Punto de Equilibrio

 

CURSO DOCENTE CICLO

: : :

ECONOMIA MINERA Y VALUACION DE MINAS. ING° ARNALDO RUIZ CASTRO. 2003 – II

ANALISIS MARGINAL El análisis ma!inal""s"n%a/ilia #na $"ami"n%a – "'(n)mi'a +"mi%""s%" al +(,"'%is%a "ali-a "l análisis " #na%&'ni'( "m+"sa ( +(,"'%(*#" m"ian%" análisis s" "s%a/l"'"n l(s si!#i"n%"s "s#l%a(s1 . D"%"m D"%"mina ina "l "s%a( "s%a( "'(n)mi' "'(n)mi'( ( !anan'ias !anan'ias ( +&ias4 +&ias4 " #na "m+"sa "m+"sa a i5""n%"s i5""n%"s ni6"l"s " 6(l#m"n " 6"n%as " l(s /i"n"s ( "'#s(s +(#'i(s. 2. D"%" D"%"m min ina a la "n% "n%a/ a/il ili ia a " la "m+ "m+"s "sa a m"i m"ian an%" %" "l 'ál' 'ál'#l #l( ( " "ll 6( 6(l# l#m" m"n n "  +(#''i)n , "l "s%a/l"'imi"n%( "l +"'i( " '(m"'iali-a'i)n "l +(#'%( "n "s%" 'as( /a7( las '(nsi"a'i(n"s " #n m"'a( " li/" '(m"'iali-a'i)n. En "l 'as( " m"'a( m" 'a(ss "s%in "s%in!i( !i(ss m(n(+)l m(n(+)li'( i'(ss # (li!(+) (li!(+)li'( li'(s4 s4 '(m( '(m( "l +"'i( +"'i( s" "n'#"n% "n'#"n%aa "s%a/l"'i( "s n"'"sai( "ali-a #n análisis "s%a8s%i'( " +(,"''i)n " "s%(s +"'i(s , "s%a/l"'" #n 6(l#m"n " a'#"( '(n l(s +"'i(s as8 "%"mina(s. 3. D"%"m D"%"mina ina la la "n%a/i "n%a/ili lia a má9ima má9ima " " la "m+"s "m+"sa. a. :. D"%" D"%"m min ina' a'i) i)n n " l( l(ss in in! !"s "s(s (s , "! "!" "s( s(ss "n #n sis% sis%"m "maa +lan +lana a " '( '(( (" "na naa ass 'a%"sianas.

 

;   

INGRESOS < RUTOS > >

?"'i( " 6"n%a #ni%ai( Can%ia +(#'ia , 6"nia C(s%( 6aia/l" #ni%ai(

FUNCION DE RENTABILIDAD.-

La 5#n'i)n " "n%a/ilia "s a*#"lla 5#n'i)n *#" "+"s"n%a la "n%a/ilia n"%a " #na "m+"sa "n "la'i)n '(n s#s '(s%(s an#al"s. L(s '(s%(s an#al"s %(%al"s '(s%(s " +(#''i)n +aa "l 'as( " la min"8a4 *#"a "5inia  +(1 F + Vu.Q

D(n" @ "+"s"n%a a l(s '(s%(s 5i7(s V# l(s '(s%(s 6aia/l"s +( #nia , = la 'an%ia  +(#'ia , 6"nia 6"n ia +#"" s" min"al " mina min"al "'#+"a( ( m"%al4. Si '(nsi"am(s a  '(m( la #%ilia #%ilia n"%a  "s i!#al a la i5""n'ia i5""n'ia "n%" l(s l(s in!"s(s  /#%(s ?=4 , l(s '(s%(s %(%al"s %(%al" s '(s%(s " +(#''i)n +(# ''i)n "n "l 'as( " la min"8a4.  ’ = PQ - (F + Vu.Q)

