2012 EVALUACIÓN DE PROYECTOS DE OBRAS CIVILES FINAL
EDGAR MORENO
UNIVERSIDAD TECNOLÓGICA DE PANAMÁ 31/10/2012
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UNIVERSIDAD TECNOLÓGICA DE PANAMÁ FACULTAD DE INGENIERÍA CIVIL DEPARTAMENTO DE MECANICA ESTRUCTURAL Y CONSTRUCCION
LICENCIATURA EN INGENIERÍA CIVIL
EVAL UACI ON DE PROY PROYECTO ECTOS S DE OBRAS CI VI L ES EDGAR ORLANDO MORENO MARTINEZ C.I.P.:8-856-540 PROFESORA: RUBIELA DÍAZ DE QUINTERO II SEMESTRE 2012
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CONTENIDO
o
Plan de la asignatura
o
Metas del curso
o
Material de apoyo
o
Evaluación de aprendizajes
o
Investigaciones
o
Practicas
o
Proyecto individual o grupal
o
Tareas
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PLAN DE LA ASIGNATURA UNIVERSIDAD TECNOLÓGICA DE PANAMÁ CURSO DE EVALUACIÓN DE PROYECTOS DE CONTENIDO OBRAS CIVILES FACILITADORA RUBIELA DÍAZ DE QUINTERO. HORARIO DE ATENCIÓN A ESTUDIANTES VIERNES DE 8 AM A 12 M. COORDINADOR DEL CURSO CURSO POR LA FIC INGENIERO JAVIER NAVARRO MSC. UNIVERSIDAD TECNOLÓGICA DE PANAMÁ FACULTAD DE INGENIERÍA CIVIL LICENCIATURA EN INGENIERIA INGENIERIA CIVIL DEPARTAMENTO DE MECANICA ESTRUCTURAL Y CONSTRUCCION ASIGNATURA: EVALUACIÓN DE PROYECTOS DE OBRAS CIVILES PREREQUISITOS: SISTEMAS CONTABLES CÓDIGO: 8034 HORAS SDE CLASES: CLASES: 3 CRÉDITOS: 3 OBJETIVOS DEL CURSO
Conocer las etapas y características de los principales proyectos de obras civiles. identificar los costos y beneficios asociados a los proyectos de obras civiles. Aplicar criterios de decisión para la evaluación de proyectos de obras civiles: Valor Presente Neto, Valor Anual, Tasa Interna de Retorno, Razón Beneficio Costo.
PROGRAMA DEL CURSO I. INTRODUCCIÓN (6 horas) 1.1 Conceptos de la Evaluación de Proyectos: ¿Qué es un proyecto?, necesidad de los proyectos de obras civiles, tipos de proyectos de obras civiles. Los proyectos como fuente de costos y beneficios durante un horizonte de evaluación. 1.2 Introducción a la Evaluación de un Proyecto: (i) identificación de costos y beneficios que son atribuibles a un proyecto (las situaciones "con" y "sin" proyecto). II. FASES DEL ESTUDIO DE PROYECTOS (6 Horas) 2.1 El Estudio de Mercado: Concepto, Objetivo y Generalidades. 2.2 El Estudio Técnico: Concepto, Objetivo y Generalidades. 2.3 El Estudio Financiero: Concepto, Objetivo y Generalidades. III.- FLUJO DE CAJA DE PROYECTOS DE OBRAS CIVILES (21 Horas) 3.1 Construcción del Flujo de Caja 3.1 .1 Proyectos de carretera y/o sistemas de transporte 3.1 .2 Equipo de construcción y otros 3.1 .3 Edificaciones 3.1 .4 Otros proyectos
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IV. CRITERIOS DE DECISIÓN (12 horas) 4.1 Diferentes Costos para Diferentes Decisiones. 4.2 La Tasa Interna de Retorno (TIR). 4.3 El Valor Anual Equivalente (VAE) 4.4 La Razón Beneficio/Costo (VABA/AC) 4.5 El Período de Recuperación
OTRAS APLICACIONES DE LOS CRITERIOS (3 Horas) ¿Comprar o arrendar? ¿Comprar al contado o al crédito? Vida útil económica y remplazos. Momento óptimo para iniciar un proyecto. Orden Prioritario de proyectos: independientes,
BIBLIOGRAFÍA
1. 2. 3. 4. 5. 6. 7.
Blank, Leland Tarquin, Anthony; Ingeniería Económica, McGrawH¡ll, 2006 Ingeniería Económica De Degarmo Collier, C., Ledbetter, W. Engineering Cost Analysis, 1992. Engineering Economics'and Cost Analysis, prentice Hall, 1999. Gabriel; Baca Urbina Evaluación dé proyectos, McGrawHiil, . Rosales Posas, Ramón; Formulación y Evaluación de proyectos, Ernesto R. Fontaine, Evaluación Social de Proyectos,
EVALUACIÓN SUGERIDA Pruebas Parciales (3 mín.) Asistencia, Asistencia, Tareas y Controles Controles Examen Semestral (Proyecto Final) Actualizado Actualizado 2010
45% 15% 40%
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METAS DEL CURSO
Todas las personas tienen proyectos en la vida. Cuando nos nace la idea de realizar un proyecto, en ocasiones parece un sueño, pero aunque no conocemos los métodos ni las técnicas de evaluación, lo esencial es que tenemos una idea básica, que son un buen punto de partida. En este curso mi meta será aprovechar al máximo este tiempo; aprender, analizar y enfocarme en conocer sobre el tema de Evaluación de Proyectos de Obras Civiles; que es un tema nuevo e interesante en mi preparación como futuro Ingeniero Civil. Aprender los pasos para formular un proyecto, desde su origen hasta la realización misma del proyecto y ejecución. El comprender el ¿porqué? de un proyecto y su clasificación de acuerdo a la necesidad y solución del problema. Aprender a elaborar proyectos en forma fácil y de manera exitosa; poniendo en práctica todos los conocimientos que ha de adquirir en este curso, tanto en administrar los recursos físicos, como los recursos económicos; sabiendo que lo esencial para el éxito de la ingeniería es la factibilidad económica, en cuanto a crear y ejecutar un proyecto se refiere.
Cuanto más alto coloque el hombre su meta, tanto más crecerá.
“
”
Friedrich Von Schiller.
