 1 )1 & "# . 7
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Pr V GB
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(5.50)
k"+ kNP kHE kB k+ kt k3 ,
(5.51)
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k"+ – # !, # *; k"N – /#/ ) !*; kHE – #/ # 1; kB – ))!#/ # 1; k+ – "*' ! # (! ); kt – # # )’ )/ ! !!'#; k3 – "*' "# )&#. ?# " "*' #%# )# ) ' #!) ! ) !!'# % * ! & !)-" )/ #%#/ )# . 152
1. % ! /#. 2. / " !/ #!1 # !) – «) ! !!'#». 3. / " " ", "## !*, !# !*, ")'# !*. 4. N !) )'/# 1#/ # 1? 5. ?) , + !(/ ) 1#/ # 1. 6. N 1 )1 & "# ? 7. / )1 " / ) "*' #%# )# . 8. &/ # "*' " ) #%# )# .
153
Ãëàâà 6. Ô²ÍÀÍÑÎÂÅ ÏËÀÍÓÂÀÍÍß
² ÏÐÎÃÍÎÇÓÂÀÍÍß Ä²ßËÜÍÎÑÒ² ϲÄÏÐȪÌÑÒÂÀ 6.1. !/ ; ;/ ?@ =E %&1 !!'*/ /# ' ! , # "#. P" ! "# !!'# & / ) ! # "# !, !*# # !!'#. $# ! !!'# # ) *#! ( #!#/ /#/ *, #’' #!( ) ( F "# !% #*/ 1/ ) ))!# & "# , !)* # !) * )/. $# ! #’' /#/ (% / ' !) )/, )'/# ) ’' )#% ##!/ ), * "# ##, ), )/# 1 ! ) "# !*%. 3 ) !*# ' # ## ! , * 1/, #/ ) # / #(/ , + ))!'/# ) , , #( "*'( #!*#. 4F "# !) "# !*%, )/#/ / #!#/ 1/, # '/# !*# "# ! !) . & )/ ! % % !* # &((/# . $ "# !) ' ! !( )%#( * # (! ) &# ! "# ## - - ). H !( "# ! )(/# !), )(/# 1 , !), )'!’ ) ) , !##/ )*, & , + #! (/ # ( . 154
– * % !*# F !% ! "# ## !!'# ! "# #. */ ’' ! ' "# /#/ !!'#. " # ) " 1 )'/# ##, "# #, !#(/ , # !!*. ? #- !!'# & )%#(#/ ! . E !’ ) ) ) )/ ) ##, ), % & )## !*. % * ! !!'# #/ 1/"% , # #. 8 0& $ – ))! !/ &#% #!1 #!#/ /#, & */ 1 * !# # !# !!'#. ? )#' )+#/ "# ! , #/ &% !!'# !’ )% ) ), !#/ ' !!/ )%, % ) , !1 & !% 1 . $#% # #’' #!( , % / "* , * )/, &, #, )&/ # 1. 3 !) 1/" "# ! – * ) ! 1, # # , ) "# & #!#/ "# !* !# #' #’'. H !( "# ! !)(/# , */% )! ) # & # (/ !*# * )/. */ F(/# "# ) , !), + )(/ "# ## ) # , ) (/# "# #.
!’ ), ) , ) )! ! ) "#, ) 1 – ) )1 # # &#%. @ , A ; * * ;*G ED : =E A @ 155
; ; @ ( @) = /;* =E=+* = /G E@/ A / F* A C A ? /*; . 8 ) $ /# !!'# : – ))! "# ## , #*% "# /#; – ) 1 " !, * #! */ % # ; – 1/#!#/ ) )/1 ! ) # 1; – # */ "# # ) (&, 1 !!'#; – # * 1 #; – / ) "# #, !#!&#( #!&#( !!'#. # ! # ) ! "# ! )# )/ ), ) (/ % ) ' ## ! . &/ # ’', #" ! , ! , " # !): – ’' "# ! )& ' "# /#/ !!'#, #! ' #% ! "# # # !!*%; – #" % /# !(' # !)!/ !*#, )%#((/# ) !( "# ! , )! # " 1; – "# ! ) # # , % # ! ' F "# &#% ))! % ! / "#; – "# !), ) , ! )& )(/# #% ", # / #% , )(/# !), #!(/ !# & . !*# F "# )/ )%#('/# !# ! / #, )'/# "#/ % , 156
*/ " )* , )!, ) */# * )/.
' !!'*/ # # ! , + ) # # ! )( ! !/#/ #/ # !!'#. & ' */ #, % )%#(' ! ##!/# % % #*/ #. 4 ) # "*% & – # ! # ( ##. & ' % ) , + !%(/# & . @ , ('/# . ( # & )%#(# ) #!#: – 1 # ( !; – ) / )*( "* (, ", ( "’(# &, #*% # +); – 1 # &# & ( (( ( / % /#, & /# ! % !# . .). J#* "# ! % * )'/# , + ! – * ) "*% ! , "# ! – "* ! "#. $* ! !(' #/ !# ) !*( ! )/ ! *#! & . 4 ! ) ", (/ 1 )## "# ! ## , (/ & ", + &(/ % # !!'# . &/: – #% #!/ )# #/ , !’ )% ) / ) # #" ##!/ & ; – ##/ " -! ) #" 1/ "# ! ; – & "# &# !!'# )%# #%) "# ) ) ! . 157
)%# " "# ! /1 &# (/ !!'#, #/ #/ "# )# ) #" #!*#, ))!(/ ! 1#1 ! ) "#. !!'#, !, */ #' 1, ! "# ! # # #1, & !!'#. ? #1 !(/ ) !) 1 ))! #' #!#/ /#. */, )1' #+ #! ' )% ! ( /#/ & !'/# (. 4)* "# ! , !' ’' , !' /1 !# % # !*!. ? ! # )('/# ) )* )& ) #, % / 1 ". J "# ! )'/# %&1 !*!: – !*! ’' # # "# ! ! # ! "# !!'#. )', + % !*# %, #' ’ ) %&1% # #!# ) "# &#% !!'#, !) */ # !!*%, #, ! % 1 ## # !, )/; – !*! "#, % &' # # !*# '' % # !) "# )/ ) !* /# & !) !!'#, # & #*/ "; – !*! !## '# , % !' )& "# ##, ! ) ! !!'#. */ ! !' )/&, ## # # . @/ ) */ !158
*! !' ) 1 & ) ", ) "# ! !!'#; – !*! #, % )/(' # # ! , ))!' /#/, "#/ )! )/.
# 1 (' F#/ ! )/ ) ##!/ ## !, )#% ) ##!/#, *% # 1 !!'#, ’' * #*/ #*, & # ##, * "# )/ # !#. F#/ "# ! !!'# )' / /#/, % !' + 1/ ) # . #( )&/ !# F & #!# "# # ), */ )! ##, !)* # !!*% "# )'#, #((/ !# !*#. @ */ # ) # )/, ))!/ %+ 1 ) ) ! "# #, !)* , #)* , !. H "# ! !!'# ! ' , + : – (' ) # * " "# !); – ' &# ) &')# "# !; – #&/ # & )1/ "# . 1. ! ' ##/ "# ! ? 2. 4)% # ) "# ! . 3. / # ) "# ! . 4. N #!# & )%#(# ( #? 5. / &( " 1 )## "# ! . 159
6.2. J: A C ; * $# ! !!'# ' #( #% !*# (' ! (#. 6.1).
*# "# ! ! ! ! IV ! V ! VI !
E) "# #*
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. 6.1. A C ; * /G
7 )(/ "# !) /# !!'# ) !!% !. ?#(/ "# *: #/ #, ) ! "# )/, ) ! 1 1. 4# ! '/# !), # )*, , !. % ) ) ' * "# )/ /# !!'# ) !, + # / ! . $ ! / ) "# # "# ! ) # ! "# /# !!'#, #(/ # !) , ##(/# !#! "# !. ((/ )(/ # !) !) "# ) !( # ! "# !. _* !' ’ ) !) "# ! ) , *%, #*% 1 ! !, + ) (/# !!'#. ’ )%#((/ ! "# ! , )' ) ! , *% "# /# !!'# !' * "# )/ % /# *.
*# "# ! !!'# )1'/# ) "# !. % 160
7* ! ' ) " * "# )/ /# !!'#, ! ) )! !), ! / ! !), )* ) + # +. $# ! #/ (#. 6.2). $# !
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# !## "# ! )'!’ ) )', ! )%#('/# !% !##. %&1 ! ! ' !) # ! "# /# !!'#, )%#('/# !*# !#! ! . */ ! )(/# ) ! ! "# ! . #( )( ) ! "# ! #&/ # ! "# ! .
6.2.1. J A ; * T#!#/ ! &' )#/ !, )’ )(/# !*# ! #*/ ) ##!/#. T ! ## ! , ! ' / # )* ! &, #’', & # !!'#. )’ ) ) # ) #*/ !*#, + (/# ##!/#, 1( )( ’( 1/ )1/ , #( ))! #/ ) ##!/# #% !#! - #*/- ## # /1 )#' $
.
#! "# ! )' %&1 !), !!* % ! )1 , ' ( "( )* *% !!'#.
#! ! (' ) "# # !!'# !) "# /#.
) "# # ' #( # )/ "# ! , #/ ' #( #( )/ # ) !!'#. ? ! )&# ) * ! , ) )/( #'(. 4 "# # # #! ' )% ! " )/ # ) !!'#. '/# ) ) #* "# , + ', !, "# )/ # ) !!'#. * A C* ' #( #% !162
/# (% – "# , ! ' )* # "# 1/ ( " !), !, ! !), + !(/ # *% #% "# /# !!'#, )* ))!' " "* #% !#!, 1 !*( )1/ #+. = "# !( ! #: – #! #/ #/# # !#! ( ! /1 ); – '* )’ ) (, )/ "# ## !!'# *%, # )&/ % & ; – ’ ) # *% ) # #( ##, ! # ; – ! !% ’' # )1 ", ) ) #!1 )’ ) )/ ! "# ##; – !% , )#/ ! ) )1/ 1/ #+ "# ! ’' !## !*# % "* .
*# " "# # !!'# (' # !: – ) ! )* #; – ) " )1/ "# #+ !!'#; – " # *% "# /# !!'#; – ) "# !; – ) ## ) ))! )* "# #; – * ) "# #.
