https://r2.erweima.ai/mathbot/image/1726259832540k6j0hy8l.jpg

To solve the problem based on the image, I'll summarize the key information:

### Problem Summary:
- The company "Produktion & Dienstleistung AG" plans to adapt their products for the Asian market, which requires new tools produced by a specialized machine.
- Key data provided:
  - **Acquisition cost of the machine**: 2,400,000 €
  - **Residual value after 5 years**: 0 €
  - **Other fixed costs (without capital cost)**: 500,000 € per year
  - **Variable cost per tool**: 1.60 €
  - **Sale price per tool**: 3.10 €
  - **Calculation interest rate**: 10%

- **Marketing forecasts**:
  - In years 1 and 2: 900,000 units sold per year
  - In years 3 to 5: 800,000 units sold per year

- The board requires a yearly profit of 100,000 € over the 5-year lifespan.

### Steps to Solve:
1. **Calculate total costs**: Fixed + variable.
2. **Determine yearly revenues**: Multiply units sold by sale price.
3. **Profit Calculation**: Subtract costs from revenues.
4. **NPV/Profit Comparison**: Use Net Present Value (NPV) or a similar method to evaluate profitability against the required 100,000 € annual profit.

Let me calculate the details.### Solution:

1. **Yearly Profits**:
   - Years 1 and 2: 850,000 € profit per year.
   - Years 3 to 5: 700,000 € profit per year.

2. **Net Present Value (NPV)**: The NPV of the project is **513,881.32 €** after 5 years.

3. **Average Yearly Profit**: The average yearly profit is **760,000 €**.

4. **Conclusion**: The investment is **worthwhile**, as the average yearly profit (760,000 €) exceeds the required profit of 100,000 €.

Would you like further details or explanations? 

Here are 5 related questions to extend this topic:
1. How is NPV used to assess investment decisions?
2. What role does the discount rate (interest rate) play in NPV calculations?
3. How would the result change if fixed costs increased?
4. What is the impact of a lower interest rate on the NPV?
5. How could a sensitivity analysis be applied to this case?

**Tip**: Always review the impact of variable costs, as changes in production can dramatically affect profitability.

Analyze the profitability of a machine investment based on fixed and variable costs, sale prices, and projected sales. Includes profit calculations, NPV analysis, and the required profit margin over 5 years.

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