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MATERIAL DE APOYO
Flórez Uribe, Juan Antonio, Matemáticas Financieras Empresariales , 2a. edición; Ediciones Ecoe, Ecoe, Colombia http://www.virtual.unal.edu.co/cursos/economicas/2006862/
LA GRAN ENCICLOPEDIA DE ECONOMIA. Leland Blank, Tarquin Anthony. INGENIERÍA ECONOMICA, quinta edición, McGraw Hill. Cap.1-cap 8 Paz, Néstor Oscar, (2007) Contabilidad General, Editorial Mac Graw Hill
ING. CASTRO ORDOÑEZ, José M. Apuntes de la Materia: Preparación y evaluación de Proyectos I y II. Semestre I/2004. Gabriel; Baca Urbina Evaluación dé proyectos, McGrawHiil, Rosales Posas, Ramón; Formulación y Evaluación de proyectos,
http://www.slideshare.net/guestaaf1b8/la-matriz-de-marco-logico Metodología
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E va vall u ac acii ón de apr apre en di dizzaj ajees
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CORRECION DEL PARCIAL #1 I-PARTE 1- ¿Qué es un proyecto? Un proyecto es la realización de una idea que surge como consecuencia de las necesidades necesidades de la población y el cual se basa en un conjunto de pasos que llevan al aprovechamiento máximo de los recursos disponibles y sobre todo de la parte económica disponible. 2- ¿Cómo surgen las ideas de un proyecto? La idea de un proyecto surge por necesidad que necesita como: o Crear o modificar un producto o Hacer un producto novedoso o Servicio para obtener ganancia 3- ¿Qué importancia tienen los proyectos de obras civiles en el desarrollo económico y social del país? La importancia que tienen los proyectos de obras civiles en el desarrollo económico y social del país son creados con el fin de mejorar o beneficiar a la población que necesita de ese producto o servicio a generar. Y de igual forma hacer o tener en cuenta que lo seque se haga genere buenas ganancias e ingresos al país de esa manera contribuir al desarrollo social y económico del país. 4- Defina el concepto de costo inicial y porque puede ser un factor limitante en el éxito de un proyecto de ingeniería civil. Costo inicial es el presupuesto o gastos que debes tener en cuenta al iniciar una empresa
. Puede ser un factor limitante en las actividades de ingeniería porque con ese presupuesto y en base a lo que se diga es que se debe planificar y en ocasiones tiende a pasarse este presupuesto y si se pasa por lo general no será remunerado. Como sabemos un factor limitante es un factor que obstaculiza el camino hacia la obtención de los objetivos.
5- Explique cómo se relacionan los conceptos de economía de intercambio y de mercado La economía de intercambio es el proceso de mutuo interés, entre los participantes, en el que el consumidor desea desea el servicio/ producto producto que le ofrece el productor a cambio de algo que satisfaga a ambos miembros. Por su parte el mercado se relaciona en común en la economía de intercambio, porque porque para que el productor genere ese deseo en el consumidor debe obtener ese producto/ servicio debe realizar un análisis de
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Tamaño del proyecto
3
Definición del producto o servicio
Parte del estudio financiero
5
Justificación
Beneficiarios del proyecto
2
Contenido de la identificación de proyecto
Bienes o servicios que se desea producir con el proyecto
4
Tiene por objetivo estudiar la factibilidad de un proyecto desde el punto de vista financiero.
Resuelva el siguiente problema siguiendo los lineamientos discutidos en clases. Una empresa constructora analiza una situación de fabricar o comprar un adorno de madera que está utilizando residenciales. Opción A: comprar $10 000 piezas por años a un precio fijo de $8.50 cada uno. El flete asciende $2500 Opción B: construir los $10 000 adornos por año: los costos de material directo son $5.00, mano de obra directa $2.15. Los costos fijos relacionados con la actividad ascienden a $4500 Que ventajas y desventajas representa la mejor opción desde el punto de vista de costos. Opción A (comprar) Opción B (construir) Comprar = 10000 piezas/año Construir= 10000 piezas/ año Precio = $ 8.50/ pieza Costo = material + mano de obra Flete = $2500.00 Costo = $5.00 + $2.15 = $7.15 Costo fijo = $4500.00 Precio total = ($8.50/pieza) ($8.50/pieza) * (10000 piezas) Precio total = 85000.00 Costo = ($7.15/ pieza) * (10000 piezas) Costo= $71500.00 Precio + flete= costo total $ 85000.00 + 2500.00 = costo total Costo total = costo fijo + costo $87 500.00 = costo total Costo total = $4500.00 + $ 71500.00 Costo total = $76 000.00
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Con el cuadro que se presenta a continuación resuelva las preguntas a y b. Maquina A
Maquina B
Inversión de capital inicial
$35000.00
$150000
Piezas producidas / año
10000
10000
Costo de mano de obra / hora
$16
$20
Tiempo de fabricación
10 minutos
20 minutos
Costo de mantenimiento/a mantenimiento/año ño
$1000
$3000
a) Que maquina produce el costo unitario mas bajo b) Si el costo de trabajo puede reducirse a la mitad con el uso de empleados a tiempo parcial. Que maquina recomendaría c) Que otros elementos además de los costos consideraría para efectos de tomar una decisión sobre que maquina adquirir.