)* "# # & " ' ) ! )*, #/ )&/ # " )/ # ) !!'#. 4# !*# " "# # ) ) " )1/ #+ 163
1 -! "# /# !!'#. , # ! '/# ( " ). $ # *% "# /# !!'# – * #!% ! # ! , # #(/# ! : #/% ! )# # "# ##, + "(/# ) 1 &; / # # !; /#/ # !; #!1 !!'# +. H "# # "'/# "# ! !!'# ) ! "# /#: !, )*%, . . )/ ) ## ), ))!(/ )*( "# #, !!'# "(/# #&, !/ ) )/ )*. )( ! ) "# # !!'# !/# * "# ) ## ) ! !: – 1 #! )&# *%, ! ! )* # *('/# ) "# # ; – *('/# ’ ) "# # ) !) ) )1/ #+; – *((/# &# !!'# + " # !) & "# ; – *('/# "#/ ) "# #. 4# !#! "# ! #/ !) , + ' #( # !!'# . ) ! ' & "# # !!'# !#!. ) )'/# )/ ) "* ) !/1 ( & ) #*% "# !). H 1 ! !) ! (/# : # ; !; #; #/#; #. = !) (/ ! %&1 ! " 164
’' #/#% /1 % !#!. 4! !) !) &#% 1 ! # !) !% /# #% !#!. 4!% !) ' ! )! 1 # * ; #% – 1 # * 1 ; #/#% – 1 5 ; #% – /1 5 . H # % % (! !) ) !) ! (/# : !1 () (). 1% !) F'/# !& %/ * ) #& ’' !1/ ('/# ("), ) ) * ). % (%) !) ) '/# ) ))/ ) *%. > ) ! ' ) 1 # # & # ’' !) %/, !% ) *. 1% !) ! ) %/ # ’' !) 1'/# % !1/. % !) ) '/# ) ! : ) # %/ #( *% ) # !# . ?& ! )%# !) #!' ) " #/# ) !) /# !!'#.
6.2.2. J + A ; * =# ! ! "# /# !!'# F'/# )% "#% # "#% !* ) #! "# /#. % "# ! )'/# )( "# !. ? (/ &#/ !!'# ) !% ! # & "# % ), #" # % , ))! !#% !#!&#/, & ) # ! " */ ! !. H )/ ! "# ! ) (/# # : 165
– ! 1 1; – ! ) ! "# )/; – ! #/ #. 3( ( ) * ' * "# ! !!'# */ ! !. H ) ) )# ) !)*'( #(/ !% "#% ! ) )( ! . , ( ! "# !, )(/ !: – "# #( !!'#; – )/ "# ) ) !!% !; – ! # * )* !*, & 1 !) !*% /# !!'#; – ## ) !!'# ##; – ## ! ; – ## )*% /; – # # !) !* "# +. !*# )%# ! "# ! # "# & !/ ) # ) !*. )* !*#, " )! 1. N !, !) # )* #(/ . % !) )'/# % # *, ! */ 1% ! !), 1 1 "* , + #/# /. ) # )* !' ) ! # *, * ) !* "# ! ". . 6.2 /# !) # )* !*. ?#( !) + # )* !*, )(/ /#/ / ##, )(/ # *. !# & ) (/ !% ) ! "# )/, ) !( )'/# & ! ! !. $ « ) ! "# )/» . 6.3. 166
A&# 6.2 JC= E*C ;=:? 2005 . U 2005 .
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% !
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#/ 015 E*)% ) 020 1 ) 030 #% () 035 ) !* =#/ ) 040 !* ?% ! ()) 050 1 !*% 060 E# 070 ? ) 080 1 !*% 090 $# )/ !*%100 /#: ! ()) ( . 050+060–070–080–090) # ! 110 1 "# 120 1 130 $# 140 ? # ! 150 1 160 $# )/ )% /#: ! ()) ( . 170 100+110+120+130–140–150–160)
) ! )% 180 /# $# )/ )% /#: ! ()) 190 ( . 170–180) 167
=( ! ) ! "# )/, # ! (/ )( )* !*. H #, !, /# ) )* ) !!% . * #('/# ! * ) ) ## !( !*, * ) !!'# !*(, * ! !(, * # )# !/, ! !* !* !!'#. )(/ ! #/ # )*% / !# ! #/ # #/ # " )*% /.
1 ) (/ ) !! (& !&), ! ( ) ) # 1 ! (1 "*). $ &' 1 ! ) !(, #*%( "#( /#(. !*# "# /# !!'# )& ! /# ! )* ! 1 ) ' !+ )/#/ ! 1 !.
1 #(/ ) )( ! ((/ / & . ) &/ &(/ )* !*, )* # )# / , !))*% !*% 1 , !!'# ' & ! . % # &(/# * ) !*, # ! !&, !1 # !), #! !* ) # #/ . 4' " ! 1 !!'# ! . 6.4. @ " ! ) ' ! /#/ & & 1 F#/ , ##/ / , #'# ) & ! !) 1. J ) # ! – ) !# ) ))! / 1/ )##, & " !/ # !, #( "# #%#/ 168
A&# 6.4 J; @ H 2005 .
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EH4J ) ) 3. ? "# /# 3.1. H/1 # ! 3.2. H/1 )# 3.2.1. 4& !) 3.2.2. ?!# *% ?=j434 &/ ? 1. H !( /#( 1.1. ? * ) !* () )*% / !, # / ##/ !*%) 1.2. & (& 1.2.1. , ( ## !*% 1.2.2. ! 1.2.3. , ! ) !, % )1'/# )! & !!'# 1.2.4. , # "#% )/
169
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EH4J ) ) 3. H "#( /#( 3.1. 1 # !) 3.2. =! !* ) # !) 3.3. # "# 3.4. ?! 3.5. ? ) " 3.6. 1
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! ! "# # !!'# ! ## ! #. !*# % # '/# ! # ", ) # / )!# +. $#% ! )' %&1 !), !!* % ! )1 , #!' ( "( )* */ #, # #*% ! !/. . 6.5 ! ! # )* ) . A&# 6.5 J; / + / ;=:?
) 1. ? )*, # 1. J/ 3. $ ! !* 4. ? !)(& " (37,5% . 3) 5. E)* 6. 1 7. ) ##/ ) !* 8. )* ( 1–7)
@#. 81 285 27 474 24 873
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9 327
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"# ! ) (/# # !#! 1 )* % )*. /# ’ ) & / ) & "# . */ )% #(/# 1# " 1 1. 171
( ) "# %&1 ) !/ & !! " # # ##.
6.2.3. A ; * 4! ! !(' ! #'/# ) ( ( ) & ! )% "# ##. !!'# "# ! ) ' )%#(# ) ) 1, * ' " ( ) " # "# ##. )%# ! ! "# /# ) (/# !# # ! )/ + "# ))! # ! #!#/ /# !!'#. 4! "# ! (' # # !& , # ! ) ! # . # $ 1 ) : – ) !& # 1 &/ % !!'#; – #" "*% ) + 1 !; – # +% ) "*%% ); – ) !& () # & ), ! ) ! ; – ) ! # ! !) 1; – ) () # #) # / 1 1 !!'#; – ) "#% ) !)* %/1 % )+ # / 1 1 !!'#.
# # !& # ) * % )*, # )!#, #/ )# ) ( )! ( "# !. &% #(/ ) )( ! # * 1 !. 172
!& ' )# & 1. / #% !&% ) ' "# ! , , "# +. # !& "*% ): – ! )* !*; – 1# *; – ! !/ /; – !# ) !!'# ; – ; – 1 ); – " ! )!; – -"; – # # !& ) "# )’ ) . 4)( !1 "# # !!'# #&/ !+ ! & , + )' ##/ # &#% ! . * ! 1 ) : – !# # #!% !; – !# & )*( !*; – & ) !1 & "# . 1 1 !( ( #/ ! "# #%#/ !#!&#/ !!'#. . 6.6 !) " !& .
) ) !& # !% , ), ! ! )# ' ! !!'#, + ) ' !#/ #*%. )* & ) !& ) 1. !, !&% + ) ) !#/, !&% + # +. #% ! ! 1 &' & ! ) #. #% ! 173
A&# 6.6 JE;= A ; M ( 'b ) z f ( 'b ) f @ M * z , j
M
j
~ & f ( 'b )
(6.14)
f M * z , ~ & M * z f ( 'b ) f.
(6.15)
(6.14) (6.15) #!(/ #!1 : M
M
~ & f ( 'b )
f M * z , M
~ & M * z f ( 'b )
f. 195
6.4.2.2. L :* ;@ =/+ ;C C *
% ! , !#% ! / - ), ###/ ## &/ – + #/ ). %#1 b ) !+ 'b !/ )’ )# ) (6.7). ? # &/ ! ) !, ! / ) !#. J&, !, ( !+ 'b, + !)*% ) m ½ ° ° min ® u j 'b j : Ax d b 'b, x t 0 t 1, x Z ¾ , °¯ j 1 °¿
¦
>'b1,..., 'bm @T
'b, u j ! 0, ( j
(6.16)
1,..., m ).
*/ u j & ! , !’ ) ) )( ## 'bj *(. H )# !# !+ 'bj &/ ’', m
"* #
¦ u 'b j
j 1
j
! u j 'b j
/ ’'. + 1, )# #!' , !! !)*%% ) m ½ ° ° min ® u j 'b j : Ax d b 'b, [ x, 'b] t 0¾ . °¯ j 1 °¿
¦
(6.17)
) !* ## 1- ) L !’ ) ) ## "*. ) )(/ $
# . 4 !( ### & !# #/ ) b, %& # !) # / &% . E !*( ## 2- ) L !’ )(/ ) #( "* . ( ### '/# ! ) c. !* # ) % ! 3- * , + # #. ) L # * ' : 196
(6.18)
1 ( ) L*, & max{( c 'c, x ) : Ax d b 'b, x d 0}.
^
`
min ( b 'b, u ) : AT u t c 'c, u t 0 .
(6.19) % K = {['c, 'b] En+m: ) (6.18) )’ )}, M('b) = {x : Ax d b + 'b, x t 0}, M*('c) = {u : ATu t c – 'c, u t 0}, Kb = {'b : M('b) z}, Kc = {'c : M*('c) z}.
4, Kb z Kc z . J& K, Kb Kc !’ ) #!1 K = Kb Kc. %#, # ###/ ## Ax d b + 'b, x t 0, ATu t c – 'c, u t 0
(6.20) (6.21)
) 'b 'c ' )’ )#/ (6.18), (6.19). H 1 , + ) 'b 'c ) (6.18) )’ ), )’ ) ) (6.19), ## &/ (6.20) (6.21) ##. 6.4.2.3. /; C * ;@ =/+
)’ ) - ) "# ! !!'# !)', + # % ## – #/ )% #* . H%, ) 1 /, & &/ ) !#, # # , + ) )’ )(. ) &1% */1% !, % F'/# )## ’' !* * , ! )’ ). 6.4.2.3.1. /; *? :?
H!1 ) ! C : sup{f(x) : fj(x) d 0, j = 1,..., m, x t 0}.
(6.22)
H #%# ! ): sup{fo[yo](x) : fj[yj](x) d 0, j = 1,..., m, x t 0}.
