Analysis of Internal rate of return algorithm

Internal rate of return (Internal Rate of Return, IRR) is a key index in the evaluation of investment projects, which is used to measure the profitability of investment projects. In this paper, the algorithm used to calculate the internal rate of return will be analyzed in detail to help investors better understand and use the index.

I. definition of internal rate of return

Internal rate of return (IRR) refers to the discount rate that makes the net present value (Net Present Value, referred to as NPV) of an investment project equal to zero. In other words, the internal rate of return is the expected rate of return achieved by investors in the project. When the internal rate of return is higher than the investor's cost of capital or the required minimum rate of return, the project is usually considered feasible.

Second, the calculation principle of internal rate of return

The core of calculating the internal rate of return is to solve a polynomial equation about cash flow. The cash flow of an investment project usually includes initial investment (usually negative) and future cash flow (positive). The internal rate of return can be obtained by solving the following equationSabongbonus:

Where CFt represents the cash flow of the t period, r is the internal rate of return, and t represents the number of time periods. Because of the complex relationship between cash flow and time, the solution of internal rate of return usually needs the help of numerical method.

III. Calculation method of internal rate of return

oneSabongbonus. Manual trial and error method

Manual trial and error is a simple solution, by gradually trying different discount rates until the discount rate that makes NPV close to zero is found. Although this method is intuitive, it is inefficient and easy to make mistakes when the cash flow fluctuates greatly.

two。 Newton method (Newton-Raphson method)

Newton method is an iterative method, which approximates the solution by calculating the derivative of the function. The specific steps are as follows:

Compared with manual trial and error method, Newton method has higher efficiency and accuracy.

3. IRR function in Excel

The IRR function in Excel calculates the internal rate of return directly, using IRR (value 1, value 2,..., value n), where values 1 to n represent the cash flow of the project. This method is simple and easy to use and is suitable for most scenarios.

IV. Limitations of internal rate of return

Although the internal rate of return is an important index to evaluate the profitability of the project, it also has some limitations. For example, the internal rate of return cannot handle multiple positive and negative cash flows at the same time, and for projects with non-traditional cash flows, the internal rate of return may not provide accurate assessment results. Therefore, in practical application, investors also need to combine other indicators and methods for comprehensive evaluation.