--IRR (INTERNAL RATE OF RETURN) CALCULATOR--

The Internal Rate of Return (IRR) Calculator is a financial tool used to compute the IRR for a real estate investment. The IRR is a crucial metric that provides investors with insight into the profitability of an investment opportunity. Here's how the IRR Calculator works:

1. Initial Investment: Users input the initial amount of money invested in the real estate project.
2. Cash Flows: Users input the cash flows generated by the real estate investment over time. Each cash flow is separated by commas and includes both positive (income) and negative (expenses) values. For example, "-1000, 300, 400, 500" represents an initial investment of $1000 followed by cash inflows of $300, $400, and $500.

1. Preparation: The initial investment is added as a negative cash flow at the beginning of the cash flows array.
2. Newton-Raphson Method: The calculator utilizes the Newton-Raphson method to iteratively determine the IRR. This method involves making an initial guess for the IRR and then refining it through successive iterations until the difference between the calculated net present value (NPV) of the cash flows and zero is sufficiently small.
3. NPV Calculation: The calculator computes the net present value (NPV) of the cash flows using the IRR guess and the NPV formula. The NPV represents the present value of all future cash flows discounted at the IRR rate.
4. NPV Derivative: The calculator computes the derivative of the NPV function with respect to the IRR using the NPV derivative formula. This derivative is used to refine the IRR estimate in each iteration of the Newton-Raphson method.
5. Iteration: The calculator iterates the Newton-Raphson method until the difference between the calculated NPV and zero is below a specified threshold or until a maximum number of iterations is reached.

Once the calculation is complete, the calculator displays the calculated IRR as a percentage. This value represents the discount rate at which the net present value of all cash flows equals zero. A higher IRR indicates a more profitable investment opportunity.

In summary, the IRR Calculator enables investors to evaluate the profitability of a real estate investment by computing the internal rate of return, thereby aiding in investment decision-making and comparison of different investment opportunities.