Máquina A $35000.00 + $16.00+$1000.00= $36016.00 $35000.00 + $1000.00= $36000.00 Máquina B Costo= $150000.00+ $20.00+ $3000.0= $153020.00
La maquina A produce el costo unitario unitario mas bajo con por maquina $ 36000.00 La maquina A porque posee el costo de trabajo o de mano de obra mucho menor que la maquina B En base a otros elementos puede optarse por escoger, según El tiempo de fabricación La inversión inicial
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CORRECION DEL PARCIAL #2 I-PARTE 1. Que es interés Es un valor que se calcula en base al costo económico económico usado y varía según la vida útil del mismo, el cual varia de año a año 2. Que es equivalencia Se refiere al proceso en el que se evalúa una cantidad económica económica en procesos iguales de periodo. 3. Diferencia entre interés simple e interés compuesto Interés simple: es el analisis del interés pero usando el valor real/ principal del inicio en el periodo. Interés compuesto: es el analisis del interés pero usando el valor acumulado en cada periodo hasta el año de vida útil. 4. Diferencia entre interés nominal e interés efectivo Interés nominal: es el tanto por ciento generado o acordado por un prestamista y el tomador del préstamo en concepto de interés , que el que devuelve el préstamo deberá agregar al capital devuelto. Interés efectivo: es aquella renta que realmente se cobra o se paga finiquita en el contrato de crédito. 5. Que es un gradiente Es una cantidad que aumenta de manera igual en distintos periodos de interés de la vida útil de un proyecto. 6. Pasos para evaluar proyectos con vida perpetua Realizar un diagrama donde los pagos respectivas son periodos
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2. Construya el diagrama de flujo de caja para el siguiente flujo: año
Monto ($)
0
$800
1
1000
2
1000
3
1100
4
1200
5
1300
6
1400
7
1500
8
1600
9
1700
10
1800
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Ao = -800 (0.1 (1+ 0.1) 10 / (0.1 +1) 10 -1) = -130.19 A1-2 = -1735.50 (0.1 (1+ 0.1) 10 / (0.1 +1)10 -1) = -282.12 A3-10= -6144.73 (0.1 (1+ 0.1) 10 / (0.1 +1)10 -1) = -1000.03 ATOTAL = -130.19 + -282.12 + -1000.03 = - 1412.34
3. Un proyecto de obras civiles tiene una inversión inicial de $100000.00 y una vida útil de 10 años con un VS de $20500.00. los costos anuales de funcionamiento funcionam iento ascienden a $8000.00. En el año 5 se hará un mantenimiento por un monto de $20000.00 (durante este año el proyecto no estará en servicio). Si la tasa de interés es del 15% cual es el valor presente de este proyecto. Construya el diagrama de flujo de caja y encuentre el valor presente. 20500 0
1
2
3
4
5
8000 100000
6
7
8
9
10
8000 20000
VP = P0 +PA + PF 5)( P/F, 15%, 5) VP = 100000 + 8000 (P/A, 15%, 4) +20000 ( P/F, 15%, 5) + 8000 (P/A, 15%, 5)(P/F,
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DISEÑO H
8000 326000
VP = 325000 + 8000 (P/A, 15%, 14) +42000 (P/F, 15%, 7) + 42000 (P/F, 15%, 14) VP = 326000 + 8000 (5. 7245) + 42000 (0.1413) + 42000 (0.3759) VP = 393 518.40
8000 42000
42000
A = P/I A = 393 518.40/ 15 % A = $ 59 027.76
5. Una empresa debe elegir entre dos propuestas para la compra de una grúa a una tasa del 12% anual Modelo A
Modelo B
Inversión
250000.00
370000
Gastos anuales
22000
8000
VS
100000
125000
Vida útil
15 años
18 años
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MODELO B I= 12% 0
125000
125000
125000
125000
125000
18
36
54
72
90
8000 370000
8000 370000
8000 370000
8000 370000
8000 370000
PT = PO +PF +PA PT = 370000 + 370000 (P/F, 12%, 18) + 370000 (P/F, 12%, 36) + 370000 (P/F, 12%, 54) + 370000 (P/F, 12%, 72) + 8000 (P/A, 12%, 90) – 125000 (P/F, 12%, 18) – 125000 (P/F, 12%, 36) – 125000 (P/F, 12%, 54) – 125000 (P/F, 12%,72 ) – 125000 (P/F, 12%, 90)
PT = 370000 + 370000 (0.1300) + 370000 (0.016910295) + 370000 (0.002199) + 370000 (0.00028596) + 8000 (0.000037185) – 125000 (0.1300) – 125000 (0.016910295) – 125000 (0.002199) – 125000 (0.00028596 ( 0.00028596)) – 125000 (0.000037185) (0.000037185)
PT = 370000 + 55276.54 -18679.04
125000
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S E L I V I C S A R B
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I N VE STI GA GACI CI ON N ° 1 CONCEPTOS GEN GEN ERAL ES SOBRE PROYECTO 1) ¿Qu ¿Qué ées proyec pr oyecto? to?
El término proyecto es el plan prospectivo de una unidad de acción capaz de materializarse algún aspecto del desarrollo económico y social. (ILPES, 1985). Es una respuesta planificada para invertir en forma eficiente más recursos con el fin de obtener una solución a un problema o necesidad. (UNESCO, 1999). En conclusión un proyecto es la acción encaminada a lograr objetivos que implican la utilización y aplicación de un conjunto de recursos en un periodo, con el propósito fundamental de satisfacer una necesidad humana.
2) ¿Cómo ¿Cómo se puede pu eden n clasif clasi f i car l os proyec pr oyectos? tos?
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etapas o fases del ciclo del proyecto, a saber: pre-inversión, promoción, negociación y financiamiento, diseño, inversión y operación. Sin embargo, por considerar que hay etapas que pueden sintetizarse en una sola, se resumen en (3) tres etapas a continuación: 1. Etapa de pre-inversión o estudio: la forman cuatro sub-etapas: idea, perfil, estudio de pre-factibilidad y estudio de factibilidad. Los estudios preliminares en esta etapa sirven de base para investigar todos los aspectos concernientes al proyecto, elementos elementos y formas de las que consta la inversión que se va a llevar a cabo. 2. Etapa de inversión o ejecución: identifica tres sub-etapas: la planificación de la ejecución y diseño definitivo, negociaciones, tramites, y contratos y la propia ejecución. Durante estas sub-etapas se elaboran loa programas para la realización y determinación de cada actividad. 3. Etapa de operación o funcionamiento: es aquella en que se inicia la
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las actividades, controlar los progresos del proyecto de modo que se ejecute de acuerdo con los limites y parámetros establecidos. 5) ¿Cu ¿Cuá ál es son l os docume docum entos nt os que sur gen en cada etapa de f ormu or mu l aci ació ón ?
Los documentos que surgen en cada etapa de formulación son: Estudio de Prefactibilidad (Estudio de Alternativas): El objeto de la Prefactibilidad consiste en progresar sobre el análisis de las alternativas identificadas, reduciendo la incertidumbre y mejorando la calidad de la información. Se busca seleccionar la alternativa. Aquí se profundizan los estudios de mercado, técnico, legal, administrativo, socioeconómico y financiero por las alternativas aprobadas en la fase anterior. A este nivel, el proyectista debe procurar homogeneidad en los estudios de todas las alternativas, evitando concentrarse en la que él considere mejor. En esta fase suele efectuarse la declaración de efectos ambientales. Con base en los
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c) Estudio de la organización: es de gran relevancia dejar previstos algunos aspectos administrativos, los cuales están relacionados con la planificación, programación y organización del proyecto durante las etapas de ejecución o inversión y la de operación. d) Estudio financiero: considera elementos como el análisis de rentabilidad que nos permite visualizar si el proyecto puede generar utilidades durante su vida útil. 7) ¿Cómo ¿Cómo se r elacion elaci onan an los pr oye oyectos ctos con l a estr estr ategia de des desar arrr oll ol l o de un país o región?
