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Aluminum

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Submitted By adaovega
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Pregunta 1.
Usando la información proporcionada sobre aluminio construya y estime la oferta de la
Industria para el aluminio primario.
Dado que cada planta tiene diferente tecnología dependiendo de su antigüedad y cada tecnología produce con un costo variable determinado, consideramos que la oferta total de la industria puede definirse en base al costo variable, ya que en este tipo de industria el precio es definido por el costo. Por lo que se estimo la oferta de la industria para el aluminio usando la siguiente especificación linear:

Q = a + bPE + cPA + dOth + ePpf + fCo +gMA+ hLA + iFR + jGA

Donde Q es la capacidad (tpy), PE el precio de la electricidad ($/kWh), PA el precio de la alúmina ($/t alúmina), Oth es el costo de otras materias primas, Ppf el costo de energía de la planta y combustibles, MA el costo de mantenimiento, FR el costo de fletes ,y GA los gastos generales y administrativos. Los resultados de la regresión son los siguientes:

Regression Analysis R² 0.243 Adjusted R² 0.196 n 157 R 0.493 k 9 Std. Error 105.476 Dep. Var. Capacity (tpy) ANOVA table
Source SS df MS F p-value
Regression 524,369.3834 9 58,263.2648 5.24 3.53E-06
Residual 1,635,389.5142 147 11,125.0987
Total 2,159,758.8976 156

Regression output confidence interval variables coefficients std. error t (df=147) p-value 95% lower 95% upper
Intercept 221.4214 90.8935 2.436 .0160 41.7946 401.0481
Electricity price ($/kWh) -1,999.3728 845.8835 -2.364 .0194 -3,671.0359 -327.7098
Alumina price ($/t Alumina) 0.7489 0.3852 1.944 .0538 -0.0123 1.5101
Other raw materials -0.5990 0.2142 -2.797 .0058 -1.0223 -0.1758
Plant power and fuel -0.5320 1.2667 -0.420 .6751 -3.0354 1.9713
Consumables -0.5917 0.2241 -2.640 .0092 -1.0347 -0.1488
Maintenance 0.4110 0.6108 0.673 .5021 -0.7962 1.6181
Labor -0.3061 0.0882 -3.471 .0007 -0.4804 -0.1318
Freight -1.1275 0.7355 -1.533 .1274 -2.5809 0.3259
General and administrative 0.0883 0.1757 0.502 .6161 -0.2589 0.4354

Conclusiones sobre el cuadro de salida de la regresión:

• Ya que R2=0.243, la ecuación de regresión explica cerca de 24% del total de la variación de la variable dependiente sin embargo un 76% de la variación de Q queda sin explicar.
• Realizando la prueba global al modelo a un nivel de significancia del 5 por ciento obtenemos que,

Dado que :

k = 10 y n= 157
Entonces, k-1 = 9, n-k = 147 grados de libertad

F-distribution df1 = 9 P(lower) P(upper) F df2 = 147 .9500 .0500 1.94

El valor crítico para F para un nivel de significancia de 5% es de 1.94, el valor calculado del estadístico F por la computadora es de 5.24, el cual excede 1.94 por lo que el modelo es estadísticamente significativo.

• Haciendo la prueba de significancia estadística de los parámetros estimados a un nivel de confianza de 5%, lo cual significa que exista un 95% de confianza de que el verdadero valor del parámetro pertenezca a la distribución del parámetro que resulto estimado; dado que el numero de observaciones es de 157 y las variables son 10, los grados de libertad son 147, para el cual nos da un valor critico de t de 1.655.

t-distribution df = 147 P(lower) P(upper) t .9500 .0500 1.655

• Comparando los valores calculados de la razón t para a, b, c, d, f y h correspondientes a las variables PE , PA ,Oth , Ppf y LA respectivamente son superiores a 1.655, por lo que podemos establecer la significancia estadística de dichos estimadores. Aplicando el mismo concepto de análisis, podemos ver que los parámetros estimados e, g, i y j correspondientes a las variables Co, MA, FR y GA no son estadísticamente significativos, pues son menores a 1.655.
• Para estimar la oferta de la industria para el aluminio primario sustituimos los valores de las variables en la regresión estimada, se consideraron aquellas variables que no son significativas ya que en conjunto con las que si lo son ayudan a que el modelo sea mas completo. La regresión estimada es:

Q = 221.42 – 1999.37PE + .7489PA - .5990Oth - .5320Ppf - .5917Co +.4110MA - .3061LA – 1.1275FR + .0883GA

Pregunta 2. ¿Qué determina el precio cuando existe exceso de capacidad?

