Money Matters

# Internal rate of return (IRR): What is it and how is it calculated?

To know the future profitability of your projects when investing in them, it is necessary to know the internal rate of return (IRR).

Companies and investors need to be able to assess the various investment options available to them. To do so, it is crucial to know how to calculate the IRR.

• We’ll explain what the internal rate of return is and why it’s one of the most commonly used formulas for choosing from among several investment options.
• We’ll show you the different ways of calculating the IRR.

#### Here’s what we’ll cover

When considering whether to invest in a project, there are two key points for investors: an executive summary that entices them and an internal rate of return that guarantees the project’s profitability.

Companies also use the IRR to decide which projects to invest in.

## What is the internal rate of return?

The IRR is an indicator of the profitability, or yield, of projects or investments, such that the higher the IRR, the higher the yield. By calculating the internal rate of return for different projects, it becomes easier to decide which to invest in.

In the simplest terms, we can define the IRR as the percentage of revenues or losses that will occur as a result of an investment.

This financial concept can be compared with the minimum acceptable rate for investing, which is the risk-free rate of return, or with the interest rate that will be applied to the financing of a project.

• In the first case: if the IRR is higher than the risk-free rate of return or the opportunity cost, the investment is selected; if not, it is rejected.
• In the second case: the IRR has to be higher than the interest rate of the project’s financing. Here, the internal rate of return would be the maximum interest rate for the financing at which the company or investor would not lose money in the investment.

## What is the IRR formula?

The IRR is the discount rate at which the net present value (NPV) becomes zero or, putting it another way, the rate at which the sum of the present value of outlays becomes equal to the sum of the present value of the forecasted revenues.

## Interpreting the IRR

If you’re an investor with your own money to potentially invest in a project, the following cases are possible.

#### IRR > 0

The project is acceptable, given that its yield is higher than the minimum required yield or opportunity cost.

This means that if you invest in this project you would make more money than if you had invested in Government Bonds.

#### IRR < 0

The project should be rejected.

The reason is that the project’s yield is lower than the minimum required yield. In this situation, it wouldn’t make sense to proceed with the investment given that you’d make more money investing in Government Bonds.

#### IRR = 0

In this case, it makes no difference whether you proceed or not, given that you wouldn’t make or lose money.

When the IRR is zero or close to zero, you have to take into consideration other types of advantages you’d get by investing.

If you need financing to invest in a project, you have to compare the IRR with the cost of money, which we can call k.

#### IRR – k

In this case, the net yield of the project is the difference between the IRR and the cost of the loan (IRR – k).

• If IRR > k. The project can be accepted. The yield is higher than the cost of the capital lent to you.
• If IRR < k. The project should be rejected. The yield of the project would not cover the cost of the loan.
• If IRR = k. Other factors would have to be considered, given that you would neither make nor lose money.

If you’re considering which one of two projects to select, in theory it is recommended to choose the one with the higher IRR; however you also need to consider each project’s risk, duration and initial investment.

## An example of calculating the Internal Rate of Return

To carry out a project, a company has to make an initial investment of \$10,000, from which two cash inflows are expected: \$4,000 in the first year and \$9,000 in the second year. You can calculate the internal rate of return in one of two ways:

Using the internal rate of return formula, in which NPV is made equal to zero:

IRR is the unknown quantity. Solving the equation gives an internal rate of return of 0.17, so the investment’s yield is 17%.

Using a financial calculator or a spreadsheet such as Excel.

In Excel, the calculation is straightforward: first you need a column or row containing the flow of profits generated by the investment, with the initial flow given a negative sign as it’s the initial capital outlay; next, insert the IRR financial function in another cell — for the formula, select the range of capital flows for the project, including the initial one.

If you need to assess various investment projects, you have to use the Internal Rate of Return to select the best option and avoid choosing a project that would lose you money.