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# What is the formula for calculating internal rate of return (IRR) in Excel?

Updated at 2018/07/13
A:

The internal rate of return (IRR) is the core component of capital budgeting and corporate finance. Businesses use it to determine which discount rate makes the present value of future after-tax cash flows equal the initial cost of the capital investment. Or, to put it more simply: What discount rate would cause the net present value (NPV) of a project to be \$0? We expect that projects to grow our business will give us some return over time, so what is the lowest level of return we can tolerate? The lowest level is always the cost of capital to fund the project.

If a project is expected to have an IRR greater than the rate used to discount the cash flows, then the project adds value, while if the IRR is less than the discount rate, it destroys value.  This decision process to accept or reject a project is known as the IRR Rule.

One advantage of using IRR, which is expressed as a percentage, is that it normalizes returns – everyone understand what a 25% rate means, compared to the hypothetical dollar equivalent (the way the NPV is expressed).  Unfortunately, there are also several critical disadvantages with using the IRR to value projects.

In the first place, you should always pick the project with the highest NPV, not necessarily the highest IRR – because, at the end of the day, your financial statements are measured in dollars, not percents.  If faced with two projects, Project A with 25% IRR and Project B with 50% IRR, but Project A has a higher NPV, you would pick Project A.   The second big issue is that mathematically, the IRR assumes you can always continue to reinvest any incremental cash flow at the same IRR, which is infrequently the case.  A more conservative approach is the Modified IRR (MIRR), which assumes reinvestment at the discount rate.

## The IRR Formula for Excel

The IRR cannot be derived easily. The only way to calculate it by hand is through trial and error, because you are trying to arrive at whatever rate which makes the NPV equal to zero.  For this reason, we'll start with calculating NPV:

NPV= ∑ {After-Tax Cash Flow / (1+r)^t} – Initial Investment

Broken down, each period's after-tax cash flow at time t is is discounted by some rate, r.  The sum of all these discounted cash flows is then offset by the initial investment, which equals the current NPV. To find the IRR, you would need to "reverse engineer" what r is required so that the NPV equaled zero.

Financial calculators and software like Microsoft Excel contain specific functions for calculating IRR, but any calculation is only as good as the data driving it. To determine the IRR of a given project, you need to first reasonably estimate the initial outlay (the cost of capital investment), and then all the subsequent future cash flows. In almost every case, arriving at this input data is more complex than the actual calculation performed.

## Calculating IRR in Excel

There are two ways to calculate IRR in Excel:

• using one of the three built-in IRR formulas
• breaking out the component cash flows and calculating each step individually, then using those calculations as inputs to an IRR formula.  As we detailed above, since the IRR is a derivation there is no easy way to break it out by hand.

The second method is preferable because financial modeling best practices require calculations to be transparent and easy to audit.  The trouble with piling all of the calculations into a formula is that you can't easily see what numbers go where, or what numbers are user inputs or hard-coded.

Here is a simple example. What makes it simple, among other things, is that the timing of cash flows is both known and consistent (one year apart).

Assume a company is assessing the profitability of Project X. Project X requires \$250,000 in funding and is expected to generate \$100,000 in after-tax cash flows the first year, and then grow by \$50,000 for each of the next four years.

You can break out a schedule as follows (if table is hard to read, right-click and hit "view image"): The initial investment is always negative, because it represents an outflow.  You are spending something now, and anticipating results later. Each subsequent cash flow could be positive or negative; it depends entirely on the estimates of what the project delivers in the future.

In this case, we get an IRR of 56.77%.  Given our assumption of a weighted average cost of capital (WACC) of 10%, the project adds value.

Keep in mind the limitations of IRR: It will not show the actual dollar value of the project, which is why we broke out the NPV calculation separately.  Also, recall that the IRR assumes we can constantly reinvest and receive a return of 56.77%, which is unlikely.  For this reason, we assumed incremental returns at the risk-free rate of 2%, giving us an MIRR of 33%.

## The Bottom Line

The IRR helps managers determine which potential projects add value and are worth undertaking.  The advantage from expressing project value as a rate is the clear hurdle it provides – as long as the financing cost is less than the rate of potential return, the project adds value.

The disadvantage to this tool is that the IRR is only as accurate as the assumptions that drive it, and that a higher rate does not necessarily mean the highest value-add project.  Multiple projects can have the same IRR but dramatically different return profiles due to the timing and size of cash flows, the amount of leverage used, or differences in return assumptions. Another factor to keep in mind: IRR's assumption of a constant reinvestment rate, which may well be higher than a conservative risk-free rate.