Una empresa normalmente tiene un intervalo en el que puede fijar el precio. El límite inferior de dicho intervalo son los costos variables, por debajo de los cuales nunca se debe vender. El límite superior lo establece el nivel de demanda por encima del cual no se demanda ningún producto. Cuanto más amplio sea este intervalo mayor libertad tendrá la empresa para fijar sus precios. Cualquier empresa ha de tener en cuenta tres elementos esenciales para fijar sus precios: los costos, la demanda y la competencia. Sin embargo una de las razones que puede motivar la reducción de precios es el exceso de capacidad.
Cuando existe un exceso de capacidad, el precio tiende al punto de equilibrio con los costos variables, por lo tanto el precio es determinado por los costos variables cuando se tiene un exceso de capacidad. Es decir, como este tipo de industria es de proceso continuo, en la cual una vez iniciado el proceso de producción no se tiene flexibilidad de reducir la misma, este tipo de fabricas trabajan a su máxima capacidad instalada lo que resulta en que su curva de oferta es plana en el corto plazo donde todos los costos tienden a ser fijos. Para poder vender su producción (ley de la demanda), las empresas tienden a reducir sus costos para desplazar la demanda al punto de equilibrio de tal forma que la demanda sea igual a la capacidad de producción. Es importante recalcar que mientras el precio cubra los costos variables la empresa se podrá mantener en el negocio en el corto plazo, sin embargo a largo plazo deberá buscar la manera de generar valor agregado en caso contrario está destinada a desaparecer.

Pregunta 3.

Los precios convergen al costo en tiempos de exceso de capacidad. ¿Pero por qué son los precios tan cíclicos?

En un escenario de producción continua, los precios son tan cíclicos por la falta de flexibilidad de las empresas para ajustar su capacidad de producción en el corto plazo, es decir, dada esta limitación, cuando existe exceso de capacidad como se explica en la respuesta 2, los precios tienden a reducirse hasta el punto de equilibrio, manteniéndose así la oferta plana hasta que las empresas puedan ajustar su capacidad de producción en el largo plazo, que en el caso de las empresas de fundición de aluminio es de aproximadamente 4 años, lo que nos lleva a un escenario cíclico en la fijación de precios debido a que el ciclo se inicia de nuevo, ya sea aumentando la capacidad instalada o cerrando plantas, lo cual desplaza la demanda a un nuevo punto de equilibrio.

Pregunta 4.
¿Debería Alusaf construir la planta de Hillside? ¿Tendría caso construir la planta a los precios actuales?

Capital estimado de inversión 1.6 billones $/ton
Precio de venta aluminio $1,110.00
Costo de energía 16% del precio de la tonelada de aluminio
Costos de alúmina y energía 41% precio de la tonelada de aluminio
Capacidad instalada 446,000 ton/ año

Precio de venta aluminio 1,110.00 Costos totales explícitos. Costos de alúmina y energía 202,974,600.00 Costos operación Hillside(tabla b) 165,020,000.00 Costo variable total 367,994,600.00 Costos totales implícitos. Rentabilidad sobre capital (3%)* 48,000,000.00 * Se asume que el costo del dinero en 1994 era del 3%. Costos totales aplicados Costos totales explícitos 367,994,600.00 Costos totales implícitos 48,000,000.00 415,994,600.00 Ganancias económicas 1994 Ingresos por ventas 495,060,000.00 Costos totales aplicados 415,994,600.00 79,065,400.00

Análisis marginal 1993 1994 Capacidad 170,000 466,000 Utilidad $8,600,000.00 $79,065,400.00 Rendimiento marginal $50.59 $169.67 Si debería Alusaf's construir la nueva planta considerando los precios actuales, ya que esto representaría una utilidad anual de $79.0 millones de dólares con un ingreso teniendo un ingreso marginal de más del triple.

