This online Internal Rate of Return Calculator performs calculation of the internal rate of return (IRR) of any investment given the size of the investment and the cash flow occurring at equal periods. To add or subtract a cash flow period click the “+” symbol or the “–” symbol respectively.
Internal Rate of Return Formula
The internal rate of return (or IRR) is a metric used in financial analysis to estimate the profitability of potential investments. IRR is a discount rate that makes the net present value (NPV) of all cash flows equal to zero in a discounted cash flow analysis. The term internal refers to the fact that the calculation excludes any external factors, such as inflation, the cost of capital, or financial risk.
The internal rate of return calculations rely on the same formula as NPV does:
$$\mathrm{NPV}(r,N) = \sum_{t=0}^{N} \frac{C_t}{ (1+r) ^{t}} = 0,$$
where:
\(t\) – the time of the cash flow (the cash flow period number);
\(r\) – the discount rate, i.e. the return that could be earned per unit of time on an investment with similar risk;
\(N\) – the number of cash flow periods (usually years);
\(C_{t}\) – the net cash flow i.e. cash inflow – cash outflow, at time \(t\). Note that \(C_{0}\) is (minus) the investment.
Thus, finding the internal rate of return reduces to finding the roots of the above equation. In case of \(N = 1\) or \(2\) our calculator uses the formulas for finding the roots of linear or quadratic equations. For any other value of \(N\) a numerical solution can be used to estimate \(r\). Our online IRR calculator uses the secant method that, despite its simplicity, gives good results.
The internal rate of return is widely used in capital budgeting to measure and compare the profitability of investments. The higher IRR, the more desirable is the project. IRR can be applied to liabilities as well as investments. For a liability, a lower internal rate of return is preferable to a higher one. IRR may also be compared against prevailing rates of return in the securities market.
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