(6.23)
@ {yo, y1,..., ym } – ## !, &/ * !#. )', + ) !197
^
`
0 #! )/ * ! y 00, y10,..., y m #:
> @
f0 y 00 ( x )
> @
f0 ( x ), f j y 0j ( x )
f j ( x ), ( j
1,..., m ).
( y = [yo, y1, ... , ym ] )#/ (6.22), & # )!# C(y) : sup{fo[y](x) : fj[y](x) d0, j = 1,..., m, x t 0}.
(6.24)
" ) : sup{fo(x) – ('c, x) : fj(x) d 'b, j = 1,..., m, x t 0},
(6.25)
sup{fo(x) – D||x||2 : fj(x) d 'b, j = 1,..., m, x t 0},
(6.26)
D> 0.
# 'c Rn 'b Rm ) max{(c – – 'c, x) : Ax d b + 'b, x t 0} ' #( )/ # ) ) (6.1). T/1 )/ " ) ) (6.1) # ! ) )'/# : max{(c – 'c, x) : (A + H) x d b + 'b, x t 0}.
(6.27)
% V – 1 ##/ ) C ( )’ )(, #( +). (6.24) & KV = {y : c(y) ' ##/ V}. J ! !#* !’ ) ) )’ ) ) inf {d(y) : y KV}
(6.28)
) 1 / "* d(y). !. % V – ##/ )’ )( ) max{(c – 'c, x) : Ax d b + 'b, x t 0},
(', 'b) R+ . d('c, 'b) = ||'c||1 + ||'b||1. *% #* n+ m
KV = {['c, 'b] t 0 : M('b) z, M*('c) z}, M('b) = {x t 0 : Ax d b + 'b}, M*('c) = {u t 0 : ATu d c – 'c}.
= ) !#* (6.23) )/# ) % ! : 198
m ½ ° ° 'b j : Ax d b 'b, [ x, 'b] t 0¾ , min ® °¯ j 1 °¿
¦
½° ° n min® 'ci : AT u d c 'c, [u, 'c] t 0¾. °¿ °¯ i 1
¦
(6.29)
(6.30)
)’ ) ) ! ) ! #-
>
@
!' 'c~, 'b~ , 'c~ c AT u~ , 'b~ Ax~ b , x~ u~ – !/ )’ ) ) (6.29) – (6.30) !. $* d('c, 'b) & + )/1% : m
d ( 'c, 'b )
¦
n
R j 'b j
j 1
¦ r 'c , i
i
i 1
Rj > 0, ri > 0 ( j = 1,..., m, i = 1,..., n). @ ) (6.29) (6.30) / min{(R,(Ax – b)+) : x t 0}, min{(r,(c – @Tu)+) : u t 0},
R = [R1,..., Rm], r = [r1,..., rn]. 4# &/ # ! #-% ) ! . 6.4.2.3.2. + :* =/+ ;C C *
?!1 ! # ) % ! : L : max(c, x), L* : min(b, u). Ax d b, x t 0; ATu t c, u t 0.
) * ) b c. H *'( ( ) L L* !# ! ) L(') : max{(c – 'c, x) : Ax d b + 'b, x t 0}, L*(') : min{(b + 'b, u) : ATu t c – 'c, u t 0}.
@ ' = ['b, 'c] En + m. K = {' : ) L(') )’ )}.
(6.31)
) )’ ) ) min{d(') : ' K}
) ) "* # * d('). 199
)
* # . !#, M('b) = {x : Ax d b + 'b, x t 0}, M*(') = {u : ATu t c – 'c, u t 0}, K = {' = ['b, 'c] : M('b) z, M*('c) z}.
H!# ) ) (6.32) ! d(') = ||'||1. K !# , + & K, ) ! (6.31), & ) K+ = {' K : 't 0}, )(( !/ ) ) (6.32). @ # )#/ (6.32) & ) ) min{d(') : ' K+},
)!'/# ##%: min{||'b||1 : Ax d b + 'b, ['b, x] t 0}, min{||'c||1 : A u t c – 'c, ['c, u] t 0}. T
(6.33) (6.34)
H (6.33), (6.34) & !!# min ( Ax b) 1, min (c AT u ) . x t0
u t0
(6.35)
1
?)/ ! d(') "*( m
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n
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j 1
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i
,
i 1
)# ) ) *1. @ R j > 0, r i > 0 (j = 1,..., m, i = 1,..., n). E ) (6.35) */ ) / (6.36) min R, ( Ax b ) ,
min r , (c A u ) . x t0
T
(6.37)
u t0
! * L L* ) (6.36) (6.37) !&: )/ )’ ) ) /# 'b Ax b 'c c AT u , x u – !/ )’ ) ) (6.36), (6.37). *( ( #!' )’ ) ) L(' ) L * ( ' ) , ' 'c , 'b . ! !1 ' )’ ) , !, ) L(' ) & ’' ). E #: % L – # ) 1- , 'c 0 , ) L(' ) )!1
>
200
@
^
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M ( 'b ) – & !/ )’ ) ) (6.36), + -
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D> 0. ) ' #( ! #-% !, & !!# ) % ! : ° max ®(c, x ) D °¯
½ ° R j t j : Ax b d t , [t , x ] t 0¾ . °¿ 1
m
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N+ & L – # ) 2- , 'b = 0, ) L * ( ' ) )!1
^
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M * 'c – & !/ )’ ) (6.37), + ) ° min ®(b, u ) E u t0 ° ¯
½
n
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&) F # . d (')
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n
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i 1
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2
j 1
H #( & ) (6.35) ! ) ° min ® c AT u °¯
2
min ® Ax b ¯
2
½° : u t 0¾, °¿ ½ : x t 0¾, ¿
(6.38) (6.39)
' *% ! M (u )
\ (x)
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n
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i 1
m
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l j ( x )ai »
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(6.40)
lim \ t ( x0 )
x,
(6.41)
t of t of
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xo, uo – / ! !*# (6.40) (6.41), x, u – !/ )’ ) ) (6.38) (6.39). !1% # !!'# !(/ !( ( # !)* ) )+ *. !!'# )’ ) ) !)* )/ #' )## !1 #&/ !) )’ ) ). ?# /1 ) ' &#/ ! ) P4J, + ) ' ! #% ) ) )+ * !!% # !*( "# !. 4# )# - % ) ! % !#! "# ! !!'# #!' ) !/ #( !&#%. ? ((/ !/% )! ## ( # #) & ) !) !!'# # &. 4 ), + / #&/ *% ) ! + ))! ) ' ## ) !)* "# ! !!'#. H !( - ## % )’ )(/# %)1 ) !#! "# ! . ! # % %/1 / : !-!1, !)* ) %, ' !&/ ! - ), # " )’ ) ) P4J , !, )* % ## #!*" & )’ ) ) ) )+ *. 202
1. N ) 1 !!'# ! !1 % "# #? 2. N - #(/# "# !? 3. / ! ## ) "# ! . 4. N ! # "# !? 5. 4)% ! ## &/ ) !#! ! "# ! .
6.5. A ;
E=-; * ? #! /# !!'# )( ( )'/# # ! , + !' / !*( !/, !’ ) ) -#!#/( /#( !!'#. 4 ) %&1 !*# ! * ' # & -
. H& #1 )+# !/, ) )#-!, % & #% ! ) !!'# % /1 1 ! %. T)#-!, !, #/ ( !), + F(/ */#/ !, )' #/ #( ! ) !!'#. ) # , % ' # * !!'# ! ) !#! % ). ?##/ & !)# " )! & "# / ##, )/ #* )# !* %/1 !#! ! /# !!'#. T)#-! ' &#/ F ! "# ##, * # &# !!'#. H !)* *% ' "*. 203
+7 # !’ ) ) &#( # )#! " *!* ) !!'#. "* ' )% &( # # !!'#, & ! )* !*! ! /#. )## !' ) # "*, + "'/# " . $ # ' !' ) ' # !!'# ) ", # ) ##. 1. *% #'/# * #! # !!'#? 2. / # ! #! * # !!'#. 3. 4)% # *.
8.3. @/ A @ :
/ : ?!# )+ " #% * !! (*% ! *%) #'/# )* # / 1 ) !!'#. !! &/ ’' !*%: – !# (#) ! )+ " ; – , !-!& 1 */! ; – !1 , ) ) !( # ! ; – )# # ; – # (!* "’(# ).
)#/ * !! )' &#/ #"*. " ) % . !! !#(/# % )% ". 4##/ * !! ! ' , + / # #((/ !# !’ " & #" * !! 239
! % ! ) )!# « !» !). = 0 & % . H * !! ! (/# 1 !/. # )!) 1% #1 &(/# 1 !! ( ). &/ *% #/ #, !) #" )! , #, , 1 # 1 . O # #(/ !&% )# ) "# )’ ) . !/ * !! !#(/# " )/1 # ! # !#, + )1 (/ /# !!'#. ? (/# !. > % . &/ # *%, #/ )#(/ 1 !). 4* &/ # () !1 ) # () !1 ! ). # ) ! !)/ )’ )% ! )) * #. ?# ) ! * !(/ ) ! ! &(/ ) ! "# )/ (". 2) # !*% . ! % . " "*(/ & ! * !! (!*, , "’(#). ? )#(/ ! / # !! !& * !! !% /# ) "#( *( %/. @ , ) "# '/# ! ! & !!'# ) , ))!'/# "# ! #*%, #*/ !. H !( " # (/ &#/ #/ ! % . * !! ) ' *) #!# ! (&% "*.
!!'# 1 * !! 1 !!'#-# ' ! " ! " !" ) ( !+ % #, # )! / !. ( ! & #!1 1 ) !( #"240
* * !!, + / !" , & , # ## . ? ! #/% "% ' )# ! (( ! &. *% #* & ) ' !% )# # #, + !+' #!/ / * !!.
)!( #*% )(/ # & ) #/#/ & . N !, )! # '/# ) # )# # /. #/ / # !) "# )##'/# "# !. % #% !) %)/1 & !#% ( "(: k
ABF > A@ > 100%,
(14.6) A , A , A , A – ! ! )# !, # )*, # !, # (!), %.
) #!1 #% !* & ) «) ! !!'#»1. !% /# !!'# #/ # #!(/ */ !. ! / &/: # ! #" #' % *, )* #* ( !!'#. #. 14.8 ! !/ ! )# !) !, # )*, # ! #! ! () ?E@ «4! » 2001–2003 . () )%#('/# !# . 14.1, 14.2). ?E@ «4! » !/ #!1 ! )# ( !!/ , %) ) !) #!## / 2002 .: 209,3 > 127,5 > 107,1 > 102,2 > 100% 209,4 > 141,9 > 121,4 > 100,3 > 100% !. !’ ) ) , + ! 2002 . )% #% !’ / , + ) /1 " # "# ## )/1 #!% !. 1, #! )1 , ) ) )/1 % #% , # 1 !) 4,4 ) % 2002 . B+
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. 14.8. = * = «=; C ; /G » !% «;*» 2001–2003 .