Equipo 23.
Calificación: 97
Pregunta 1:
Dada la enorme confusión que se generó en el período asignado para la solución de este caso con respecto a la estimación de la curva de oferta, solo me queda dejarles el siguiente instructivo para la solución de la estimación de la curva de oferta para la industria del aluminio (dado que los paquetes econométricos no nos arrojan un coeficiente para el precio si consideramos un mismo precio para todas las industrias). Tómenlo en consideración para cuando deseen hacer una estimación en sus empresas y tengan una problemática similar.
Para resolver la primer pregunta del caso Harvard: Aluminium Smelting in South Africa: Alusaf´s Hillside Project, en donde nos piden estimar una curva de oferta para la industria del aluminio, debemos considerar lo siguiente:
1. Nos piden estimar la curva de oferta de aluminio o bien la función de oferta del aluminio para toda la industria.
2. Para estimarla debemos considerar una variable dependiente: cantidad ofrecida de aluminio o bien si no contamos con esta variable, como es nuestro caso, utilizamos una variable proxy de esta cantidad, que para nosotros será la capacidad instalada.
3. Las variables independientes necesarias para estimar la función de oferta serán: todos los costos variables que tenga la industria, en nuestro caso todos los costos variables que tenga cada empresa (el valor esperado para el coeficiente de estas variables debe ser negativo), y el precio por tonelada del aluminio (el valor esperado para el coeficiente de esta variable debe ser positivo) .
4. En el archivo aluminio.xls, tenemos que todos los costos están expresados en $/ton, lo que significa que todos los costos presentados en el archivo son variables y por lo tanto todos deben ser considerados.
5. Como necesitamos considerar el precio por tonelada de aluminio también para que nuestra estimación sea verdaderamente una función de oferta, y el archivo aluminio.xls no presenta un precio tal cual, debemos recurrir al artículo para indagar con respecto al precio o buscar una variable proxy de el mismo.
a. En el artículo se menciona que el precio a principios de 1994 se había mantenido en de 1100 dólares por tonelada, por lo que podemos indagar que en 1993, el precio del aluminio era también de 110 dólares la tonelada, sin embargo si ponemos este precio (el mismo) para todas las fundidoras, ningún paquete econométrico te dará un resultado estimado para el coeficiente que acompaña el precio, pues simplemente lo eliminará del análisis para evitar problemas de singularidad. Entonces debemos buscar una variable proxy para el precio.
b. En el artículo se menciona que aproximadamente la mitad de las fundidoras de aluminio del mundo realizan contratos con los proveedores de electricidad en los que se acuerda atar el precio del kw por tonelada al precio del aluminio por tonelada, pero también nos dice que estos acuerdos se complican con fórmulas que establecen precios techo y precios piso, por lo que podemos ver precios de la electricidad en kw por tonelada que no reflejan en realidad la variación en el precio que se carga en realidad por tonelada de aluminio, por lo tanto los costos de la electricidad medidos en kw por tonelada no pueden ser usados como variable proxy del precio del aluminio por tonelada.
c. En el artículo también se menciona que una práctica común entre las fundidoras de aluminio es realizar contratos con los proveedores de óxido de aluminio (alumina) en los que se ata el precio de la tonelada de óxido de aluminio al precio de la tonelada de aluminio, es decir: si sube el precio de la tonelada de aluminio, pues las fundidoras de aluminio le pagan un precio mayor al proveedor de óxido de aluminio y viceversa. Además nos dice el artículo que aproximadamente la mitad de las fundidoras del mundo realiza este tipo de contratos. i. Entonces vamos a suponer que el precio de la tonelada de óxido de aluminio (Pal) suba por causa del mercado, pero el precio de la tonelada de aluminio (P) se quede sin cambio o baje. En este caso, los proveedores de óxido de aluminio estarán obligados a vender a el precio pactado su producto (que será menor al de mercado) a aquellos con los que haya pactado acuerdos, pero a los que no tenga acuerdos pactados, les buscará vender al precio de mercado, pero dado que el precio de mercado aumenta para un insumo, la oferta de aluminio de parte de las fundidoras que no tienen este tipo de contratos se reduce y por lo tanto se reduce la demanda de óxido de aluminio lo que provoca que el precio del óxido de aluminio por tonelada caiga hasta igualar el precio al que le venden el óxido de aluminio a las fundidoras con las que tienen contrato. ii. Un raciocinio similar podemos utilizar si suponemos que el precio del aluminio aumenta. iii. Por lo analizado en i y ii podemos darnos cuenta que el precio por tonelada del óxido de aluminio se moverá de la mano con el precio por tonelada de aluminio, lo que nos indica que podemos usar el precio por tonelada del óxido de aluminio como variable proxy del precio por tonelada de aluminio con el fin de poder introducir esta variable a un modelo econométrico y que este modelo econométrico represente la función de oferta y pueda ser estimado.
