lawnmowingsimulatorcrashingepicgames| Detailed explanation of the calculation method of quoted internal rate of return, including the derivation of quoted internal rate of return formula

Detailed explanation of the calculation method of Internal rate of return of quotation

Internal rate of return (Internal Rate of Return, IRR) is an important index in the evaluation of investment projects.LawnmowingsimulatorcrashingepicgamesTo measure the level of return on project investment In this paper, the calculation method of internal rate of return of quotation is analyzed in detail, and the derivation process of its formula is discussed.

I. definition of internal rate of return of quotation

The quoted internal rate of return refers to the discount rate at which the net present value (Net Present Value, NPV) is equal to 00:00 in the process of project investment. When investors use this index to evaluate a project, they can judge which project has more investment value by comparing the IRR values of different projects. In general, the higher the IRR value, the greater the revenue potential of the project.

Second, the calculation method of internal rate of return of quotation

The calculation of the internal rate of return of the quotation involves solving an equation about cash flow. Suppose the cash flow of an investment project is shown in the following table:

Among them, the minus sign indicates investment expenditure. We need to find a discount rate to make the net present value of the project equal to zero. The specific calculation process is as follows:

First, we need to build an equation about the discount rate. If the discount rate is r, then there are:

-1000 + 300,400 / (1 + r) ^ 2 + 1000 / (1 + r) ^ 3 = 0

This is a cubic equation about r, which can be solved numerically. The commonly used numerical methods are Newton method, dichotomy and so on. Taking the Newton method as an example, the calculation steps are as follows:

oneLawnmowingsimulatorcrashingepicgames. Suppose an initial discount rate r 0, for example, r 0 = 0Lawnmowingsimulatorcrashingepicgames.1 (10%); 2. Calculate the value of the function f (r) at r 0, that is, f (0.1) =-1000 + 300 / 1.1 + 400 / 1.21 + 500 / 1.331; 3. Calculate the derivative of the function f (r) at r0, that is, f'(r) = 1 / 1.1-400 / 1.21 ^ 2-500 / 1.331 ^ 2; 4. According to the formula of Newton method, the next approximate solution R1 = R0-f (R0) / f' (R0) is calculated. Repeat steps 2-4 until the value of r converges, that is, the internal rate of return of the quote.

III. Derivation of the formula of internal rate of return of quotation

The formula of quotation internal rate of return is based on the concept of present value and future value. For an investment project, we can regard its cash flow as a series of future cash flows. By looking for an appropriate discount rate so that the net present value of the project is equal to zero, we can get the internal rate of return of the quotation.

Suppose the investment cost of the project is C, the duration of the project is n years, and the cash flow is CF1, CF2,..., CFn respectively. The internal rate of return of the quotation can be calculated by the following formula:

C + Σ [CFt / (1 + IRR) ^ t] = 0

Where Σ denotes summation and t denotes time (1,2,..., n). By solving the above equation, we can get the internal rate of return of the quotation.

The quoted internal rate of return is an important reference index for investors to evaluate the investment of the project.LawnmowingsimulatorcrashingepicgamesWith the understanding of its calculation method and formula derivation, investors can evaluate the income potential of the project more accurately.

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