# The IRR, XIRR and MIRR functions in Excel

In this article, Léopoldine FOUQUES (ESSEC Business School, Global Bachelor of Business Administration, 2017-2021) presents the IRR function in Excel to compute the internal rate of return of a series of cash flows.

## About Excel

Excel is by far the most used financial modeling tool across the world to build models and perform analysis. Knowing which Excel function to use can help employees in the financial sector (financial analysts, fund managers, risk managers, traders, etc.) to work faster and build a more powerful model.

## The internal rate of return (IRR)

### Definition

The computation of the internal rate of return (IRR) is based on the net present value (NPV) of an investment. In financial modelling, an investment is represented by a series of cash flows: CF_{0}, CF_{1}, CF_{2}, …, CF_{T}. For a classic investment, the first cash flow, CF_{0}, is negative (outflow) and the future cash flows, CF_{1}, CF_{2}, …, CF_{T} are positive (inflows).

The net present value (NPV) of an investment is computed according to the following formula:

where r is the discount rate that takes into account the risk of the project.

The IRR corresponds to the value of the discount rate for which the NPV is equal to 0:

The IRR is the solution of a non-linear equation:

### Use in finance

One of the most important functions is the Internal Rate of Return (IRR) function, as it’s an easy function to compare an investment’s return, based on a series of cash flows.

The function is very useful in financial modeling. Indeed, it’s frequently used to compare scenarios before deciding about a project. An example is when a company is presented with two opportunities: one is investing in a new factory and the second is expanding its existing factory.

By using IRR, we can estimate the IRR for each scenario and verify which one is higher than the average cost of capital of the business (the Weighted Average Cost of Capital or WACC) is a calculation of a firm’s cost of capital in which each category is proportionally weighted).

## The Excel functions to compute the IRR

Building a math-based calculation is time-consuming and complicated, so Excel offers three functions for the calculation of the internal rate of return: IRR, MIRR, and XIRR.

### The IRR function

The IRR function uses one required argument and one optional:

- The values: they represent the series of cash flows, including net income value and investments.
- The guessed number for the expected internal rate of return. If omitted, the function will default to 0.1 (= 10%).

You can download the Excel file below in which I illustrate the use of the IRR function in Excel based on a simple example.

Note that the IRR corresponds to a period rate. Monthly cash flows lead to a monthly IRR, quarterly cash flows lead to a quarterly IRR; and annual cash flows lead to an annual IRR. As, in practice, the standard is to work annual rates, monthly and quarterly IRR have to annualized.

Note that the use of the IRR function assumes that the period between each cash flow is the same (equal-size payment periods), for example one year.

### From the IRR function to the XIRR function

If the period between each cash flow is not the same, the IRR function should not be used. It is the case with monthly cash flows as the months of the year may contain 28, 29, 30 or 31 days.

In this case, the XIRR function comes into play to calculate a correct internal rate of return, taking into consideration the periods of different sizes.

The XIRR function has three arguments:

- The values
- The dates for cash outflows and inflows.
- The guessed number for the expected internal rate of return (optional argument).

You can download the Excel file below in which I illustrate the use of the IRR and XIRR functions in Excel based on a simple example.

### From the IRR function to the MIRR function (Modified Internal Rate of Return)

The MIRR function is quite the same as the IRR function, except that it takes into consideration both the cost of borrowing the initial investment funds (discount rate) and reinvestment rates for future cash flows.

In contrast to IRR, MIRR assumes that cash flows from a project are reinvested at the firm’s cost of capital (rate of return on a portfolio company’s existing securities).

To compute the MIRR, the Excel function uses the following parameters:

- The values
- The guessed number for the expected internal rate of return (optional argument).
- The financial rate: the finance rate of interest paid
- The reinvest rate: the interest rate earned from the reinvested profit

Where FV represents the Future Value of positive cash flows at the cost of capital for the company, PV represents the Present Value of negative cash flows at the financing cost of the company, and T represents the number of periods.

You can download the Excel file below in which I illustrate the use of the IRR and MIRR functions in Excel based on a simple example.

Some of the accountants say that the MIRR function is less valid than the other because not all the flows are reinvested fully. Although we can use a less important interest rate to compensate the partial investment; but we think the best approach will be the inclusion of the three calculations (IRR, XIRR, and MIRR).

## Limits of the IRR

The non-linear equation for obtaining the IRR may have one solution, several solutions or no solution according to the sequence of cash flows. These represent limits of the IRR as an investor would like one value when estimating its investment.

Another limit of the IRR as a decision criterion for investing is that the result is not in agreement with the decision criterion based on NPV, which represents the value created by the investment.

You can download the Excel file below in which I provide an example to illustrate the limit of the IRR when selecting investment when two projects are available.

## Useful resources

Mazars Excel IRR Function And Other Ways To Calculate IRR In Excel

## Related posts on the SimTrade blog

▶ Chollat-Namy R. Bond valuation

▶ Longin W. How to compute the present value of an asset?

▶ Paulen J. The IRR function in Excel

▶ Roero de Cortanze R. The Internal Rate of Return

## About the author

The article was written in November 2021 by Léopoldine FOUQUES (ESSEC Business School, Global Bachelor of Business Administration, 2017-2021).