0,5, * )', + # !) 1 &/ /- % !# ) # !. #. 15.2 !/ "*' "# )&# (F ), & #, ) # ! ?E@ «4! » (2001–2003 .). ?! )!! #* , + ## !!'#, & * #! , #!#'/# #/ )# !) "# )&#. )#/ !!'# ! !)% ! # !’ ) ) #( ) . E) F * ) ' !) "# )&#/ !)/ !#!, + ' &( #( % .
#!&#/ !)/ )' #/ % #, &#/ 1 #" # 383
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01.01.2004
01.10.2003
01.07.2003
01.04.2003
01.01.2003
01.10.2002
01.07.2002
01.04.2002
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. 15.2. L ; A:G A ? =;0, ! ' /1, & #/)& #/ !, !. */ ! ! & % #.
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U !/! 1 2 3
4 5 424
) 4# # 1,
#!*, 4 1 & () – #/, #: 1-% 2-% 3-% 4-% # #, %
)% #/% ! " *, %
U1 U2 35 30 3 4 54 60
30 17 7 – 12 9
15 15 15 15 14 9
. 17.6 ) %# # 1 &/ ) !. A&# 17.6 =@ /? CH @ /@/ WACC.
IRR < WACC ! &'/# ". 1 ! (. 17.5 17.6) ) ! U1 )% ) # # (r), ) ( !1 #/ 1 &/ (45,32 ) ) ! # 1 (35 ). ) *' # #/: ª§ 10,32 · º 100 ¸ : 3» «¨ 35 ¹ ¼ ¬©
9,83%.
? &' 1( ! ) ! U1. O (IRR) + #/ ! " * (9,83% > 9,0%). E )/# IRR ! U2: ª§ 13,72 · º 100 ¸ : 4» «¨ 30 ¹ ¼ ¬©
11,43%.
IRR ! U2 & /1 #/ ! " * (11,43% > 9,0%). % !) 1%, & ! U1. * (MIRR) ' #( # / IRR. % #' ! &# # ) ! * ! ' /1 !/ * # # . > )# ! ' : 1. H #( #/)& # ! (WACC) # 1 ! ! ! ! /# %/ # !#(/# . 2. H '( #( IRR # !/# !1/ #. 3. # ! #/ NPV ! #('/# : ) !1/ # '/# !1 #/ #*% . 4. ?)'/# / 1/ # (/#) ! (MIRR) ) "(: MIRR
NPV 100 . I
(17.15) 429
# ) * (/ &#/ "# & !!'# # ! !% !/ 1 . # !% #*% 1/ &/: – ##/ /1 ; – )* ) " *; – % !# !/ /; – # #/ !; – ))! #/# & ! ! #; – # /#/ #*% / /#/ !!'#; – # #/ #*% !# # +. ?#( ) * !% 1/, "#% & & !% F% !.
/% !*# !% !#/ 1/ !' ) # "* / "# ), + )/ & #*% ! !!'#. 1. N ) /#/ #*% ) #/ #? 2. 4)% * "# / #*% !. 3. / !, + & !% # # . 4. ? ! #('/# # ! #/ (NPV) !? 5. )% )# * ! # 1/ ! (#). 6. / # !% #*% 1/.
430
ÐÎÇÄ²Ë V² Ô²ÍÀÍÑÎÂÈÉ ÌÅÍÅÄÆÌÅÍÒ: ÄÎÄÀÒÊβ ÐÎÇIJËÈ
Ãëàâà 18. ÓÏÐÀÂ˲ÍÍß Ô²ÍÀÍÑÎÂÈÌÈ ÐÈÇÈÊÀÌÈ 18.1. ;A :* A @ =
/G $# /#/ !!'# # " !''/# ) # ), #!/ ! )/ % #!#/ /# #/ #. ) )'/# &#/ !# / )/ ) 1 !# * . % * ) !#('/# " ), + !' /#/ !!'#. ), + #!&(/ "# /#/ !!'#, (/ # ! ), + (/ ) A = . 3 (/ ’' )# ) )#/ )1/ #+ ## !!'#. H1' #+ #/ ’' , #*/ ! , !!'# !/ #( /#/. )#/ )1/ #+ , + )&/ & ), ! )& & ! (!!)* , 1, " *, #/ #" # !, )#/ ! # 1, &#/ "* +). P 1 )# !%(/# ) !% 1/ – !431
%+ (/) !## %. H& #! )# & # ) %, ) #'/# "#% &, !% 1/ ) (/# ! %: – 1/ )#, + ## & , + !)/ ; – 1 ! ), + & !)/ ) & & , ! &% ' #( #! *( &#/ ! ; – 1/ ! )#, 1 / % (/ # # & , &# !#( (/ ##. $# ) (/ #’' #, #/ )& )(/# ) (. @ , A = – *, !-!1, )! !*% &, % ## & ! ) , + )% */ # ## % #" /#; !-, &#/ & # !, !’ ) ) ). ? ) */, "# ) &/ ! #! ), + )/ &/ !)# , 1. $# ) (/ # "# ##. ? )(/# ( )#(. H ( " ! "# ) & #" ) ): – %
– #% ), #% ); – – !#% ), % ), #"% ); – %
– )1% ), 1% ); – % &
– !)% ), !)% ); – – !#%% ), #% ); – – ), + ' "# ; ), + ' !+ ; ), + ' ; 432
– &’'
– ) "# !*, ) ) "# /#, ) "# /# !!'# *; – ) % 7 # – !#% ), #% ).
) ) ) ! ' & !% 1/ ! */#/ # ! % ** #. ##/ ! ) ) ! #. 18.1. ? # !*/ ), !’ ) ) "#( /#( !!'# ? ", + !(/ / "# ) E) ) E) & !*% ) ? ) 1 %)* "# ) H## 4* )/
) ) + )& ) . 18.1. '; -@ ;= =
? & # #" ) /# /- !!'#: – & – ! )%# "# !*% !!'# )', # /- , !!'# &', , )% !. @ ! ! ! !!'# &%; –
$ – )/ /# !!'# )' #( #'( ( # !; – $ – !!'# )' , + 1 ! /# ! # , + – &/ ! 1% ). & /#/ ) # ; 433
– $ – !!'# )' / !, % 1 ) #% ) & ! ; – $ ( $) – /#/ !!'# !)/ #, #*%. #"* "# ) & )%#('/# ) (#. 18.2). ? "# ) " *%% )
% ) % ) !)% ) ?(% ) #*%% )
*% ) T)#-) . 18.2. / A @ =
A;*: = – "# ), % ! ' &# )* / # ! ( " "), & ! !!'# "# ! !*% )’ ) ) )# " *. % ) #/ !#%% #!&' # "# !* !!'# " *% . ! " * !/ #!&#/ 1 1 #/ ## !!'# ) )&(/# . & ) ' !#%#/ ! " *. % ) ! # #*% ! * )/ ).
/ = )(/ %#/ , & )) !!'# )/ ’( ) ! )# )/ !, !+ 434
!!'# ! # ! !&. % ) &/ # ! )1, 1 "# ). / = ' "#% /# !!'# ) % #/ . / ) !+'/# ) )/1 # #, % /# . = = – %#/ )/ ! !) !!'# . #/ #% ) !’ )% ) !/( *( )%# !) !*% !!'#. !;D = – ) & ) )/ #! # # / # ( & "# . / %++ ) – %#/ "# !*# )%# #*% /# !!'#. ?! &#% #*% /# (/ # #*% ): ) "# # () * !!) ) / # (! )). J: = ' ) ! ) !* # "# . ? !)/ ) ! !* #*, &, ) # # #% ! #% ! ! ) # #. !* ) – ) ’( "# ! '( )1/ #+, ) !!)* / 1 ##, & ( 1 ". '=-= – ) "# ), !# * #, ! ' &# !!'# ! / * , + )&# . #& ) */ ! % !##: – ’' #’' ", + !(/ % ); 435
– ) "; – * ) ) "# !)*%, + )' "# #!&#/ !, % */#/; – # !# ); – ) !*% ) ); – ) ) + )& ).
) ) (/# % & !. H
)) (/ ): # #!#/% !’ )% ) ###( (. %
(/ ), + ' #: )# %/, !# ! !, # "*. # ! ) 1 !’ )% ) # "*% ))! 1 . 1. N # ! "# ) !*# /# !!'#? 2. ! (/ ## "# )? 3. N & #" "# ) !!'#? 4. N # #" ) (/ /# !!'#? 5. N # "# ) #(/? 6. N & ) (% )? 7. N & #" #*%% )? 8. % !## !/# #& )?
