Question

A company is considering replacing a machine on a production line to reduce operating costs. The equipment to be replaced was purchased two years ago for $1,000,000 and can be sold for $700,000. The machine to be replaced can be used for five more years, after which it can be sold for $100,000. The machine's operating costs are $800,000 annually. The company pays 10% taxes on profits. The new machine is worth $1,600,000 and can be used for five years before having to be replaced and in five years it can be sold for $240,000. During the period of use, it will allow to reduce the operating costs associated with the machine by $300,000 annually. The current machine will not be used and will be sold. All equipment depreciates annually by 20% of its value from the time of purchase. Ask Project the cash flow of the current situation Project cash flow with machine replacement Compare the alternatives and make a decision if it is worth replacing the machine. Please, I need this step by step in Spanish.

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Answer to a math question A company is considering replacing a machine on a production line to reduce operating costs. The equipment to be replaced was purchased two years ago for $1,000,000 and can be sold for $700,000. The machine to be replaced can be used for five more years, after which it can be sold for $100,000. The machine's operating costs are $800,000 annually. The company pays 10% taxes on profits. The new machine is worth $1,600,000 and can be used for five years before having to be replaced and in five years it can be sold for $240,000. During the period of use, it will allow to reduce the operating costs associated with the machine by $300,000 annually. The current machine will not be used and will be sold. All equipment depreciates annually by 20% of its value from the time of purchase. Ask Project the cash flow of the current situation Project cash flow with machine replacement Compare the alternatives and make a decision if it is worth replacing the machine. Please, I need this step by step in Spanish.

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Gene
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Claro, aquí tienes un análisis detallado y paso a paso en español para determinar si vale la pena reemplazar la máquina. ### 1. Proyección del Flujo de Caja en la Situación Actual **Datos:** - Costo original de la máquina: $1,000,000 - Valor de reventa después de 5 años: $100,000 - Costos operativos anuales: $800,000 - Depreciación anual: 20% - Tasa de impuestos: 10% **Cálculo de la depreciación:** La depreciación anual es el 20% del costo original de la máquina. \[ \text{Depreciación anual} = 1,000,000 \times 0.20 = \$200,000 \] **Flujo de caja anual (sin reemplazo):** \[ \text{Utilidad antes de impuestos} = \text{Ingresos} - \text{Costos operativos} - \text{Depreciación} \] Dado que no se mencionan ingresos adicionales, solo consideramos los costos operativos y la depreciación. \[ \text{Utilidad antes de impuestos} = - \$800,000 - \$200,000 = - \$1,000,000 \] \[ \text{Impuestos} = \text{Utilidad antes de impuestos} \times 0.10 = - \$1,000,000 \times 0.10 = - \$100,000 \] \[ \text{Utilidad neta} = \text{Utilidad antes de impuestos} - \text{Impuestos} = - \$1,000,000 - (- \$100,000) = - \$900,000 \] **Flujo de caja:** El flujo de caja es la utilidad neta más la depreciación (ya que la depreciación es un gasto no monetario): \[ \text{Flujo de caja anual} = - \$900,000 + \$200,000 = - \$700,000 \] **Flujo de caja total en 5 años:** \[ \text{Flujo de caja total} = (-\$700,000 \times 5) + \$100,000 = - \$3,500,000 + \$100,000 = - \$3,400,000 \] ### 2. Proyección del Flujo de Caja con Reemplazo de la Máquina **Datos:** - Costo de la nueva máquina: $1,600,000 - Valor de reventa después de 5 años: $240,000 - Reducción de costos operativos: $300,000 anuales - Costos operativos con la nueva máquina: $800,000 - $300,000 = $500,000 - Depreciación anual de la nueva máquina: 20% de $1,600,000 **Cálculo de la depreciación de la nueva máquina:** \[ \text{Depreciación anual} = 1,600,000 \times 0.20 = \$320,000 \] **Flujo de caja anual (con reemplazo):** \[ \text{Utilidad antes de impuestos} = - \$500,000 - \$320,000 = - \$820,000 \] \[ \text{Impuestos} = - \$820,000 \times 0.10 = - \$82,000 \] \[ \text{Utilidad neta} = - \$820,000 - (- \$82,000) = - \$738,000 \] **Flujo de caja:** \[ \text{Flujo de caja anual} = - \$738,000 + \$320,000 = - \$418,000 \] **Flujo de caja total en 5 años:** Incluimos la venta de la máquina anterior y la nueva al final de su vida útil: \[ \text{Flujo de caja total} = (-\$418,000 \times 5) + \$240,000 + \$700,000 = - \$2,090,000 + \$240,000 + \$700,000 = - \$1,150,000 \] ### 3. Comparación de las Alternativas - **Flujo de caja total sin reemplazo:** -$3,400,000 - **Flujo de caja total con reemplazo:** -$1,150,000 ### 4. Decisión **Conclusión:** Reemplazar la máquina resulta en una menor pérdida total ($1,150,000) en comparación con mantener la máquina actual ($3,400,000). **Por lo tanto, es recomendable reemplazar la máquina** ya que reducirá significativamente los costos operativos y las pérdidas a lo largo de los próximos 5 años.

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