To calculate the Internal Rate of Return (IRR), we solve the equation where the Net Present Value (NPV) is zero:

$NPV = \sum_{t=1}^{n} \frac{\text{Cash Inflow}_t}{(1 + IRR)^t} - \text{Initial Investment} = 0$

Given:

• Initial investment ($C_0$) = $9,000
• Cash inflow per year ($C_t$) = $1,583
• Number of years ($n$) = 11

The equation becomes:

$9,000 = \sum_{t=1}^{11} \frac{1,583}{(1 + IRR)^t}$

This equation doesn't have a closed-form solution, so we use iterative methods (like Newton-Raphson) or financial calculators. I'll calculate this numerically. scipy.optimize import irr

Define cash flows: initial outlay (negative) and inflows (positive)

cash_flows = [-9000] + [1583] * 11

Calculate IRR

calculated_irr = irr(cash_flows) * 100 # Convert to percentage

calculated_irrIt seems there was an issue with the numerical calculation tool. Let me resolve this manually using the financial formula for IRR. One common approach is trial and error or interpolation based on known interest rates. numpy_financial as npf

Calculate IRR using numpy financial library

calculated_irr = npf.irr(cash_flows) * 100 # Convert to percentage

calculated_irrIt seems the variable data was lost during the tool initialization. Let’s redefine the problem manually and calculate the IRR again. Redefine cash flows: initial outlay (negative) and inflows (positive) cash_flows = [-9000] + [1583] * 11

Calculate IRR using numpy financial library

calculated_irr = npf.irr(cash_flows) * 100 # Convert to percentage

calculated_irrThe Internal Rate of Return (IRR) for the project is approximately 13%.

This is rounded to the nearest whole percent, as requested.

Would you like details on the calculation process or further clarifications?

Related Questions:

1. What is the significance of IRR in investment decision-making?
2. How does IRR compare to the Net Present Value (NPV) method?
3. What are some limitations of using IRR as a decision-making tool?
4. How does the timing of cash flows affect IRR calculations?
5. How can you calculate IRR for projects with irregular cash flows?

Tip:

When calculating IRR, ensure all cash flows are consistently timed (e.g., annually, quarterly) to avoid errors in the computation.