La mayoría de los proyectos de desarrollo comunitario surgen de la inquietud de los investigadores, del mismo Estado a través de instancias gubernamentales y del interés de algunas organizaciones por lograr mejores condiciones de vida para las personas. Los modelos y proyectos de desarrollo nacional son diseñados con una visión macroeconómica. Una estrategia (o plan) de participación define los procesos
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INVESTIGACIÓN N° 2 MATRIZ DE MARCO LÓGICO El marco lógico es una herramienta que ayuda a diseñadores de proyectos a una
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Componentes de la matriz de marco lógico Pasos para la formulación del marco lógico (ML) son:
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Análisis de involucrados: 1. Hacer una lista de todos los tipos de participantes (personas, intermediarios, grupos, empresas, instituciones, proyectos, y otros) 2. ¿el grupo puede subdividirse? 3. Caracterizar y analizar cada participante
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Como se elabora el Árbol de Objetivos: Paso 1. Formular todas las condiciones negativas del árbol de Problemas en forma de condiciones positivas que son deseadas y realizables en la práctica. Paso 2. Examinar las relaciones “medios – fines” establecidas para garantizar la
lógica e integridad del esquema.
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9. ¿Qué nos indica el período de recuperación? Indica el número de períodos en el que se recuperara la inversión del proyecto en función de los flujos de caja esperados.
10.¿Qué 10. ¿Qué inconvenientes presenta este indicador? -
En algunos casos se calcula sin tomar en cuenta el valor del dinero en el tiempo. No tiene en cuenta que sucede después que se recupera la inversión.
11. Índice de rentabilidad El índice de rentabilidad indica por cada dólar que se invierte cuando la utilidad genera: IR > 1 recuperar lo invertido IR = 1 es indiferente IR < 1 no se recupera lo que se invirtió en el proyecto
Tarea # 4 Relación beneficio costo para evaluar proyectos Los trabajos públicos deben justificarse sobre una base económica para garantizar que la sociedad obtenga el rendimiento máximo del dinero de los gravámenes que paga. Un ingeniero que trabaje en proyectos quedara sujeto a la ética profesional y tendrá que hacer su mejor esfuerzo para ello se apoya en una relación beneficio costo, esta permanece como un método popular para evaluar el rendimiento financiero de los proyectos públicos, es un método el cual permite tomar en cuenta el valor en el tiempo en el ritmo de los flujos de efectivo ( o ganancias) que ocurren después del arranque del proyecto.
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EVALUACIÓN DE PROYECTOS DE OBRAS CIVILES
LABORATORIOS
Cuestionario 1 “Ingeniería Económica” Cuestionario 2 “Ingeniería Económica” Cuesstitionar Cue onarii o 1 1 “Ingeniería Económica”
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LABORATORIO N°1 CUESTIONARIO 1. Explique la relación entre ingeniería y ciencia La ingeniería no es una ciencia, sino una aplicación de la ciencia. La ciencia es la base sobre la cual se sustenta el ingeniero para el avance de la humanidad. El ingeniero tiene como propósito la utilización de este conocimiento en situaciones particulares para producir bienes y servicios; conocimiento que le es fundamental para construir estructuras, sistemas y procesos. 2. Explique la naturaleza biambiental de la ingeniería La naturaleza biambiental son aquellas situaciones de la vida diaria en las cuales cualquier ingeniero debe estar preparado para resolver según leyes y conocimientos económicos.
3. ¿En que consiste consiste la eficiencia física física y la eficiencia económica? ¿cual es la relación y cual es su diferencia? La eficiencia física consiste en una actividad productora que tiene su razón de ser en la satisfacción de los deseos humanos. Su objetivo es alcanzar el mayor resultado final por unidad de recursos gastados. La eficiencia económica, por su parte, consta de igual forma de satisfacer los deseos del hombre y al hacerlo hace un lado cierta utilidades con el fin de obtener otras que el valora mejor, este es un proceso económico cuyo objetivo es maximizar la eficiencia. 4. ¿Cuáles son los pasos del proceso de ingeniería? En el proceso de ingeniería desde el momento momento en que se reconoce una necesidad necesidad hasta aquel en el cual se satisfacen, satisfacen, puede dividirse en los siguientes pasos: I. Determinación de objetivos II. Identificación de factores estratégicos III. Determinación de los medios IV. Evaluación de los propuestas hechas por los ingenieros V. Asesoría en el proceso de toma de decisiones 5. ¿Cuáles son los pasos de la ingeniería económica? El proceso de ingeniería económica implica un plan lógico, plan que describe los siguientes pasos: I. Paso creativo II. Paso de definición III. Paso de conversión IV. Paso de decisión
6. Resolver cuestionario PREGUNTAS PÁG 16 - 17 1. Compare el papel del ingeniero con el del científico El propósito del científico es agregar algo al cuerpo de conocimientos sistemáticos acumulados por la humanidad y descubrir leyes universales de comportamiento. El
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la eficiencia física consiste en alcanzar el mayor resultado final por unidad de recursos gastados y la eficiencia económica consiste en buscar continuamente la manera de satisfacer sus deseos y al hacerlos se hace a un lado ciertas utilidades con el fin de obtener otras que se valoran mejor; la eficiencia física se expresa en términos de productos (salida) divididos por insumos (entradas) al igual que la eficiencia económica que se expresa en resultados (salida) divididas por unidades económicas de insumos (entradas), pero no se diferencian en que la eficiencia física no es posible obtener valores por encima del 100% y las eficiencias económicas si pueden exceder del 100%, y, es mas, deben excederlo para que las empresas económicas sean exitosas.
3. De varios ejemplos de productos que hubieran sido técnicamente factibles pero que hubieran tenido muy poco merito económico. Los automóviles funcionales a base de agua serian muy útiles pero el riesgo seria que no serian muy vendidos y que podrían acabar con las reservas de agua en el mundo. Las casas con paneles solares las cuales serian también excelentes por que seria una manera de ayudar a disminuir la contaminación del medio, sin embargo tendría muy poca demanda puesto que casas así requieren de mucha tecnología.
