Home # Trading tool: IRR: Internal Rate of Return

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IRR: internal rate of return, definition and calculus of the IRR from the cash flows values

The internal rate of return is the rate of growth (or reduction) of a financial operation (constituted by a succession of cash flows) and comes calculated annulling the net present value.
For an investment the IRR corresponds to the medium percentage annual gain calculated considering as initial expense the invested capital and as incomes those perceived in the successive years through dividends, reimbursements and from the sale or from the final residual value of the financial instrument initially purchased.
The internal rate of return often is used in order to confront between various opportunities of investment; greater percentage of IRR (between investments with the same risk) is naturally prepreferred; therefore the IRR must be greater regarding the risk free interest rate (as that one obtained on a banking deposit account) of a quantitative that can recompense the investor of the greater risk associated to the financial instrument.
In this page it is possible to insert the values of the cash flows in order to calculate the internal rate of return of an investment operation.
The result is calculated resolving the polynomial equation in which the unknown quantity is the interest rate that allows to annul the net present value that it is gained bringing up-to-date all the cash flow with the unknown rate.
Mathematically the equation has the same degree of the number of movements beyond the first one and the solution is obtained with the method of the tangents of Newton Raphson (that it will be modified with the method of the secants for a greater stability).
The equation admits n solutions in the field of the complex numbers, but in order to admit sure at least one real solution, it must be of odd degree.

Insert the following values:
ShowHide variables and formulas

 \$cf = 01234567891011121314151617181920-1000 50 30 20 40 70 110 980 The first value is the invested amount that is the initial cash flow, while the following values (one for each row) are the cash flows of the following years (indicate positive values for the incomes and negative values for the expenses)

The results are: 2

 \$fx = Polynomial equation that is originated setting to zero the the sum of the present values of all the cash flows with the unknown x interest rate \$fx=polynomial_str(\$cf)."=0"; \$tir = IRR: Internal Rate of Return \$tir=internal_rate_of_return(\$cf);

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