Master the calculation formula of internal rate of return and improve the ability of investment analysis

Internal rate of return (IRR,Internal Rate of Return) is a very key indicator when analyzing investment projects. By understanding the calculation formula of IRR, investors can more accurately evaluate the profitability and risk level of the project. This article will introduce the calculation method and application of IRR in detail to help readers improve the ability of investment analysis.

I. definition of internal rate of return (IRR)

The internal rate of return is the discount rate that makes the net present value (NPV,Net Present Value) of the project zero. To put it simply, it is the expected rate of return of the project investment payback period. Projects are generally considered attractive when the IRR is higher than investors' expected returns.Poppyplaytimechapter2crashingOn the contrary, it has no investment value.

II. IRR calculation formula

The calculation formula of IRR is based on the formula of NPV. The NPV calculation formula is as follows:

NPV = ∑ (CF / (1 + r) ^ n)-I

Where CF represents the cash flow of the project in the nth year, r is the discount rate, n is the time, and I is the initial investment. When NPV is 00:00, the discount rate is IRR. Therefore, the IRR calculation formula can be expressed as:

0 = ∑ (CF / (1 + IRR) ^ n)-I

III. IRR calculation method

Because the IRR formula has no direct analytical solution, it usually needs to be solved by iterative method or numerical method. Here are two commonly used IRR calculation methods.

onePoppyplaytimechapter2crashing. Trial and error method

Trial and error is a simple and intuitive IRR calculation method. First, you need to select an initial discount rate as the starting point. Then, the NPV values under different discount rates are calculated to approach IRR step by step. As NPV approaches 00:00, the estimated value of IRR will get closer and closer to the real value.

2. Newton-Raphson iterative method

Newton-Raphson iterative method is a more efficient and accurate IRR calculation method. Based on the derivative of the function, the method approaches the real value of IRR step by step through the iterative process. The specific steps are as follows:

1. Select an initial IRR estimate (usually based on the average rate of return of the project)

two。 Calculate the NPV value corresponding to IRR

3. Calculate the derivative value of IRR according to the relationship between NPV value and IRR

4. Update the estimate of IRR with an iterative formula: IRR_new = IRR_old-(NPV * NPV' (IRR_old)) / NPV (IRR_old)

5. Repeat steps 2-4 until the difference between the new and old estimates of the IRR is less than the preset threshold.

IV. IRR application example

The following is an application example of IRR computing. Suppose investors consider investing in a project with an initial investment of 1 million yuan, and the cash flow in the next five years is expected to be 300000 yuan, 400000 yuan, 500000 yuan, 600000 yuan and 700000 yuan respectively. We can use the above method to calculate the IRR of the project.

Through the trial and error method or Newton-Raphson iterative method, we can calculate that the IRR of this project is about 22.35%. Assuming that the expected return of investors is 20%, the project can be considered an attractive investment opportunity because the IRR is higher than the expected return.

V. matters needing attention

In practical application, investors need to pay attention to the following points:

1. The calculation result of IRR is affected by the cash flow hypothesis, so it is necessary to be cautious about the cash flow forecast of the project when carrying out IRR analysis.

two。 When there is a non-traditional pattern of project cash flow (such as mismatch between input and recovery), IRR may have multiple values, so it is necessary to make a comprehensive judgment combined with other indicators (such as net present value).

3. When comparing the IRR of different projects, we need to consider the scale, duration, risk and other factors of the project to avoid the limitations of a single index.

By mastering the calculation formula and method of IRR, investors can evaluate the profitability and risk level of the project more accurately, so as to provide strong support for investment decisions.