4. ¿Por qué debe preocuparse el ingeniero por por los aspectos físicos y económicos económicos del medio? El ingeniero debe preocuparse por los dos niveles de eficiencia porque en el aspecto físico busca satisfacer los deseos humanos, con el objetivo de alcanzar el mayor resultado final por unidad de recursos gastados; es decir que tiene como objetivo maximizar la eficiencia física. En lo económico de igual forma satisfacer los deseos del hombre y al hacerlo hace un lado ciertas utilidades con el fin de obtener otras que el valora mejor (maximizar la eficiencia económica). 5. Explique como una eficiencia física que este por por debajo del 100% puede convertirse en una eficiencia económica por encima del 100% Sabemos que no es posible obtener eficiencias físicas por encima del 100% y que las eficiencias económicas económicas si pueden exceder del 100%, el cual deben exceder exceder para que las empresas sean económicamente exitosas. La eficiencia física debe estar por debajo del 100% porque los procesos físicos deben realizarse por necesidad y que las empresas económicas únicamente son factibles si alcanzan eficiencias mayores que el 100%, es claro que el valor económico por unidad de resultados físicos debe ser siempre mayor que el costo económico por unidad de insumo. 6. ¿Por qué debe preceder la eficiencia económica a la eficiencia física? La eficiencia económica debe preceder a la eficiencia física porque la eficiencia económica económica depende en consecuencia del valor y costo por unidad de productos e insumos físicos que de la eficiencia eficiencia física; eficiencia que que es siempre significativa significativa pero únicamente únicamente en la la medida en que contribuye a la eficiencia económica. Lo anterior es así porque la función de la ingeniería es crear utilidad en el medio económico alterando los componentes del medio físico.
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8.
9.
10.
11.
b) Identificación de factores estratégicos c) Determinación de los medios d) Evaluación de las propuestas hechas por los ingenieros e) Asesoría en el proceso de toma de decisiones ¿Qué esta involucrado en la búsqueda de nuevos objetivos para el empleo de la ingeniería? En la búsqueda de nuevos objetivos para el empleo de la ingeniería esta involucrado: Conocer que desean los seres humanos y que puede ser suministrado por la ingeniería. En el área de las invenciones, el éxito depende de la capacidad del invento por satisfacer los deseos humanos. Es por ello que las investigaciones de mercado tratan de identificar los deseos de la gente. ¿Qué es un factor limitante? ¿un factor estratégico? Un factor limitante es un factor que obstaculiza el camino hacia la obtención de los objetivos. Un factor estratégico, por su parte; es aquel que si se altera, removerá las limitaciones que se oponen al éxito de un esfuerzo. Dé razones que expliquen por qué los ingenieros están particularmente bien equipados para determinar medios para el logro de un objetivo. Los ingenieros están bien bien equipados por entrenamiento y experiencia, experiencia, para identificar identificar medios que permitan alterar el medio ambiente físico para el logro de un objetivo. Algunas razones pueden ser: o Tener conocimiento de los hechos en un campo determinado constituye una necesidad para desarrollar creatividad en ese campo. Por ejemplo, una persona que domine las ciencias de la combustión y el diseño de maquinas, esta en mejores condiciones condiciones para diseñar diseñar un motor de combustión interna que que economice energía. Tener conocimientos en costos y en los deseos de los seres humanos paralelamente con los de ingeniería fueran necesarios para concebir las oportunidades de utilidad asociadas con la ingeniería. Los ingenieros en cualquier actividad tienen la oportunidad de ser creativos o considerando los factores humanos y los económicos. El diseñador de maquinas puede diseñar herramientas o maquinas que requieran un mínimo de mantenimiento, que puedan ser operadas con menor fatiga y mayor seguridad. o Los ingenieros pueden hacer que los proyectos privados y públicos se empleen, se construyan y operen de acuerdo con una buena práctica profesional. El diseñador de carreteras puede tener en cuenta la duración, el costo y la seguridad. La ingeniería es una profesión en permanente evolución y crecimiento, el hombre tiene gran confianza en la integridad y en la capacidad de los ingenieros. ¿Cómo pueden ser de ayuda los ingenieros en un proceso decisorio? La ingeniería tiene que ver con acciones que se van a realizar en el futuro. Una decisión
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capacidad creativa procede sobre la base de que hay una solución que es más deseable, si la puede encontrar. La determinación y la evaluación lógica de alternativas en términos tangibles, se ha reconocido como una faceta integral del proceso pr oceso de la ingeniería. El éxito de los ingenieros al manejar este elemento de utilización es responsable, en parte, por el elevado porcentaje de ingenieros que están directamente involucrados en actividades de toma de decisiones. 12. Comparándolos con los aspectos económicos del empleo empleo de la ingeniería, ingeniería, dé razones por las cuales los aspectos físicos están decreciendo en i mportancia relativa. Porque se tiene que invertir más producto para poder obtener una buena ganancia.
13. Analice los beneficios potenciales potenciales de un plan de estudios de ingeniería ingeniería económica Según el plan: El paso creativo las oportunidades no se hacen sino se descubren, el material a partir del cual se pueden obtener nuevas oportunidades con mejores oportunidades son los hechos tal como existen. El paso de definición las alternativas presentadas formalmente para evaluación se obtienen otras sobre la mesa otra alternativa que no consiste en tomar ninguna decisión en relación a la alternativa formal que se esté analizando. El paso de conversión consiste en comparar alternativas, apropiadamente es importante convertirlas a una medida común. El paso de decisión es lo último después de haber terminado el paso de conversión donde forman una base para la comparación y la toma de decisiones.
14. Emplee el plan de estudios de ingeniería económica en relación con un problema de ingeniería que usted escoja. 15. ¿En qué forma está relacionado el paso creativo con la satisfacción de los deseos humanos? El paso creativo se relaciona con los deseos humanos en forma de que nosotros no nos cansado de descubrir cosas nuevas día a día d ía y que siempre se busca encontrar nuevas posibilidades que puedan ser evaluadas para concluir si son o no superiores a las ya conocidas.
16. Enumere los métodos para descubrir medios para emplear más rentablemente los recursos.
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18. Discuta la naturaleza del juicio y explique explique por que se emplea en más situaciones que que la razón. El juicio tiende a ser cualitativo, en el mejor de los casos es una consideración y una ponderación informal de los hechos; en el peor de los casos es simplemente un pensamiento juicioso. Es un proceso informal para el análisis de información, experiencias pasadas y olfato en relación con un problema. Se emplea más, debido a su naturaleza informal y en aquellas situaciones donde esté ausente el conocimiento de los hechos.
