# Internal Rate of Return

Internal Rate of Return (IRR) is a discount rate at which the Net Present Value (NPV) of a project is zero. In other words, IRR is the discount rate at which the present value of all cash flow from a project equals its initial capital investment. IRR is one of the most commonly used and popular metrics when it comes to investment appraisal and capital budgeting. The IRR method, through its use of NPV, follows the time value of money concept.

### How to calculate the Internal Rate of Return?

Before calculating the internal rate of return of a project, it is crucial to calculate its net present value at two different rates of return. The calculation of IRR also produces more accurate results if one of the NPVs calculated is positive, and the other is negative. Similarly, the closer both NPVs are to each other, the more accurate IRR it will produce.

Below is the formula to calculate the IRR of a project.

IRR = L + [NL / NL – NH x (H – L)]

In the above formula, ‘L’ represents the lower rate of return used in the calculation of NPV of the project. Usually, the lower rate of return will return a higher or preferably a positive NPV. Therefore, ‘NL’ denotes the NPV of the project calculated based on the lower rate of return. Similarly, ‘H’ represents the higher rate of return, while ‘NH‘ denotes the NPV of the project calculated using the higher rate. It is preferable that the value of ‘NH’ is negative to produce a more accurate result.

### How to make decisions based on the Internal Rate of Return?

The decision made based on the IRR of a project is straightforward. Usually, all businesses determine their required rate of return, which is the minimum return they want from a project. As stated above, IRR represents a point at which the NPV of a project is nil. For decision-making, any project that has an IRR higher than the required rate of return of the business is considered viable.

On the other hand, if the IRR of a project is lower than the required rate of return, then it is considered loss-making and often rejected. Sometimes, even projects with positive NPVs might get declined if their IRR is lower than the required rate of return of the business.

### Example

A company, Jet Co., wants to take up a new project. The company has already calculated the NPV of the project at two different rates of return. At a 10% rate of return, the NPV of the project is \$5,000. At 15%, the NPV is -\$3,000. Jet Co.’s required rate of return for the project is 12%. The company must, therefore, calculate the IRR of the project to make a decision.

The calculation of IRR for the project is as follows.

IRR = L + [NL / NL – NH x (H – L)]

IRR = 10% + [\$5,000 / (\$5,000 – (-\$3,000)) x (15% – 10%)]

IRR = 10% + [\$5,000 / \$8,000 x 5%]

IRR = 13.13%

Based on this calculation, Jet Co. can approve the project as the IRR of the project (13.13%) exceeds its required rate of return (12%).

### Conclusion

Internal Rate of Return represents the discount rate at which the net inflows and outflows of a project equal to zero. Businesses must calculate the NPV of the project, that they are evaluating, at two different rates of return to calculate its IRR. If the IRR of the project exceeds the required rate of return, then it is considered viable.