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Internal Rate of Return (IRR) of an investment is the rate of interest at which NPV is 0. It is the rate value for which the present values of the positive cash flows exactly compensate the negative ones. When the discount rate is the IRR, the investment is perfectly indifferent, i.e. the investor is neither gaining nor losing money.

Consider the following cash flows, different interest rates and the corresponding NPV values.

As you can observe between the values of interest rate 10% and 11%, the sign of NPV changes. When you fine-tune the interest rate to 10.53%, NPV is nearly 0. Hence, IRR is 10.53%.

## Determining IRR of Cash Flows for a Project

You can calculate IRR of cash flows with Excel function IRR.

The IRR is 10.53% as you had seen in the previous section.

For the given cash flows, IRR may −

• exist and unique
• exist and multiple
• not exist

## Unique IRR

If IRR exists and is unique, it can be used to choose the best investment among several possibilities.

• If the first cash flow is negative, it means the investor has the money and wants to invest. Then, the higher the IRR the better, since it represents the interest rate the investor is receiving.
• If the first cash flow is positive, it means the investor needs money and is looking for a loan, the lower the IRR the better since it represents the interest rate the investor is paying.

To find if an IRR is unique or not, vary the guess value and calculate IRR. If IRR remains constant then it is unique.

As you observe, the IRR has a unique value for the different guess values.

## Multiple IRRs

In certain cases, you may have multiple IRRs. Consider the following cash flows. Calculate IRR with different guess values.

You will get the following results −

You can observe that there are two IRRs – -9.59% and 216.09%. You can verify these two IRRs calculating NPV.

For both -9.59% and 216.09%, NPV is 0.

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