18.2. / ;= = !*# ! "# ) & & !/ ) ) & "# , &/ )’ # ! # )* ) ! ) "# ). ) & "# , !, )'/# )%#( "# !*% # ) )* !!'#. ! "# ) !# ) ", !(/ / ) !!'#, + / # . # "436
, + !(/ )/% / "# ), ! (/# 1 )1 (#. 8.3). $, !(/ / "# ) H1 – / ) – & ( "# /# !!'# – ! " * – ’( !! !!)* "# – / * # "# – #+ ) /# – / # /#
?1 – # ! "# # – #/ "# ## !!'# – ) # ! !!'# – # # !!'# – */#/ # "# ## !!'# – # "# # – / "* "# & "
. 18.3. , F ; D A @ =
#! ! !/# * ), )%#('/# # ) %# "# ). ? * ) 1 ## * %# "# ), %#1 #(/# #!%, ##%, )-% % . # )##'/# !, + !!'# # "* ! ) ! /. ?)% F'/# ! " #!*# ) "# # ) !/1( ( ( )/ ! ! . P#! * 1 #(/# ! ) %# " *%, #*%, ( 1 ). =
)##(/# * ). ? ((/ #!#%%, #%% "% ). =/ ## ! ' , + '/# ## !, #* ) !!'#. ?#437
('/# # & ' 1 #'/# !) %'. !# / !) %'. !*# )## )%#((/ ) *, #!# # . ?* &' ) (#!/ ) /# * ) ! ! ! () 1. !, ) # #*% & ), #( " )/ /# (Ri) ! %# (Pi): n
Ri
¦R P . i
i
(18.1)
i 1
= )'/# % / ) #/)& #!# ( < ). + % )/, /1 ) ' )% !. ! */ # )(/ ! #/#/, – #/ ) , ##/ )#/ & #, ! + ! ) . . H ( ) ) #!#/ /# * )##(/# #/ . 4 # # ! !! #/ ) $ . " -
)##(/# %#1. O ! ! ' , + #/ !*/, !# ) !(/ # ! . &/: # , ) !# , ) ))# *, ) #%# +. @ $ ! (/ 1 # #&#, !# +, !, ##, !!)* (/ # )# ) 1, /1 1 ’'. */ !!#'/# , + ##, )'/# !, !/ # . 1. N " !(/ / "# )? 2. / # * &# "# ). 438
18.3. : = / A :* " $% ' #( ) %/1 " 1 %)* "# ). #"* ) ' )& "# ): %, !)%, #*%%, (%. #. 18.4 ! " #"*: #"* "# /# !!'#
#"* ( )
#"* !) !" !!'#
? #"*
#"* !" * !! !!'#
#"* !!*
#"* ! / #*%, )%#( !!'#
. 18.4. !/ / A :?, F D * /;* ;=:? A @ =
– #"* "# /# !!'#, !' # / &#% & ) "# !*%, )!#/ !’ ) ) (. N+ )/ ! !% ) "# !*% /# )(, 1 !* / !# !; – #"* !" * !!, ) ' )& #*% ), )1( ! */ / # #*% !" ; – #"* ! / # . ? # " / #*% !" !!'# '/# ! ! )* / ! # !## ! !, #(/# ) #*% !; – #"* !!* !* (, !#) !!'#, #! )& ), + ' ! *% ; 439
– #"* !) !!'#, !' )+ # # / 1 1 ) ( & ! / . )+ 1 ) # ) (/# , ! #"* !) )&'/# / !) ), / # !) !" ! */ )&'/# ; – #"* ( ) !!'#, !' / ( !*# )%# !!'# )1/ !*%, + ' &#/ ) ( ); – #"* "# , !' )*( # / # "# . ) & !# #! 1. H& & ) & #" * *. H & ) !' & * !!'# ) % #/. < *, # * *, (operating risk) !’ )% ) ) / # 1, #!&(/ ) # *% /# !!'#. = # / ##/ ). ) * #!(/ )#/ # , *% /#/ !!'#. N+ ' & "# !!'# ' *% !, #*, ! *( (earnings per share – EPS) # # ! (return on equity – ROE) &/ # ) ).
* # # (capital asset pricing model – CA M) # ! # " : 1. # (/# ). 2. J/ ) % !, #/ !!#'/# , + # (/# #) ! */ & !. 440
3. "# # # , ! #/ )#/ . 4. " * !! (/ #( #/ #/ #. 5. #(/ )) ) #( Rf. H *'( #( #! & #. 6. # !(/# . 4# & &%. J/ * # ) ) ! : (18.2) E (Ri ) Rf E i [E (Rm ) Rf ] 1, E(Ri) – #/ i; Rf – #/ )) ; E – !) ## ) («») i; E(Rm) – #/ !" . ' &#/ !!#, + ##% ) + (E ) ' ' # !) ) , !". #. 18.5 )& )')’ ) ) % # *. % " )(/ % #
(security market line – SML). #/ (R )
Rm
Rf
0
Bm = 1
) («»)
. 18.5 /; : /@/ @ (SML) 1
$. , &)" . $. $# !*%: , !: . # . – J.: $ E-J, 2000. – QVII. – =. 175. 441
!'#-#, !/ #)* !, / &#, )1 ! % !, / # / !" #/ ) #! !" ) . J/ * # (=E J) !', + #!% % !"/ ) ' /. @ ( ) + /- #'/# !) * ) ) #! ) !" . =! */ )'/# "*' «» ) ( "(: Ei
cov(Ri , Rm ) var(Rm )
ri ,mV i V m
ri ,mV i
2 Vm
Vm
,
(18.3)
Vi – #/ # i; Vm – #/ # #; ri,m – "*' * Ri Rm. N+ ri,m = 1, (18.1) )/# : E (Ri )
Rf
Vi [E (Rm ) Rf ]. Vm
(18.4)
*/ &'/# , + ! "% !"/, + * % , ' #!1 # ), *. 4&, / ! ! & ) ( "(: E (R p )
Rf [E (Rm ) Rf ]
Vp , Vm
(18.5)
Rm – #/ !" ; R – #/ !" , % (' )) !"/ ; Vi V m – #/ !" ; E – !, + )' . T)) (/ #/ Rf, % !"/ – #( #/ Rm ) Vm, !"/ " – #( #/ Rp ) Vp. )*( & Rm Rf )(/ % '% (market risk premium). $# )'/# ) & !1 )#, # !!'# & # 442
. 3 * (financial leverage) )/1' ! ), & ) !( . 4&, #' )')’ ) "# ) "# & . = "# & )'/# #( # # # ! !!'#. =!1 # !) 1 ' ) !) "# ). #. 18.6 !) #!1 #! ) "# & .
) (#/ )
= =!% )
$#% ) E
? % )
T / ?##/ («&/») . 18.6.
/H* C = A C « ) (' 0,94. #/ ! &#/ !#!&# !!'# %& 1#/ # *. A&# 19.2 : E; /G
) 1. "*' ! # 2. "*' ))!# # 1 3. "*' !#!&# 4. "*' !#!&#
! */ 1,98 1,93
"*' 1 2
0,392
0,403
1 0,1
–
0,94 –
1 1,0 –
H # !# ) # # !!'# )/(, / &# !!'# !#!&#/ # # !%(/# 1 ! ) # # )/(, !!'# – !#!& # 6 # *. 1. / " "*' !#!&# ! )/% # #. 2. 4!1/ " "*' !#!&# ! )/% # #.
19.4. ;= = ’*= ; TEKE= – " # ) !!'#, ) ! "# !#/ ). E3 P=?E =@ E@P3N $E=?EN 4T4 4@434 E @EK – # "# , ! % # !# !!'# !(/ ("#) !#%% % ! (## # ! ). */ #% % ! (' /% 1, )%# -#!#/ /# !!'#, )% % ! ( # ! ) !#( !'/# #( #/( )#(. E@? – !, ' !!'#. N (/ #( # # ( ) ! !!'#. E@? TEKE= – # / # ! )+ !, + '/# )! & !!'#, ! % / *#, ! !!'# * )*( !* ! )1 / . & )+ ! !' # #. E@? ?=44K? – # # "# / 1 !!'#. E@? 4@4 – # ! !!'# ) ! #/ #/ )#, !& ) (/# /1 & ) 12 # *. E@? 4 P EO – 1 !!'# ) & ! * !!. EP @ – !& ! ! #/. E4P > E @EK – 1, * # % # (*). E*% ! (477
' #% !, % ! )!% !. E*% ! #' " )% !% *%, ! # &/ , . EN H?E>E – *% !!, + ' # (&() ! # ) *, & ! & (!# ! # !% *%). EN
?KP>4?EE – *% !!, + ' # ! # ) *, !#/ "# . EK4q – 1 # , /# # (!% !#). EJ4 @HEN – ) !1 (!# !*() # ’' # " / . EJ4 @HEN – ' #( !#! !# # # ! #( !*( ! ! ! # ) ( "# )#. E)*% , )) !% * !!'#, ) (/# # % . @ , )* )&' ! !. EEKH TPHHT@4?4=@ – ) )/ /# !!'# !# #!1 !#, ! , + ) ' ) ! )% % # !!'#. EEKH ?@ E@ – ) , # ) ( 1 & )& /1 " # ## !!'#. EEKH K? 4=@
6J=@?E – ) &# !!'# ! # "# )’ ) . EEKH Q 3 4\4?Q 4\@? – ) !! !!'#. E P
E>@3 – 1) )+ * !! ) !( !!#( ) !#, "* )% (/ #*% ; 2) !!# *; 3) !% # (%, +) # . E@J44 4KjP HE44 E?=@?4 – !# ! , #! ! #+ ) #" !!'*/ /#; ! !) #% *. 478
EO@P@ (annuity) – 1 !& (! &/), + (/# ) !& #. ! )% (ordinary annuity) 1% ! !'/# !* ! !. )% ' !. E @4 – #! #/ ", + (' "# /#/ !!'#, & ' # ) #/ ) # ! !*'(. E4 – !& % ( ") # 1 ! . TEKE=4?E ?E @=@j – #/ , (' % !#% # ) ! )*. TE ?P=@>> – ) *% , + #!*)'/# # * !! )+. TE 4?E>> – ) *% , ## #(/# #! )* !& /, + ) (/ ))! * #" !*, !+ #!&# , + !#'/# . TE 4@P> – ) *% , + !, #!*)'/# ! !). > ##( ' #/ #&, )%#((/ ! !#!&# ' * !& %, ! )# ! #! #. TE?=j> P @ – 1, + (/# ' !% ! ! # */ # . TE @=@?4 – )#/ !!'# /- 1 #!(( #’' )/ ) ! !* (, !#), (( &#/ ))! ’ ) !& (& !)(& " )’ ) ) !+ )’ )/ & % %. TPHE >> T4 3 – # !# #/ )#, #/ !1 ) ! !!'# . TP@E-4P$6@ EO – ) *, + !)' #/ # * ## # #/ (# !" ). TP@E-4P$6@ 4 @$PKN Q E P ? – ' #( #/)& ) -"*', ( !"/ . 479
THP=- KE – !# #!# % )%# !!'*/ /#, )#-!*%, )* )#-!. T)#-! #/ !# *% )/ !!'*/ !*, # !!'*/ !, #!& , !, + ! )/ , +. 4' # )#-! (' % !, ! , )*%% !, "#% ! * ). THP=-
4P@ – )/ )%# !!'*/ !*, + !#/ ! ) ' # 1 !# *%. THP=- H – ) "# ), !1 * #, ! ' &# !!'# ! / *( )& . T qE $4 4?E – )*% "%, "*(% !-!& * !!. T4$EN – 1) * , #/ + ! #; 2) ! !, # ) #! ) ( !+ / #!&#. T4= Hq – * )&, + (/# ) ! !!* ( !, !#% ') ) ( (, ) % # . TS qP@
6J=@?E – "#% ! !!'#, + (' 1 , #! / )!# !% ! # !# *% -#!#/ /#. ?EKS@ @ E=$P @ – ) )1/ . ( #" & #& & #/ ! (!!'#) ) ("() ! (. */ ! #'/# #!% ) #" : ’ ) " '/# % #/ , ’ #/ ! – (% ) . */ ('/# #, ) ('/# (. ) " #' ( ) # #/ , #/ !!'# – ( ) # ) . ?E E@ – *% !!, + #/ !/ ! !( *% ! ! ()% ! / ) ! ) !( *(. ?E @=@j E @EK – * #! !, + # / % #, ) !)* */# " ) 480
1 )1 & ! # #!#/% /# !!'#. ?P=PKj – ) !#/ )’ ) , '( #( (#*) 1% # (#&(). ?P=PKj