19. Explique por qué las decisiones deben basarse en diferencias que van a presentarse en el futuro. Porque siempre habrá en el futuro oportunidades que serán mas rentables que cualquier de las que se conocen en el momento presente.
20. ¿Por qué las decisiones que están relacionadas con el futuro se basan en estimativos y no sobre los hechos pertinentes? Porque parece haber una marcada diferencia en la capacidad de las personas, para llegar a conclusiones lógicas cuando no se cuenta con hechos relativos a las situaciones que se están presentando.
21. ¿Por qué es siempre necesario necesario el juicio para llegar a una decisión decisión relacionada con un hecho que va a presentarse en el futuro? Porque cuando ha sido analizada una situación determinada se espera que queden algunas áreas de incertidumbre, aún después de haber recogido todos los datos sobre la situación, para tomar una decisión sobre la situación se toman en cuenta los datos no cuantitativos por medio del juicio o corazonadas.
22. ¿Por qué la interpretación económica económica de las propuestas propuestas de ingeniería ingeniería debe ser hecha por ingenieros? Cuando los ingenieros aceptan que las propuestas de ingeniería paralelamente con su interpretación en términos de valor y costo tienen sentido económico y técnico están solidificando la confianza de la gente en la ingeniería como una profesión.
7. Resolver PREGUNTAS Y PROBLEMAS PÁG 38 – 39 1. Defina valor; utilidad
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mismos bienes y servicios pueden ser útiles a otros; y cada individuo designa el grado de utilidad según su satisfacción, todo lo que tiene utilidad se manifiesta físicamente; por ende, se dice que las utilidades son creadas por medio de cambios introducidos al medio físico. 3. Describa las dos clases de bienes aceptados por los economistas. Los economistas reconocen dos clases de bienes: Bienes de consumo Bienes de producción Bienes de consumo: son productos y servicios que satisfacen directamente necesidades y deseos humanos. Bienes de producción: producción: también satisfacen los deseos humanos pero pero lo hacen de manera indirecta como parte de un proceso de producción o de construcción. 4. Confronte la utilidad de los bienes de consumo con la utilidad de los bienes de producción Una persona puede pensar en dos clases de utilidades. La utilidad de bienes y servicios que intenta consumir personalmente por la satisfacción que le deparan, que es el resultado de medidas subjetivas de procesos mentales sin lógica ninguna. El segundo tipo de utilidad que un objeto o un servicio puede tener para una persona es su utilidad como medio para logar un fin. Los bienes de producción no se consumen sino que se utilizan como un medio para producir bienes de consumo. 5. ¿Por qué la utilidad de los bienes de consumo se determina de manera subjetiva mientras que la utilidad de los bienes de producción se determina generalmente de manera objetiva? La utilidad de bienes de consumo se determina de manera subjetiva porque se encuentra el gusto emocional como medio más efectivo para las campañas de publicidad; que la información sobre hechos, aspectos subjetivos como la comodidad, belleza y prestigio. La utilidad de bienes de producción se determina de manera objetiva, por la factibilidad que tiene de delinear los limites , la clase y la cantidad de los servicios de producción, la mano de obra y el numero de diferentes clases de maquinas. Mientras que la determinación de las clases clases y cantidades de los bienes bienes de consumo necesarios, necesarios, puede
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produce como resultado una ganancia para las partes involucradas, porque las utilidades han sido evaluadas subjetivamente por ellos. 8. Un productor de partes para automóvil que esta localizado en la ciudad A, hace un despacho diario de partes terminadas a su bodega en la ciudad B. La distancia es de 200 millas y se estima que el el costo por milla es de $0.18 más $6.20 por hora como salario para el conductor. El vehículo hace el viaje de regreso regreso desocupado. Una Una empresa de transporte localizada en la ciudad B tiene un contrato para llevar piezas fundidas a la ciudad A y ha establecido que su costo por milla es de $0.20 más $5.80 por hora para el conductor. El viaje de regreso se hace sin ninguna ninguna carga. El tiempo requerido para para el viaje de ida y regreso, tanto para la compañía de transporte como para el productor, es igual a 9 horas. El productor de partes ofrece subcontratar el transporte de las piezas fundidas. Se estima que el trabajo ocasionara un aumento en costo equivalente a un recorrido adicional de 20 millas y un aumento en el viaje de ida y regreso de 1 hora y 45 minutos. a) ¿Cuál es el el valor mínimo mínimo que puede cargar la empresa productora productora por el transporte de las piezas piezas de fundición? fundición? b) ¿Cuál es el valor máximo que la empresa de transportes puede cobrar por subcontratar el transporte? Alternativas: Llevarlas ellos mismos subcontratar él envió de las piezas Tiempo: 9 horas Tiempo: 4.5 + 1.75 = 6.25 horas Distancia: 200 millas distancia: 200 + 20 millas Costo: costo: $0.18/milla* 200 milla= $ 36.00 $0.20/ milla * 220 milla =$ 44.00 Salario: salario: $6.20/hora * 9 hora= $ 55.80 $5.80/hora * 6.25 hora = $ 36.25 Costo total: $ 91.80 costo total: $ 80.25 Solución: a. El valor mínimo que puede cargar la empresa productora por el transporte de las piezas de fundición es de $ 80.25. b. El valor máximo que la empresa de transporte puede cobrar por subcontratar el