6. En conclusión, estimaremos la función de oferta usando como variable dependiente la capacidad, y como independientes todos los costos variables presentados en el archivo aluminio.xls, pero al costo variable llamado Total Alumina Cost (que representa el costo o precio por tonelada del óxido de aluminio), lo vamos a considerar como si fuera una variable proxy del precio por tonelada de aluminio, por lo anteriormente explicado. El valor teórico esperado para esta variable debe ser positivo.
7. Entonces vamos a tener las siguientes variables:
a. Variables Dependientes: i. Capacity : Variable proxy de la cantidad ofrecida .
b. Variables Independientes: i. Total Electricity Cost ii. Total Alumina Cost (que será la var. Proxy del precio por ton. de aluminio) iii. Other raw materials iv. Plant power and fuel v. Consumables vi. Maintenance vii. Labor viii. Freight ix. General and administrative.
8. Se utiliza el paquete econométrico Stata 10.0
9. Al correr la REGRESION 1 (ver archivo note-pad anexo), observamos que al 10% de significancia las variables Plant power and fuel, Maintenance, Freight y General and administrative no son significativas, entonces las sacamos de la estimación. El signo esperado es correcto para todos excepto para total Total electricity cost, presumiblemente porque se encuentra correlacionado con Total alumina cost. La R cuadrada ajustada es de 0.1981 y la de F es 5.28.
10. Hacemos una prueba de correlación (PRUEBA DE CORRELACION- ver archivo note-pad) entre las variables dependientes y observamos que las variables más altamente correlacionadas son Other raw materials y Total electricity cost (0.4234),además de Freight y Total Alumina cost (0.4073), Freight y Labor (0.4444) y Total alumina cost y Labor (-0.3053), pero como vamos a sacar Other Raw materials, del análisis no esperamos tener más problemas con total electricity costs y esperaríamos que el signo de Total electricity cost se corrigiera y fuera significativo. Con respecto a las otras variables correlacionadas, nos interesa dejar Total Alumina costs por ser la variable proxy del precio, así que podríamos optar por retirar también Freight y Labor o solo una de las dos, pero como Freight no fue significativa ni al 10% de confianza la quitamos y dejamos Labor.
11. Volvemos a correr sin estas variables que sacamos del análisis (REGRESION 2-ver archivo note-pad). Aquí podemos ver que ahora Total Alumina Cost ya no es significativo ni al 10% pero Total elctricity cost ahora tiene el signo esperado y es significativo. Pero dijimos que Labor presentaba correlación con Total Alumina Cost, pero Total alumina cost nos interesa. La R cuadrada ajustada es de 0.2032, una ganancia con respecto a la REGRESION 1 y la de F es 8.96.
12. Si quitamos labor del análisis (REGRESION 3-ver archivo note-pad) obtendríamos que ahora todas las variables que quedaron son significativas y presentan el signo correcto incluyendo a la variable proxy del precio: Total Alumina Cost. Sin embargo la R cuadrada ajustada se reduce a 0.1602, y la F estimada es de 8.44.
13. Entonces, el mejor modelo que tenemos para estimar la función de oferta es la REGRESION 2- Ver archivo note-pad anexo, en la que queda como variable independiente capacity, y como independientes: Total electricity cost, Total alumina cost, Other raw materials , Consumables y Labor, todas significativas al 5% y con el signo correcto a excepción de Total Alumina Cost que utilizamos como variable proxy del precio por tonelada de aluminio, que presenta el signo correcto pero ya no es significativa ni al 10%.
14. Dejaremos la variable proxy en la función de oferta a pesar de no ser significativa pues solo si tenemos el precio de la tonelada del aluminio (o una variable proxy de éste) podremos decir que es una función de oferta. Sin embargo lo anterior sugiere que la cantidad ofrecida no reacciona ante cambios en precio lo que indicaría que la industria del aluminio opera en competencia perfecta y el precio de la tonelada del aluminio iguala al costo marginal de esta industria.
Pregunta 2.
Los precios son determinados siempre por las fuerzas de oferta y demanda. Sin embargo, cuando se tiene exceso de capacidad, el precio tiende a los costos variables que presente la industria. Pregunta 3.
Los precios del aluminio fluctúan por muchas razones, tales como cambios en los precios de los insumos, pero sobre todo por cambios abruptos en la demanda. Pregunta 4.
El seguir construyendo exceso de capacidad sirve para dar señales a los posibles competidores de que no entren a la industria. Lo que debemos ver es si la empresa es capaz de cubrir sus costos variables, cuando ofrece su producto, lo que intrínsecamente nos dice que debemos estimar o conocer la demanda de aluminio. De ser así, el exceso de capacidad le permitirá sacar provecho de las variaciones cíclicas a la alza del precio del aluminio.

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