4=@> – !#/ )’ ) #* (&) #! !# # !1 1 # # # . ?P P $E=?EN – "# )# *%% #" * 1 * !!, *, !*. ?P P
6J=@?4 – !!'#, -#!#/ /#/ )'/# # #! ) # #&/ & ) *%% #". ?P > E @EK – !, "# )%# * 1 * !!, *, !*. ?P @EKjP HK@@N
6J=@? – " )*, ! % '/# ’' !!'#, + (/ % ! -#!#/ /#. ?P @EKj> (=@ @ >) EEKH TEKE= – ) # !# "# !) !!'# ) ( #! ! & !)* #/ )# ( #/ #) "#% )/ *. ? 4T@?4 «@44 ? =@ 4» («Just in Time Manufacturing») – #!# )* *, + )' )!# #, !* !!'#. ? 4T> KP?P q – /# )'/# #!1 & !#% ) )/% ## !' "# )/ /# !!'#. )% # )' *(& !) «! # !». ?@ E@ JE>T@Q P 4 ? – , ) !!'# ) !, ! (/ ( ## !* (, !#) % !. ?KE= 4T4 4@ 4\@ – )* & ( # ! #( / "# () !!'#. 34 H4@EKj> (E=4?>) EEKH TEKE= – ! & !)* #/ # ) !! !481
/# ) ( ! )#% ). 3 4\4?> 4@ ? ?P=@>4O NKj4=@ – ! 1, + ('/# )/ / #*% !!'#. ?)'/# # ) !#% !!'#. 3 4\4?> 4@ ? 4 P E>4O ( 4@44O) NKj4=@
6J=@?E – * & + !!'#. 1% &' !*, !’ ) ) " #/ # !. % 1% ! "' "# #%#/ !!'#. ?’'% 1% ! ) !( /#( #/ ! # 1 ## / !# . 3 4\4?> 4@ ? $E=4?4O NKj4=@
6J=@?E – ! 1, + ('/# ) ) !!'# & "# ( !1 ) # *%), & ) )/1 (!*) *%. ) 1 ! "# /# ) )/ ! 1, + ('/# ) ! &, ( ! !!'# . 3 4\4?> 4@
6J=@?E – #!#/ )! # &/ ! 1, % #!#/( /#(. 3 4\4? 4@4 ? E@?? – ((/ !: 1 ! ! (!*%) /#; 1 ! #*% /#; 1 ! "# /#. 3 ?K – # / !!'#, + )&/ !) &, # #/ )’ ), !! # " % " . P?EKj?EN – ! &( ) )1 )# 1 * )& # ( /- ## # 1 1 ) ) !. PJ 3 – 1 )& * (, !#) ) ( # . ? !/ )# ! ) '/# !# ! # * , &'/# !). P 4H@ – 1 1 * !!, ) , "#- #, # ! ! , ), ! +. 482
P 4H@> =P @$E@ TE – *% !!, + )#' # ( # ! & !# ) # # # # ) #. P$KNN – !*#, )% " *; &'/# !& 1% )/1 / !! )# + !#, & !+ # */ ( ## # ) (. ?P =$4?E=@j ? 4T@?E ( NKj4=@)
6J=@?E – ! #, + )'/# * !, !"/ * ) 1( ( !*, + !#'/# . ? P – , !% # *% ) ! * # ) !# #!#/ /# !# #! !. ? #('/# !# 1 )/ ) *, !' #/ *%. ? P E =@ E@P3N – ! !!'# #" # !. $'/# ( )& *% !!'# )', # ! !'/# * , )1'/# !!'# )! ! #'/# #!#/ /#/. HEq4 – )1 # 1 ), # 1 * !! / / #. KP – &% !# / ) * !!, )%#( # ) #% . =4@?EN – ) ! 1, & !% #. =@ T’S@4 – )&% !% !#, + )%#(' /#/ ) )! !* ) ( !& ) " ), & !!'# * #!& . #’( & ' !# ) ) !* ! #!& . $P PEK $E=4?434 KP?P q – !)' ) #!1 "*' /# !!'# #/ ) # ) . 4?34=@ 44? $E=4? H4T4?’NHEN – &/ # " "*( !!'# !) ! ) % # /1 . 4#483
" * )’ )/ ' # # !) 1, !1 + # !1 !% . 4 E@4?> E @EK – & 1 !!'# ('/# , !, )/ !* # )# 1 / *#%. ) '/# # % * #!& . 4TKPN E> – )/1 /# *% ) !( )1 / . PE@3 – #" /# !!'#, !’ ) ) ), (, #"*'(, ) " ) "# "*. PJ=N Q E P ? – !# * !!: *%, *%, 1 )’ )/, )%#(% !!'# "#- # ) ( ) "# ##. P$P@ JE=\@ET – ! #1 *, + )&(/ *( !* ! ) ! 1% )* *. P" #1 & #%, ) #% )* # *, # & ! ! )& !&#% ' 1 !& ) # *. * ! " #1 & # . P$P@ 4 P E>434 (? 4T434) ?EqPKN – ", + ! ' , + /- ) )* !* (, !#) !&' /1 #/ ) ! !!'#. P$P@ $E=4?434 ?EqPKN – & )/1 /# # 1 !!'#, & ) #( !) 1, )&( !#/ #. P" "# & )'/# "* ( ' #( )*( & ( /#( #/( )( #( # ) !) 1) ! & , + ' #!1 & !) # 1 )' # !. P$P@ $E=4?434 KP?P q – &' / ! #% ! ! # !) 1. P$P@?E E
4P@E =@E?E (effective annual rate) – %# !* # ) + , + 484
' # #, !*% #* ) ! ! ) . P$P@?> 4 @$PKj Q E P ? – !"/ * !!, + ))!' %/1 #/ ! ) ) %1% ) ! )% !. HEK\4?E ?E @=@j 4=4?Q $4 ? – #/ # " ) )*, )* !# # )*, ) ! #!*. HE E= $E=4?4O =@>4=@ – 1 )* & ! # )* (!&) !* !!'# # )* (!&) *' !* * ))# ! # )* (!&) !*, & #. HE=@E?E – #!# ))! )’ ) , ! ()#&/) )' ! ! & # "# )’ )/ !1 ) )# %. HJ ?@ E@ – # ## !* ( !#) !!'#, + ! !!*% )&/ # * (!&), !, # , ) ! # !* ! ## ! !*. ?P=@O – * ! ) ( % #! )# . ?P=@O PEKj – 1% 1 % / *#% #% ! -/ )!# !!'#. ?P=@O $E=4? – 1% 1 % / *#% *, * 1 * !!. ?P=@>E NKj=@j – #*% )%# ! % ) ( & ! () # 1 # ". ?P=@>> =@@@ – ( ") #, + )%#(' /#/ ) * !! (, + !#' !' ) 1 /#. ?P=@>> 4 E@4?> P @ – #!*"% , + ' #( # ! !&. ?P=@>>
4P@ – F */#, # )%# !/ /, # !-1# * , ) 485
! )# )& # ! # ( !), & !# ! % + )%# #*%. ?P=@4 – ( ") #, + !%' 1 )%#(' ! () !"/ #, !) ) % / *#% #*%% !. 4=EJP@ – !% !# #. 4=E@ ( 4=E@4 ) – #, + !' #/. 4=E@ – #, + !%' #/ ) # ( &' 1, !&). 4=?EN – ! !# !) # ) #. q 3 – " !# ! #! &-#/*% !# ()/, %, # +) ! # ’' / / ##. E=EN PT@4 =j4O HET4 34?E4=@ – & !!'# 1 & (), % . 4?EN – #* *, (( 1 ) , , #& . $KNN – )* !! 1% ) 1. ?' # !! !! 1 ! ! # !!. )/ )*( 1% ' ! / !/ #!&# + # * !#. $4 JE>P HETPH PPN $E=4?434 JPP qJP@ – !*# *#! ! ! !), , ), ! , ( % " ! ! !% !#/ 1/ ) # ! "# /# !!'#. 4@PE – )# # (), 1 #!). E E=@ – !# * ’', + ! (/ !(. E @EK – "# ## !!'#, )* % #!#/ /# # #!#/ & !. E @EKj ?KE PN – #* #% ! (# )#), # *, )1486
, #*( !)' ( !!'#, ! 1, # , #, (, !-# 1 . K6@ > P$P@ – , ! * )(/ ! ! ' !# ! !’ ) ) * ! ". K 3 – ## ) ) ) , * !! !# !# )' )’ )/. 4P$6@ ET=4KS@4O K? 4=@ – #!1 & #( # ( # )’ )/ !!'#. 4P$6@ E?@44JO – #!1 & #( # ! ( !!'#. 4P$6@ ? 4?KPN KE@4=
4J4q4=@
6J=@?E – #% !, + !)' )#/ !!'# # !& #!&#, !# # )’ ) ) % !. 4P$6@ 4?34=@ 44?434 HEKPN 4H4?Q 4\@? – 1 & #( # )’ )/ !!'# ( % !#% (!) !. 4P$6@ HETPH PPN ?KE=J 4\@EJ – )' #/ # 1 !!'#, % "# #/#. 4P$6@ HETPH PP4=@ 4?34=@ 44?Q ?P=@> – !)', # # (!#%) ! ) "# () !!'#. )'/# #!1 & #( ( !#% (!) ! !!'#. 4P$6@ HETPH PP4=@ HE E=? ?@ E@ ?KE=J 4T4 4@J 4\@EJ – !)', ( ( -/ )!# !!'# ! # & (/ ! ) !) & "# . )'/# #!1 & ( # 1 !!'# #( % -/ )!#. 4P$6@ JEP? P4=@ ?KE=Q 4\@? – #!1 & ( # 1 #( # ! !!'#. 4P$6@ JEP? P4=@ =@Q J4TKjQ 4\@? HE 4\@EJ – #!1 & #( 1 ( # / 1 !!'#. 487
4P$6@ JEP? P4=@ =@Q J4TKjQ 4\@? HE @4?E 4-JE@P EKjJ HE E=EJ – #!1 & #( -/ )!# ( # / 1 !!'#. 4P$6@ 4T34?4=@ – !)', #/ ) ) )% ! 1 !!'# !((/# 1. !*# "# ) )(/ #/ , # !, # ", ", -/ )!#, #/ #/ )# !!'#. 4P$6@ 4 @@N – )'/# 1 # 1 )/ # ! )’ )/ ! , 1 !) 1 ) ) )' ##/ 1 !!'# !1 # . 4P$6@ 4 @@N ?P=@> – !)' # !#% ! )/% # !!'#. 4P$6@ 4@44O (HE3EKj4O) K? 4=@ ( 4 @@N) – !)' #!1 & #( ! ( # )’ )/ !!'#. 4P$6@ P?P=@?EN – !)', # # ! & !!'# !# ! . )'/# # )! # ! # ! !!'#. 4P$6@ $E=4?434 KP?P q – )' !) ! ) *( # !. 4P$6@ \? 4O ( @4O) K? 4=@ (
4Jq434 4 @@N) – #!1 & #( # , #/ )#, !1 1 12 # *, 1 ( # )’ )/ !!'#. 4P$6@, L4 QE E@P H6 = ?? 4\PN Jq
4H4?J ?KE=J E @EK4J ( KPP $E=4?434 ?EqPKN) – !)' #!1 & !) # ! !!'#. 4’S@ E – # , + )'/# #!1 !! !!)* , !# 1 *#, *% !!'*/ #, *, # * !! # ) !) , & 1 !). 488
4?P @4?E> > E – *% !!, + ) ! & % 1% *% !!. * * !!, !, !' 1 *. 4 P@4=
4J4q=@j
4 O ( 4T@, 4=K3)
6J=@?E – ! / # #!& # ! !* (, !#) ## !* (, !#) . 44=EJP@ – *% !!, + )#' ! !) &. N ' #( -)! % , + )#' ! % # )! &# )) & & & !# !) . 4=EK@3 – -#/*% !# !!'# )* , # !#/ #/*%, ) *%, !#, ! , ! - , )* #& +. 4=P ?E@?E =@ E@P3N $E=?EN 4T4 4@434 E @EK – # "# , ! % )% % ! * !'/# # !#. ?# ## !!'# # #/ )# ) # ! )* # # "# /%. 4@ E$EN – # & ) ( !, , + & ) #). !'#, # !1(/# "*'(, & & ) + )# ! &% % % ) ! , # )# . 4@ 4K3 – ) %&1 "*% &, + ! ' )%# ## # ! !# )/ & ) )! / # 1 * )/. 4@ 4$P @E – )# !!)* !/ & !!* !!)*( !* . J#/ ! ) ) )!! . 4 4@4=@ 44? E=? (! )’ ) ) – * )’ ) !!'# ! !#/, !*, , &( . N !, # ! ! )’ ) !!' #/ !) ! 1 !!'#. 489
4 4@4=@ 44? $E=4? H4T4?’NHEN – # !) #&/ & ! . &/ # " ) !) ! ) % # . 4@ ?EN – # # * !! ! ( ) !, + ## . P @ EP @> – '/# !#/ ! 1 *! # / #!. E*!% #'/# # )1% . P @ 4@44 P@> – , + !' ! !!'# ) !( ) , + %1, ) . */ + 1 !!'# '/# #/ !1 )’ )/, ' % & # #. @ , (!% !!'#) & , #/.