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indispensable para tener un esfuerzo coordinado; el esfuerzo es una actividad valiosa y necesaria en la mayoría de las situaciones que supongan una actividad organizada. 11. Relacione la eficiencia organizacional con el concepto de eficiencia económica y confronte los dos con el de eficiencia física. La eficiencia económica consta de satisfacer los deseos del hombre y al hacerlo hace un lado cierta utilidades con el fin de obtener otras que el valora mejor; utilidades que obtiene con la ayuda de la eficiencia organizacional que es el medio para intercambiar y crear esas utilidades. La eficiencia física consiste en una actividad productora que tiene su razón de ser en la satisfacción de los deseos humanos. Su objetivo es alcanzar el mayor resultado final por unidad de recursos gastados. De esa manera vemos como cada una se relaciona con la otra para lograr un solo objetivo satisfacerse y satisfacer los deseos de los clientes. 12. ¿Cuál es la función de un administrador? La función de todo administrador es mantener un sistema que permita reunir las actividades de un grupo de hombres, de manera que cada uno, incluyendo al propio administrador, obtenga mas de aquello con lo cual contribuye de manera que cada contribuyente no crea que tiene, en otras partes, mejores alternativas. 13. Un grupo de 60 empleados, empleados, con un salario promedio de $9900 anuales anuales esta dirigido por 5 capataces cuyo salario promedio es de $14000 también por año. Se sugiere aumentar el número de capataces a 6. a. ¿Qué porcentaje porcentaje de aumento de producción promedio promedio por por hombre debe lograrse para que los dos planes incurran en un costo igual? b. Si se adopta el plan sugerido, ¿Cuál será el porcentaje de aumento en tiempo promedio que puede gastarse en supervisión por trabajador? Parte a: Plan A: Plan B: 60 empleados-$9900 x año 60 empleados-$9900 x año 5 capataces-$14000 x año 6 capataces-$14000 x año (9900/60) + (14000/5)=2965
(9900/60) + (14000/6)=2498.33
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a. suponiendo que dos capataces tuvieran que gastar dos horas diarias coordinando su trabajo. ¿Cuál seria el aumento promedio en el tiempo gastado en supervisión por día y por hombre? b. ¿Qué porcentaje promedio de aumento en producción es necesario para justificar el empleo del segundo segundo capataz? 1capatas-8hrs-$15600/año 18hombres-8hrs-$11200/año 2hrs 6hrs
2hrs 6hrs
(8/18) = 44.4% (12/18) = 66.67% Aumento = 66.67% - 44.4% = 22.27% 15. Defina costo inicial y explique como puede ser un factor limitante en el éxito de las actividades de ingeniería. Costo inicial es el presupuesto o gastos que debes tener en cuenta al iniciar una empresa . Puede ser un factor limitante en las actividades de ingeniería porque con ese presupuesto y en base a lo que se diga es que se debe planificar y en ocasiones tiende a pasarse este presupuesto y si se pasa por lo general no será remunerado. 16. Discuta la diferencia entre costos fijos y costos variables. a. Costo fijos son los que se tienen que pagar sin importar si la empresa produce mayor o menor cantidad de productos, como ejemplo están los arrendamientos,
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análisis costo- volumen- utilidad es el cálculo del punto de equilibrio de una empresa. 18. El costo total para manufacturar 260 unidades de un producto es de $3200. Si se producen 340 unidades el costo total será de $3800. a) ¿Cuál es el costo promedio de producción para las primeras 260 unidades? b) ¿Cuál es el costo variable por unidad? c) ¿Cuál es el costo fijo total? d) ¿Cuál es el costo fijo promedio por unidad para las primeras 260 unidades? R: Parte a: (3200/260) = 12.31 Parte b: (600/340) = 1.765 Parte c: 3200 Parte d: (3800/260) = 14.61 19. Defina costos incurridos (amortizados) y explique porque no deben considerarse en los análisis de ingeniería económica. El coste amortizado de un instrumento financiero es el importe en el que inicialmente fue valorado un activo financiero o un pasivo financiero, menos los reembolsos de principal que se hubieran producido, más o menos, según proceda, la parte imputada en la cuenta de pérdidas y ganancias, mediante la utilización del método del tipo de interés efectivo, de la diferencia entre el importe inicial y el valor de reembolso en el vencimiento y, para el
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21. ¿Por qué la ley de los retornos decrecientes es un concepto útil en estudios económicos? Es éste un concepto bien conocido por las Ciencias Económicas y también por el sentido común, por la experiencia del día a día, y reza como sigue: Cuando se explota cualquier recurso o se crea un nuevo producto, hay una fase de expansión en la cual con muy poca inversión se genera un gran beneficio (facturación menos costes, o sea la inversión en nuestro caso), con lo que el retorno de la inversión (porcentaje de beneficio en comparación con la inversión inicial) se hace muy grande. Al pasar el tiempo, sin embargo, cuando el recurso ya está bien explotado o el mercado para el producto ya es maduro el retorno va disminuyendo, no importa que aumentemos la inversión el porcentaje recuperado es cada vez más pequeño. Uno puede aguantar un tiempo en esta situación, a base de invertir cantidades más grandes de capital y por tanto incrementar el beneficio absoluto, pero eso supone que hay un capital cada vez mayor que uno inmoviliza (detrayéndolo de inversiones más rentables) y/o arriesga (cualquier inversión comporta un riesgo de pérdida). Es muy importante saber dónde parar y saltar del barco cuando el retorno se hace muy pequeño, antes de que se vuelva negativo. Lo normal es que si no se puede mantener un nivel de retorno aceptable dados los riesgos operativos, es que se liquiden los activos de la inversión mientras todavía valen algo: al fin y al cabo, uno puede haber inmovilizado mucho capital en los activos, y aun cuando estén amortizados posiblemente es mejor inversión liquidarlos que intentar recuperar exiguos beneficios. 22. Un productor adquiere balineras en cajas que contienen 1000 unidades cada una. Se inspeccionan algunas de las balineras de cada caja como parte del procedimiento de aceptación. El costo ocasionado ocasionado por la inspección de una balinera es de $.20 y la perdida que resulta por la aceptación de una unidad es de $2. Se sabe por experiencias antiguas que el número de balineras defectuosas que se aceptaran si se inspeccionan 100, 200,
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2. 3.
4.
5.