La 5#n'i)n "n%a/ilia *#"a "%"minaa '(m( la #%ilia n"%a s(/" l(s '(s%(s %(%al"s an#al"s "s%a/l"'i(s. PQ - (F + Vu.Q) R = ------------------------------------------- ---  F + Vu.Q u. Q

E7"m+l(1 La #nia +(#'%i6a ?i"ina %i"n" #na +(#''i)n " 22000 TMSD "s%a/l"'i"n( #na  +(#''i)n " 2B 8as +( m"s "l +"'i( a'%#al "l (( "s " US ; .:!. US ; 2B(n-%4 "l '(s%( 5i7( an#al "s " US ; 020000.00 mi"n%as *#" "l '(s%( 6aia/l" "s " US ; 0.F0TMS. 0.F0TMS. La "'#+"a'i)n m"%al!i'a m"%al!i'a ini'ial "s " F0 H mi"n%as *#" la "'#+"a'i)n m"%al!i'a 5inal "s " 0 H "s%a/l"'" la 5#n'i)n "n%a/ilia "l  +(,"'%( ?i"ina si la l", +(m"i( " "9+l(%a'i)n "s "  !TMS. . L", m8nima +a!a/l" LM?4. LM? >  !TM 9 0.F0 9 0.0 > :.32 !TM.

2. ?(#''i)n an#al 'al'#laa ?AC4. ?AC > 22000 TMSD 9 2B iasm"s 9 2 > 00000 TMSA TMSA 3. C(n%"ni( 5in( "l min"al +('"sa( C@?4.

 

C@? > 00000 TMSA 9 :.32 !TM > 2FB2000 !aJ( " (( 5in(. :. In!"s(s /#%(s an#al"s !"n"a(s +( la +(#''i)n ?=4. ?= > 2FB2000 ! aJ( 9 ; 2.22!. > US ; 3:F3KF3B.0BaJ( 3:F3KF3B.0BaJ ( B. R"n%a/ilia R4. 3:F3KF3B.0B – 020000.00  00000 9 0.F04 R >      020000.00  00000 9 0.F04

R = 0.90 = 9.0 !

. ?"'i( #ni%ai( "l min"al " mina. ? > US ; 3:F3KF3B.0B00000 3:F3KF3B.0B 00000 TMS P = US " #.$%&TMS.

?aa 'al'#la la 'an%ia = *#" "/" 6"n" #na "m+"sa al +"'i( #ni%ai( ? +aa al'an-a  #n (/7"%i6( " "n%a/ilia R s" "%"mina "l m(( si!#i"n%"1 ?.= – @ – V#.= > R @  V#.=4   > R@  R.V#.= ?.=  V#.=  R.V#.= > R.@  @ =?  V#   R4 > @   R4   F (' + R) Q = ------------------------------------------ P - Vu(' + R)

......... ....... .. (  )

La "9+"si)n 4 +"mi%" 'al'#la1  

La 'an% 'an%ia ia  = *#" "/" "/" +(#' +(#'i is" s" , 6"n" 6"n"s" s" +aa +aa al'an al'an-a -a #n (/7"%i (/7"%i6( 6( " "n%a/ilia R. La "n%a/ilia *#" s" (/%"ná si "l +"'i( " 6"n%a , la 'an%ia +(#'ia , 6"nia s(n +""%"mina(s.

PUNTO DE EQUILIBRIO.S" "n(mina as8 al ni6"l "n *#" la 5#n'i)n " "n%a/ilia " la "m+"sa "s n#la "s "'i  R>0 "s%( "s *#" l(s in!"s(s /#%(s !"n"a(s s(n "9a'%am"n%" i!#al"s a l(s '(s%(s "  +(#''i)n.