#(/ #!*/ " , ' !!'# ! # #. ) ) ! /# ) !#(, #( , 1 #/ !& &/ ) ( # " # . P @ 4TK4?> (?P=PKj>) – '/# #&( 1 ! () # # !&. ?#&/ &' )) # # ) #, #% !& 1 . P @ 44Kj> – ) ; '/# , !, ! )# -/ *#% * !!. & ))! !' # !!'#, &( ! !1 !1 #( .
1 '/# ) 1, + %1 !!'#, ! ## * 1 – 1 )* )#. P @ =@ 44?> – %/1 )!#(& " , ! % !' # )% !!'#. @E P KE@4=
4J4q=@j
6J=@?E – )' !% "#% # !*% #, + ! */ ) , + !' !490
( ) ! !1 #! ! #, (/# ) ! !#!&#. 4 – # * *% #", + ! # !! ' # ! & # ) *. =4?E ?E @=@j Q E P ? – *, ) ( * !! !(/# !(/# . KH3 – ) )#, #! !& #/- #% !. H%#('/# #/ : ) " (*/) !' (#) % ' ( ), + !'/# )! & () #/. ?# # " (/# )( ( (). KH3 $E=4?> – ) ! ! %, + ) &'/# ##/ !!'#. K? =@j TEKE=
6J=@?E – #!/ ! )’ )/ !!'# % , !1 1% " !' !1 )’ )/. K? =@j E @EK
6J=@?E – )#/ ! !!'# !(# 1 1. KN E @EK? – , + &' )&#/ «)–#/» *%. K=@3 – # *% #!(( #’' #!# *%, + (/# % "% &. K4@ – * ! "% &; # *%, #( "( &( * . JE qEKj> 4Q4 – % % , % )/ !& * !. JE P@-JP>P – ") #, + )%#(' !* ) * !! ) #' * ) #% . JP@4 3EKHP?Q 4P$6@? – !' ) !) # !!'# ) ", ) ) ##. JP@4 3 ?EN ?@ E@ – #!# ’' , + / ##/ !* (, !#) !!'#. H& )/ ) &/ #"# ! ! () #!# # ##/), , *% # () "* -*% *), ) !#% (## # *). JP@4 =4@?EN 3 4\4?Q 4@4? – )'/# !) * ! !!'#. J% 491
1 ! !(/# ) #( #( !1( #/. # # ! ! #, % #. JP@4 @434 4T=N3
4 Eq? – ## * # & ! ' ) & #* # !# !*, + ))!' )) /#/. JP@4 K? E>4O ?E @4=@ – !' * *% # !!'#, + ' #( )*( & #( #( # % *(. JP@4 K$4 – #/ -/ )!#, + F'/# !!+, + !1 #(/# (#!&(/# ) ! )!#, + %1 #. H## */ ) ' # " *% )& ) ## !*. JP@4 E @EK – F'/# ) * ! / ! *% !!'#. > )## ' ) # "*, + ('/# " . JP@4 $$4 – #/ -/ )!#, + F'/# !!+, + )!# #(/# ! & , #!# ##/ !* )%#('/# ) *( !1 ) # )!/. JP@4 E 3 E434 EEKH – % )’ ) ) !)* !, )#% !1 # ! "* – * # !& !. J4@4 3 $E=4?> – ## ! %# "# #+ (#) !!'# ) &. J4@4 34? ?@ E@ – , !’ ) ) "#-#!#/ /# !!'#, )%#( ) ( ! " # !!'# !#/ ) , # *. ' ) ## "# /# !!'#, & # . PJE@P EKj E@? – #/ ’' !# / ## 1 % !. ?&(/ 1 !!'# (% ) / ’', + #(/# ! # ! #!492
#/% /# !# / . / &/ ! # )/ , ! ##, !, *), -, #/ !, ! ))! , / , " ) +. P KE@4=
4J4q=@j
6J=@?E – )#/ !!'# % ( # #) !# # # )’ ) . 4JEKjE ?E @=@j – # #/ !!'#. 4JEKjE ?E @=@j 434 E P E – ))/ # #/ * !!; / #/, )) * !!. 4JEKjE
4P@E =@E?E – * #, & % 1% ( ) !! " *(. 4JEKj>
4P@> 4Q4 – # # # ) *. )'/# % # !* !, % / #/ "# # (*). 4 JE EJ4 @HEO – #% ) )*% / ) !% ! # ) (!(, !!() # ", &% /1# ! # / # #. 4-QE – ) )/, #, , *% 1 "*, ! , !*#, +. 4T34?=@j – !), + )' 1#/ 1 )’ )/ !!'#. 4#/ 1 )’ )/ )'/# # )! 365 ! . 4TK3EN – *% !!, + )#' # # 1 !&(' )’ ) 1 / #/ */ * !! !% % ) !( "# #. 4TK3EN, L4
4 E6@j=N H =4@4J – * , #/ 1 / #. 4TK3EN, L4
4 E6@j=N H
PJ6S – * , #/ /1 / #. 4TK ?@ E@ E ? 4T@?4 – # !#/ ( ##. H& !*, + !#'/# , ! * & ) ! #!# ! ( . 493
4T4 4@ E@? – 1 !!'#, & , + / ! 1 #!& !)1 & ) (/ * !!, , / )!#, % !). 4?P E$@ – " # , )%#('/# 1 #!# 1 ) ' (! )1 ), )/ ('/# #/. !1 )# ! (/# # #, ) ', # )('/# & 1, + ) ' " )% !). ## " '/# %/1 % '. 4 P E@?P KE?EN – #% !*#, ) !( '/# )! ## !!'# ) # !) ( !*'(, & )(/# !) ) # !). 4 P EO P 4 – ! )% ! * !!. 4 P E>> ?EqKj – /# * ) ! !!'# )& ) # )* !*. )'/# 1 !#% !!'# % !. 4 KEP> E @EK – 1, !!'# ! / #/ )% *% ! )*. 4 4 – ! ! ! *% !! !% # ) !( *( ! , # * !!. 4 4 EJP E=j> – ' #( !*% , !# '/# ! ! !& ’' !* /- % ) !*. 4 4 6? 4 P>=j> – !*% , + ' ! ! !& ’' !* / ) !*. 4 4 4KK – ! !( ! /# * !! ) !( *( !% #. 4 4 @ – ! !& ! /# * !! ) !( *( !% #. 4 3EHE>P HETPH PPN $E=4?434 JPP qJP@ – #/ #!#/ 1 # #& !!'#, !’ ) ) )( )*'( !#/ 1/ ) ! % "# /#. 4=4? ? 4T $4 – # %, # )# !* ! * !* (, !#) 494
! !!'# ! ! !, + !+' 12 # * )%% !*%% *, ) !# %/. 4=4? HE=4T – (/ #( 1, # # " !) . 4=4? P? 4T $4 – ) ) ! !* !!'#, / )!#/ # !*# * (% &% ", #, #! #!, +).
E=? – # "# ## !!'#. # ((/ #% ! !!'#, # () !1 /1 ) # () !1 ) !#.
E=? 4@4 – # )’ )/ !!'#, + ((/ # !) 1, #/ )#/, ) ) 1 # !# !!'#.
E=? 4 P EO – ) 1 # ) # !% * !!.
P ?=E ?E @=@j 4=4?Q $4 ? – #/ " * !& ( ) * . # #/ # " ! ' ), ! , , #*, )*, # * !* ! ’'.
P P4E 4=4?Q HE=4T? – ) !# # # )# ) ( ) / # (# ) ( !* *. * # )# )%#('/# ! !# .
KPP $E=4?434 ?EqPKN – #!1 !) # 1 )/ # ) ! !!'#. Q)' # ! "# & .
4 E@4?> 4 P@4 $E=4?434 KP?P q – !)' #!/ ! " "# & )’ ) ) ) ! ! !!'#.
4 3 P@ETPKj4=@ – )* !* (, !#) !!'#, + * !' % #! ! (!#% )). /# ' #( / ! (/ ) !!'#).
4 @$PKj Q E P ? – * !!, ' *. 495
4=@>> ( P JEP@>, ?KE=>
?N> 4 j434) E @EK – # # ! # !# !!'#.
4=@>> 4T4 4@> E @EK (==@PJE E=@E
4@4Q E@??) – ! !!'#, + ) /# % !#% )! &. #%% % ! (' # 1, #/ )# )!#, # !#% ! #/ * !*.
