# Internal Rate of Return (IRR)

Internal rate of return (IRR) is the most widely used alternative to NPV. The formula for IRR is very similar to the NPV formula. Finding IRR in capital budgeting can be compared to finding YTM in bond valuation. IRR is the discount rate that makes the project's NPV equal to zero ā the project's costs equal its revenues:

$$NPV \mmlToken{mo}[linebreak="auto"]{=}\sum_{i=0}^{t}\frac {C_{i}}{(1+IRR)^{i}}\mmlToken{mo}[linebreak="auto"]{=}0$$

tā number of periods.
Σā the Greek capital sigma denotes the mathematical sum (in this case, the sum of the terms).

IRR essentially represents the project's minimum expected return. If IRR exceeds the shareholders' required rate of return, after repaying debt capital to creditors, there will be surplus funds available to be paid out as dividends to shareholders or reinvested in the company.

While the IRR calculation formula may seem simple at first glance, it can be challenging to use in practice. The issue lies in the fact that IRR cannot be easily solved algebraically or isolated on one side of the equation. IRR can be found through:

1. trial and error;
2. systematic mathematical methods; and
3. calculators, software, or web applications equipped with the respective function.