# shadowruntabletop| Calculation method of internal rate of return: Master the calculation method of internal rate of return

Master the calculation method of internal rate of return

Internal rate of return (Internal Rate of Return)**Shadowruntabletop**IRR) is an important index in the evaluation of investment projects. it represents the discount rate that makes the net present value (NPV) of the project equal to zero. When investors are faced with multiple investment schemes, the best investment scheme can be selected by comparing the internal rate of return of each scheme. This paper will introduce the calculation method of internal rate of return in detail to help investors make better investment decisions.

Before we know the internal rate of return, we need to understand the concept of net present value (NPV). Net present value (NPV) refers to the difference between future cash inflows and cash outflows of the project, after discounted net value. The formula is: NPV = ∑ (CFt / (1 + r) ^ t)-C0, where CFt represents the cash flow of the t period, r represents the discount rate, and C0 represents the initial investment.

The key to calculating the internal rate of return is to find the discount rate that makes NPV equal to zero. Because of the definition of internal rate of return, we know that IRR is an r value that satisfies NPV = 0. At this time, we can solve it by iterative method, Newton method and other mathematical methods.

Iterative method is a simple method to calculate IRR. First, select an initial r value, such as 10%, and calculate the NPV at this time. Then, according to the positive or negative of the NPV, adjust the r value (for example, increase or decrease 1%), and calculate the NPV again. Repeat this process until you find the r value that brings NPV close to zero. It should be noted that the iterative method may require many attempts, and the calculation process is cumbersome.

Newton method is a more efficient method for solving IRR. The Newton method uses the derivative of the function and Taylor series expansion to solve the internal rate of return through iteration. The specific steps are as follows:

1. Select an initial r value (e.g. 10%)

two。 Calculate the derivatives of NPV and NPV (that is,**Shadowruntabletop**? NPV/?r)

3. Using Taylor series expansion, the next approximate r value is calculated: r_new = r_old-NPV (r_old) / (? NPV/?r)

4. Repeat steps 2 and 3 until | r_new-r_old | less than the preset precision value.

In order to show the calculation method of IRR more intuitively, we take an actual investment case as an example. Suppose the investor is going to invest in a project with an initial investment of 1 million yuan and a project period of 5 years. The expected future cash flow is as follows:

Year cash flow (ten thousand yuan) 0-100 1 20 2 30 3 40 4 50 5 60Using the iterative method or Newton method, we can calculate that the internal rate of return of the project is 25%. This means that investors can expect an annual return of 25 per cent without taking into account other risk factors.

It should be noted that although the internal rate of return is an important investment evaluation index, it also has some limitations. For example, when the cash flow model of a project is complex, there may be multiple internal rates of return, which need to be evaluated comprehensively in combination with other indicators. In addition, the internal rate of return assumes that the cash flow generated by the project can be reinvested according to the internal rate of return, which may not be true in practice. Therefore, when investors use the internal rate of return to make investment decisions, they also need to consider other factors, such as the risk of the project, market competition and so on.

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