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The relationship between Internal rate of return and present value and its calculation method

When investors make investment decisionsWsopplayersVarious financial indicators need to be fully understood, among which internal rate of return (IRR) and present value (NPV) are two commonly used evaluation indicators. This article will describe in detail whether the internal rate of return is the present value, and how to calculate the relationship between the internal rate of return and the present value.

I. definition of internal rate of return and present value

Internal rate of return (IRR) is the discount rate that makes the net present value (NPV) of the project zero. In other words, the internal rate of return is the average annualized rate of return on project investment. Present value (NPV) refers to the conversion of the future cash flow of the project into the present value according to a certain discount rate.

Second, the relationship between internal rate of return and present value

There is a close relationship between the internal rate of return and the present value. When investors use the internal rate of return as the discount rate to calculate the present value, they will find that the net present value (NPV) of the project is exactly zero. This means that if investors think that their investment opportunity cost is equal to the internal rate of return of the project, then the investment value of the project is zero, which is neither worth investing nor need to give up.

Third, how to calculate the internal rate of return

Iterative method or interpolation method is needed to calculate the internal rate of return. The following is an example of a simple iterative method for calculating IRR:

Year cash flow 0-10000 1 3000 2 4000 3 5000

Suppose investors need to find the internal rate of return of the project. First, we need to choose an initial discount rate, such as 10%. Use this discount rate to calculate the net present value (NPV) of the project:

NPV =-10000 + (3000 / (10.00)Wsopplayers.1) ^ 1) + (4000 / (10.1) ^ 2) + (5000 / (10.1) ^ 3) =-10000 + 2727.27 + 3306.82 + 3972.47 = 2976.56

Since NPV is greater than zero, we need to choose a higher discount rate, such as 20%. Calculate the NPV again:

NPV =-10000 + (3000 / (1x 0.2) ^ 1) + (4000 / (1x 0.2) ^ 2) + (5000 / (1x 0.2) ^ 3) =-10000 + 2500 + 3010.17 + 3164.97 =-2424.76

Since NPV is less than zero, we need to look for the internal rate of return between 10% and 20%. Through continuous iteration, we can find the discount rate that makes the NPV close to zero, that is, the internal rate of return. In this example, the IRR is about 15.7%.

How to calculate the present value

Calculating the present value requires using the internal rate of return or other expected rate of return on investment as the discount rate. Here is an example of using the internal rate of return to calculate the present value:

NPV =-10000 + (3000 / (1x 0.157) ^ 1) + (4000 / (1x 0.157) ^ 2) + (5000 / (1x 0.157) ^ 3) =-10000 + 2572.22 + 3415.09 + 4019.47 = 0.78

From this result, we can see that when using the internal rate of return as the discount rate, the net present value of the project is close to zero, which is in line with our previous expectations.

Through the above analysis, we can draw a conclusion: there is a close relationship between the internal rate of return and the present value, but the internal rate of return is not equal to the present value. Understanding how to calculate the relationship between internal rate of return and present value is of great significance for investors to make investment decisions.