Math Problem Statement
Solution
To solve this problem, we need to calculate the Internal Rate of Return (IRR) for the project. The IRR is the discount rate that makes the Net Present Value (NPV) of cash flows equal to zero. Here’s how it can be calculated:
Formula for NPV:
Where:
- = Cash flow at time
- = Internal Rate of Return (what we’re solving for)
- = Time period
Cash Flow Data:
Using a financial calculator, Excel, or iterative numerical methods (e.g., trial and error or Newton-Raphson method), we calculate the IRR. I will compute this for you. scipy.optimize import irr
Define the cash flow series
cash_flows = [-9500, 1050, 2250, 1450, 1450, 1250, 1050]
Calculate IRR
internal_rate_of_return = irr(cash_flows) * 100 # Convert to percentage internal_rate_of_returnIt seems I encountered an issue with my calculation environment. However, I can guide you to calculate the IRR using Excel or an online tool:
Using Excel:
- Enter the cash flows in a column (e.g., A1:A7):
- A1: -9500
- A2: 1050
- A3: 2250
- A4: 1450
- A5: 1450
- A6: 1250
- A7: 1050
- Use the formula:
This will give you the IRR.=IRR(A1:A7)
If you'd like, I can solve this step manually for an approximate answer using interpolation. Would you like me to proceed with that or guide you further on calculating it?
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Math Problem Analysis
Mathematical Concepts
Financial Mathematics
Net Present Value (NPV)
Internal Rate of Return (IRR)
Formulas
NPV = Σ (CF_t / (1 + IRR)^t)
IRR: the rate that makes NPV = 0
Theorems
The IRR is the discount rate that makes the NPV of cash flows equal to zero.
Suitable Grade Level
Grades 10-12, College-level finance
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