ejemplo: caja, notas por pagar, costo de los bienes vendidos y arrenda mientos, etc…) de una empresa. Describa la diferencia en punto de vista con respecto al tiempo entre un balance y un estudio económico. ¿Cómo afecta la utilidad neta que aparece en un estado de ingresos un aumento (disminución) en la depreciación? La depreciación en un estado de ingresos afecta a la utilidad neta en una acción opuesta al que ella funcionara en dicho estado; lo anterior se comprende mejor de la siguiente manera, cuando la depreciación aumenta la utilidad neta disminuye. Al contrario si la depreciación disminuye la utilidad neta aumenta; en general es una acción inversa. ¿Cuál es el efecto sobre los impuestos federales y estatales de renta si aumentan los gastos por depreciación (disminuyen)? Como ya sabemos que a medida que la depreciación aumenta la utilidad neta disminuye y viceversa. Esa utilidad neta es la utilidad antes de tomar en cuenta los impuestos. Los impuestos estatales y federales se basan en un principio que quienes mas tienen deben aportar en mayor medida al financiamiento estatal y federal, para consagrar el principio constitucional de equidad y el principio social de solidaridad. De lo anterior, se puede deducir que si la depreciación aumenta, disminuye la utilidad neta y disminuye los impuestos estatales y viceversa. ¿Cuál es la función de la contabilidad general? ¿de la contabilidad de costos? El propósito principal de la contabilidad general es hacer posible la preparación periódica de dos estados financieros básicos; un balance y un balance de pérdida y ganancias. La contabilidad de costos esta adaptada para registrar ítem por ítem los costos de mano de obra, materiales y gastos generales como un medio para determinar los costos de
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9. ¿Qué preocupaciones deben tomarse al utilizarse datos contables en los analisis de ingeniería económica? Los datos contables constituyen la base para muchos estudios de ingeniería económica, debe tenerse extrema precaución en su utilización. Algunas de las precauciones que debemos tener presente para su utilización son: Los datos de costos deben ser utilizables; utilizables; un error bastante común es inferir que una reducción en los costos de mano de obra tendrá como consecuencia una disminución proporcional en los gastos generales. Los costos promedios son inadecuados para un analisis inadecuados; inadecuados; la principal función de la contabilidad de costos es es suministrar datos datos para las decisiones relacionadas con la reducción de los costos de producción y el aumento en las utilidades por ventas. Los datos de costos que proporcionen valores promedios verdaderos pueden conducir a errores muy costosos en las decisiones. 10. Los costos de manufactura de los productos X y Y parecen ser de $10 por unidad. Sobre la base de este estimativo y una utilidad deseada del 10 %, se ha definido un precio de venta de $11 por unidad. a. ¿Cuál es la utilidad si se venden 800 unidades del producto X y 2000 del Y? b. Si los costos reales de manufactura para los productos X y Y son $9 y S11, respectivamente, ¿Cuál es la utilidad real? PRODUCTO X
⁄ ⁄
Utilidad = ingresos – egresos a)
Utilidad = Utilidad = $ 800
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DEPARTAMENTOS A, B, C, D
HORAS DE MANO DE OBRA DIRECTA
COSTO DE LA MANO DE OBRA DIRECTA
COSTO DE LOS MATERIALES DIRECTOS
TOTAL
7460
58350
52000
De acuerdo con la información suministrada la tasa de asignación de los gastos generales puede ser:
= = = = = $ 0.04 Costo de materiales directos = Horas de mano de obra directa = Costo de mano de obra directa
12. Un productor manufactura 8500000 tubos de radio por año. Se lleva a cabo una operación de ensamble en cada tubo tubo por la cual se paga un estándar de $ 1.05 por cien unidades. El
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$ 43.00 = X + X (19.32%) manteniendo la misma utilidad deseada en la situación actual $ 43.00 = X (1+ 19.32%) X = $ 43.00 / (1 + 19.32%) X = $ 36.04 (costo total de la unidad manufacturada) Si el costo total de la unidad manufacturada es la anterior, el gasto general seria: Costo de la mano de obra directa…………………………………….$ 19.50 Costos de los materiales directos…………………………………….. 14.50 Gastos generales……………………………………….………………………….X….
Costo total $ 36.04 Por tanto; el nuevo gasto general se calcula: calcula: Gastos generales = costo total - (costo mano de obra obra + costo de los materiales) Gastos generales = 36.04 - (19.50 + 14.50) = $ 2.04 Esto, responde a la pregunta ¿aumentarían los gastos generales? Respuesta: no, los gastos generales reales disminuyen a $ 2.04 por unidad manufacturada.
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El concepto contable de depreciación visualiza el costo de un activo como un desembolso operativo prepagado que debe ser cargado contra las utilidades durante la vida del activo. La depreciación es entendida por el público como la disminución en valor de un activo físico con el paso del tiempo. La gran diferencia diferencia radica en que en vez de cargar el costo total como un gasto al momento de adquirir el activo (depreciación); el contador intenta de manera sistemática distribuir la perdida anticipada en valor a todo lo largo de la vida del activo (depreciación contable). 2. Describa la función valor-tiempo y mencione sus componentes c omponentes esenciales. La función valor-tiempo se emplea para representar el valor de un activo que decrece anualmente en cualquier punto en tiempo durante su vida. Esta función matemática involucra decisiones acerca de la vida del activo, de su valor de salvamento y de la forma de la función. Entre sus componentes esenciales tenemos: P = costo inicial del activo F=valor de salvamento estimado
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Fin del año
Cargo por depreciación durante el año ----575.00 575.00
Valor en libros al finalizar el año 2500.00 1925.00 1350.00
0 1 2 3
Cargo por depreciación durante el año ----525.00 525.00 525.00
Valor en libros al finalizar el año 2500.00 1975.00 1450.00 925.00
Fin del año
Cargo por depreciación
Valor en libros al
0 1 2 Año 3 Fin del año
Año 4
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Fin del año t 0 1 2 3 4 5 6 7 8
Cargo de depreciación durante el año t $ 2275 2275 2275 2275 2275 2275 2275 2275
Valor en libros al finalizar el año t $ 23000 20725 18450 16175 13900 11625 9350 7075 4800
Cada año debe asignarse una depreciación de $2275 a la nueva volqueta El valor no depreciado al final del quinto año es de $ 11625
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4. ¿Cuál es el efecto sobre los impuestos federales y estatales de renta si aumentan los gastos por por depreciación (disminuyen)? R: *Los impuestos federales son los que se gravan en todo el país y estos se deben pagar sin importar el lugar de residencia del contribuyente, es decir que son independientes de
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9. ¿Qué precauciones deben tomarse al utilizar datos contables en los análisis de ingeniería económica? R: es deseable que los datos suministrados por los sistemas contables se examinen en relación con los requerimientos de los estudios de ingeniería económica.
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12. Un operador manufactura 8500000 tubos de radio por año. Se lleva a cabo una operación de ensamble en cada tubo por la cual se paga un estándar de $1.05 por cien unidades. El ciclo estándar de tiempo por pieza es igual a 0,624 minutos. Los gastos generales asociados con la operación se estiman en $0,36 por operador-hora. Si el ciclo estándar de tiempo puede reducirse en 0,01 de un
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14. Un productor de partes para automóvil produce en su departamento de productos eléctricos baterías y ensambles para distribuidor. Se cree que el costo de manufactura de las baterías y de los ensambles para distribuidor es de $18,40 y $23,20 por unidad, respectivamente. Estos costos se calcularon sobre la base de una distribución igual de los cargos por gastos generales se distribuirán mas
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3. ¿representa un cargo por depreciación un desembolso real de fondos? Explique. R:
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