4=@> ?@ E@ – # ## !* (, !#) !!'#, + )((/# ! ) # *, !, )*% , !+/, , # +.
4@4E ?E @=@j – # #/ %/ 1 !.
4@4E P KE@4=
4J4q=@j – )' % "#% # !!'#, ! !% % ! # ) !% ) # #/ # / 1 # !1 ! , + !' ) )(.
4P@ (? =4@4) – 1 !, # ! ) # 1%.
4P@ (? =4@)
4=@ – !*, ! 1 , # # !, ) .
4P@ (? =4@) =KE – !*, & ! #, & # #, ) () .
PEKjE =@E?E 4Q4 4=@ – ) / !* #, ) ) !/ #!&# 1%.
PHP ? JE>T@Q ?@ E@ – #% !# !!'#, + ((/# ! * *% ( % * .
PHP ?> E @EK – / # # ! !!'#, "'/# ) # !. ? & (# ! )# ! # !!'#.
P?P=@4?E>
T@4 – )!% ! !!'#, !% "# )1 /# !!'# ). 496
P?P=@?EN – # )! ! *% "# )1 /# !!'#.
Pq 3 – #!#/ )#, !) / !!1 # !) /# !!'# 1 ) !! #( )#-!*#.
& !' "/ !## / !! )#-!*# ) ( # ), #! !!1/ #( !) /# !!'# (# !*, #, ## # . .). & & ) ! .
P>@3 434 E P E – ) * !! ! ) .
PJ@P@ – !1% !!*/ # .
P@ETPKj=@j – ) # !), + )(/ "#/ # #/ % !!'# )& & % "# . )'/# # ! (, #, )*) #/ . !* #(/# !) )/ /# , # /# , /# ) ! )* !* (, !#) !!'#.
P@ETPKj=@j ?KE=434 E @EK – 1 ! (, #, )*) #/ # !. !* #(/# !) )/ /# # ! # /# # ! ) ! )* !* (, !#) !!'#.
P@ETPKj=@j
4 Eq? – 1 ! )* !* , !’ ) ) * )*'( *' !*.
P=@ @ HEN – !# )*%-!#/ "#- ), #! ) # )*% # ! !!'#, % "# ##, ## ! !* +.
P=@ @ HEN T4 3
6J=@?E – ) !1 () !) !!'#.
P=@ @ HEN P @4 =j4O HET4 34?E4=@ – !!'# # )# ) #! , & )%#(# !# ) 1 & # ! ) !!'# . 497
P$E=?EN – ) !# )’ )/ !!'# 1 !#. H% )%#('/# ) ( )& !* #.
H ?EKS@> – ) & ) )/ #! # # / # ( & "# .
H P 4H@> – #/ )/ ! !) # !!'# . #/ #% ) !’ )%, !, ) !/( *( )%# !) !*% !!'#.
H ?P=@>> – #/ "# !*# )%# #*% /# !!'#. ?! &#% #*% /# (/# # #*% ): ) "# # () * !!) ) / # (! )).
H 4JP >> (!!'*/%) – &#/ # #, + !#/ /% ).
H P @> – ' "#% /# !!'# ! % / #/ .
/ ) !+'/# ) )/1 # , % /# .
H P==@PJE@> (HEK\4?>) – #!*"% ) * !! ". % ) #'/# ) !( #"# !" * !!.
H
6Jj> – #/ ) & ! ) !) . 4# !!'*/ ): %, *%% "#%. ?% ) !’ )% ) * !* (, !#) ) )%# /- 1 /#. *%% ) ' !*# )* !* (, !#), )! !!'#. $#% ) ' #" # !!'# ) 1 "# #.
H 4 E@4?> – )'/# #/ , + & )) !!'# )/ ’( ) ! )# )/ !, !+ !!'# ! ! !&. % ) # &/ ! )1 1 "# ). 498
H 4 @$PKN Q E P ? – &#/ # #, ) # ))' , !’ ) ) #* !"/ * !! !* + ) ## " !" * !!. ) !" * !! (' ##% ##% ).
H
4P@> – ' ) ! ) !* # "# . ? !)/ ) ! # #* , &, ) # # #% ! #% ! ! ) # #. ( !* ) ' ) ’( "# ! ! )1/ #+, ) !!)* / 1 ##, & ( 1 ".
H ==@PJE@> – ) ) * , !’ )% ) # * !!; ('/# ) -"*' * !!. =#% ) & #% ) !( #"# !" * !!.
4?E E EO (T q4?P 4@ ?EN E>) – ! #/ *, + ## " ; )&/ #!1 !! !!)*, & !#% )(# .
4 TE?=jQ 4H4 – ## #, + #'/# !*# 1 " # # )’ )/.
4 3 4\P> – 1) * !! ) !1 . 3 1 ' )%#/ (#); 2) #/ !!'# – #/, + !*% !!* )! ) !!'# # % * % .
4 E @EK? – , (/# # # "# #. ! (' *%.
4 P @? – , (/# # # )’ ) . (' 1% *%.
?Pj E @EKHEO – # # , # ) # 1 !.
4NK@ – 1) !% *)%% !& ) ! # , !, - +; 2) ! ) ! ) ! ##. 499
« 4H?4 PN» – )& # # & (#) *. =EEN – ## ) ( !), ##% +), ! !!1 "# # !!'# ) ( )! # !+ #!&#, # ! ). =PKP3 – % !* , ) ), ! ' , + ( ") # !(/ #% " ) ! # ! # )! & % ( # 1), ) ) ! !1 . =P P j4H?EqPE ?E @=@j E @EK – * # #, !% !* , !’ ) ) ! *. =P @$E@ – 1) !# , !#/ #*; 2) !) "# )’ ) & . =KE
4P@ (? =4@) – !*, # !*. =4T?E @=@j
4 O – & 1% " ! " * )*( !*. = K@ – ) *% !* /1 # *% ) #( !!*%# )! *% # *. = K@ H?4 4@> – ) / # *%, ! % # *% &' *( /1 ## ! /#/ 1 *%. =@E?E =4@?EN – !* #, # ) ! # % 1 !. =@E@@> E @EK – !, )"# # !!'# (* #); ('/# ) 1, !!'# (* #) )/ !& *%. =@ @ E E @EK – 1) #!1 & # # !) ! # !; 2) #!1 & # !" * !! !!'#. =T’6@ ?P=@>4O NKj4=@ – #, ), ! , # ’' !/ / 1 #, + )%#((/ # #*%. =T= E E ? 4? EKj=@j – !/#, ! % & ' * !!, ! # % % ! ) !/#/ !1('/# # ( + "# *(& '). 500
= > 3 4\4?> 4@ – # 1 ! !*% (!, #), #*% "# /# !!'#. =JE EJ4 @HEO – &' 1% " )# # " ) !% ! # (, # */). = )* )'/# ! # . @PJ $KNO – !), + )' ) )* ()& !/ #!&#) 1% ! !, &% !# #/ * # / ! !. @P P – !!)* , # * ", ! !( *% ) ( *(. @ & )%#(# #( "(, 1 # " . @ 4 @$PKN Q E P ? – )/ # !" ) !)* )/, + # / ! , * !!, + / !"/. @ E=@3 – #!# & 1 * !! !, !# ! !!'*. @ E=$P E E – *, # # !!'# ! ) & % ##% !). @ E=$P @ – 1) !# ) 1%; 2) ! * !! ) # 1; 3) !) 1% ) ' "# # 1 ) . @ E=E@ – #*/. @ E=E@ – ! ) #. @ E=@ – !*% #!#/% 1% #" /#. @ E=@4?> 434? – , + ' & % ! . @ E@@E ( P PEH> ?P=PKj) – *% !!, + #/ ) #* (#) ! ) # (#) #! ! # % # (# # ). @ P 4?> EEKH – ) ) ) ! ! & !)* )# ) !) !! ! ) ( ) , # * ) !), ) ! ! / ##%, + )(/ ! ).
E?KN HE E=EJ – !# ), #! ! !#/ -/ )!# 501
!!'# ! # * !&. ! )!# (' ) / !/ #, ) )!# !/ ! !#.
E?K=j ?@ E@ – # !!'#, !’ ) ) % ( *%( /#(, # ##/ !!'# !* (, !#). $E@4 3 – !& !!'# #/ )# ) )&( *( #!*) ! (") "# )* ) ( & "# ##. $@?> E @EK – !, !#% * !!. $E= – (/ #( #, + (/ #’' #!( & ) ! " , )! # *) *) 1 ))! )1 , #( ) #*/ # ##!/#. $E=4?E E34=@E
6J=@?E – ) %/1 & !), + )(/ "#% # !!'#, # ! ), ) # !#, ) ) ; '/# # #/ )#. $E=4?E ?4?E3E – #!1 # !) 1 !!'#, ! ) # 1 * !1(/# 1 . ) ) ! !, "# ) ' !!'#, ) , )/1 !) 1, ) 1 – */ # & ! # 1. $E=4?E =@>=@j – !#!&#/ # ) "# & # !) & "# . $E=4?P KE?EN – % !*# F !% ! "# ## !!'# ! "# #. */ ’' ! ' "# /#/ !!'#. $E=4?> EEKH
6J=@?E – ( ! "*', + )(/ "#% # !!'#, # % ! ), ) # !#, ) ) , "# #%#, #, /# +. 502
$E=4?> 4@ 4Kj – *#! /#/ !& + ))! #’' #!( # " )* "# #, ) / "# ) !!)*% ) #( . $E=4?> KP?P q – !)' #!/ # !!'# !) 1. /1( ( !!'# "#'/# ) & !), /1( ( )##'/# "#% &. $E=4?> JPP qJP@ – ' #( ! ! "# !!'# + ) )* !#/ 1/, !’ ) ) " , )! # "# ## !!'#. $E=4?> JPQEHJ
6J=@?E – #!#/ !& & #( !# "# ! !#/ 1/, !’ ) ) " , )! # "# ## !!'# )*'( % 1. $E=4?> 4 – ) "/ ## "# #. $E=4?> K – ! 1 !!'#, + (' & !! !. $E=4?> K – #, ! 1 !!'# # )!#, )1 *, !*( #/ )#/ ) # #/ )#, #/ !#' # 1 #/ )#. $E=4? =@ JP@ – ) " - # # , )%#('/# "# ; ((/ !*, *, "’(#, - +. $E=4? 4P$6@ – !) ("*'), + #(/# #& "# /# !!'# ( #! ) % !*%. ? (/ ! "# "*': ! !#!&# (#), # !, # /#. $E=4? 4=P P – &/ "# #: *% , ) + #, # !, !#% ", "# ! )' ". !# ) /# & * !)/ , !(( ! 1 ## !#. 503
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. 1–39. 117. finance.com.ua. 513
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