# What is Internal Rate of Return (IRR)?

Internal Rate of Return is a measure frequently used in capital budgeting and securities valuations. Financial managers might base their decision for accepting or rejecting a project on IRR, along with the NPV measure. When computing the IRR, we are simply looking for the discount rate at which the project’s NPV is equal to zero.

## How is IRR interpreted?

Projects are accepted when the IRR is greater than the opportunity cost of capital, or

Accept when IRR > r, and
Reject when IRR < r

The opportunity cost compares one economic choice to the next best one. In the context of IRR, it refers to the potential rate of return from the next highest-valued alternative investment. This said, the IRR might be viewed as a hurdle rate that should be beaten for the project to be accepted.

## How is IRR calculated?

The formula for calculating IRR is the following:

0=NPV=-Outlay+ \displaystyle\sum_{t=0}^N \frac{CF_{t}}{(1+r)^t}

The term CF_t is the expected net cash flow at time t, N is the projected life of the investment and the Outlay is the amount of the initial investment.

## Example of Internal Rate of Return

Suppose that Alpha is a large company operating in the shipbuilding sector. Its R&D department has made a scientific breakthrough. They have developed a new ship prototype that will travel 20% faster than existing ship models and will be 10% more efficient in terms of fuel consumption. However, this innovation requires the construction of a new shipbuilding plant. The project consists of an initial investment of $130 million and is expected to generate after-tax cash inflows of$70 million for the next year and $60 million and$50 million for the second and the third years, respectively.

The company’s finance department has assessed that the project’s cost of capital is 9%. Now, the firm’s CEO wants to know whether the investment would make economic sense.

We can use Microsoft Excel and its embedded IRR formula to find this out.

As the company’s required rate of return (or the opportunity cost) is 9%, the investment project appears to be acceptable on a stand-alone basis.

Excel offers three functions for calculating the internal rate of return – IRR, XIRR, and MIRR. The first one assumes that all the periods in a series of cash flows are equal.

Moving on to XIRR, it is a more versatile function. It gives you the flexibility to assign specific dates to each cash flow, making it suitable for cash flow series that occur at irregular intervals.

Finally, we have the Modified Internal Rate of Return function (MIRR). It works just as the IRR function, except it incorporates the cost of borrowing and reinvestment rate.

Internal Rate of Return is mostly valued for its simplicity. It is easy to interpret and is often included in more complex analyses. Besides, it is economically sound as it considers the time value of the money. Unlike the Payback Period, IRR takes into account the whole project’s life, which is another added advantage one should consider.

However, there are a few disadvantages that need to be examined when evaluating a project:

IRR should not be simply viewed as a measure of return. That said, the solution to the example above does not mean that the project return is ~20% of its invested amount.

In addition, it assumes that all earned cash flows would be reinvested at the same rate, while it does not reflect the real cost of capital. Reinvestment at the same rate of return is uncommon in practice.

Moreover, IRR may not be the best option for comparing projects with different timelines. A longer project may have a low IRR but high NPV, whereas a short-term project may add a small value but have a high IRR.

Lastly, you may come across unconventional cash flow patterns when calculating IRR. For instance, you might encounter the ‘Multiple IRR Problem’ or the ‘No IRR Problem’ if the sign of the cash flows changes more than once. Fortunately, these issues occur rarely.

## Conclusion

IRR simply provides us with a required (hurdle) rate above which the project is acceptable. It is a “Yes or No” tool to decide whether to make a certain investment. Of course, there are other measures of return that might also be used to rank multiple projects, such as the Payback Period and Discounted Payback Period.

Oftentimes, financial analysts include both NPV and IRR to their analysis as each of them provides a different perspective to consider.

How do we arrive at any conclusions when IRR and NPV rankings contradict? You might want to see NPV vs. IRR to find that out!

If you want to find out how to calculate IRR in Excel, take a look at our IRR Excel template.