 

Si ""m+l ""m+la-am a-am(s (s R > 0 "n la "9+"si "9+"si)n )n 4 "n'(n%a"m(s la 'an%ia =( *#" "/"  +(#'is" , 6"n"s" " m(( *#" n( s" %"n!an ni +&ias ni !anan'ias #m/al " "n%a/iliaP4. En "l 'as( " la min"8a al 6al( =( s" l" "n(mina explotación mínima del   yacimiento "l mism( *#" ma%"má%i'am"n%" s" 'al'#la s"!n la 5)m#la1

 

F Q = -------------  P - Vu

....... ( )

El "n(mina(s " la 5)m#la 4 s" "n(mina contribución marginal . ?aa "%"mina "l m(n%( "'(n)mi'( "n "l +#n%( " "*#ili/i( s" m#l%i+li'an am/(s %&min(ss " la "'#a'i)n  4 +( ? ?.=( "s "n(mina( 5a'%( "'(n)mi'( '8%i'( ,a *#" s# %&min( 6al( +"is+(n" l(s in!"s(s , "!"s(s !"n"a(s +( la "9+l(%a'i)n m8nima  *#" s(n "9a'%am"n%" i!#al"s.  

?@ ?=( >    ?  V#

  F PQ = ---------------' - Vu&P

 

........ ....... . ( )

El "n(mina( " la "9+"si)n  4 s" l" "n(mina tasa marginal de contribución o tasa del margen bruto. GRAFICO DEL PUNTO DE EQUILIBRIO.  "

  ?.=   CT > @  V   ?.=(  

V > V#.=

  PE    

@

Q =(

RENTABILIDAD MAIMA.Es%a/l" Es% a/l"'ia 'iass las '(nsi" '(nsi"a'i( a'i(n"s n"s "'(n)mi "'(n)mi'as 'as , %&'ni'as %&'ni'as " #n +(,"'% +(,"'%( ( "s n"'"sai n"'"sai( ( "%" "% "mi mina na l(s limi limi%" %"ss má9i má9im( m(ss " "n%a "n%a/il /ili ia a *#" s" +#"" +#"" %"n" %"n" "n #na "m+" "m+"sa sa s#+#"s s#+ #"s%am %am"n% "n%"" "s%( "s%( s" (/%"n (/%"n8 8aa '# '#an an( ( las las 'an%i 'an%ia a"s "s +(#' +(#'ia iass , 6"ni 6"nias as s"an s"an in5ini%as sin *#" s" +(#-'an 'am/i(s " las (%as 6aia/l"s /a7( "s%as '(nsi"a'i(n"s la

"n%a/ilia má9ima RQ s" (/%i"n" "l m(( si!#i"n%"1

 

En la "'#a'i)n 4 '#an( =     ? – V#   R4  0. RQ s" (/%i"n" "s'i/i"n( ? > V#   RQ4 ? > V#  V#.RQ  P R* = ------- - ' ........ ( ) Vu

La 5#n'i)n " "n%a/ilia " #na "m+"sa !á5i'am"n%" +#"" "+"s"n%as" "n%" #n m8nim( 00 H "s "'i la +&ia %(%al " l(s '(s%(s in'#i(s4 , #n má9im( RQ '(n R > 0 "n "l +#n%( " "*#ili/i( =(4.  

R 

 

RQ

   

0 =(

 Q

  

C(n%in#a C(n% in#an( n( '(n "l "7"m+l( "7"m+l( "s%a/l"' "s%a/l"'i( i( " la Mina ?i"ina ?i"ina "ali-a "ali-am(s m(s l(s si!#i"n% si!#i"n%"s "s 'ál'#l(s1 K. E E9+l( 9+l(%a' %a'i)n i)n (/%"n"m(s1

m8nima m8nima

"l ,a'im ,a'imi"n i"n%(. %(. R""m+laR""m+la-an( an( 6al( 6al("s "s n#m&i n#m&i'(s '(s "n 4

=( > 2B:B0.2 TMSaJ(. =( > F::F.F3 TMSD.

F. El 5a'%( "'(n)mi'( '8%i'( l( "%"minam(s " la 5)m#la  41 ?=( > US ; 3::23F2.3:aJ( . La "n%a/ilia má9ima " la "m+"sa "s " 1

 

RQ > 3.FKB > 3F.KB 3 F.KB H