# Internal Rate of Return (IRR): Definition, Calculation, and Example

The first thing to understand is that an Internal Rate of Return is not nearly as complicated as it sounds. Sometimes it seems like math guys really like to confuse us with their formulas and equations, but while it might seem complex, an internal rate of return is simply an interest rate that can help calculate how appealing an investment might be based on its current value.

**What Is Internal Rate of Return?**

The simple definition for internal rate of return is simply the rate of return at which the net present value of a project is equal to zero. Another way of thinking about it is you want the net present value to be equal to the cost of your investment, or better. You can use that information to determine whether you want to invest or not.

You can use the internal rate of return to determine your required rate of return that you'd accept in order to move forward with the investment. The idea is that if the required rate of return for a potential investment is below the internal rate of return, the net present value of that project (essentially the value of what your future investment is worth now), will be above $0, making it more acceptable in terms of risk.

Another way of thinking about it is this: You're trying to figure out whether the future returns on an investment are costing you anything in today's dollars.

I know. It sounds complicated.

**The Formula**

In this equation, CFt represents the cash flows in the period, r = your rate of return (this is where you're trying to find IRR to plug in), and t = the time period.

If you're not a mathematician, the Net Present Value, or NPV = The future cash flow returns on the investment that have been discounted to their value today, with your current investment subtracted from that value.

You actually cannot calculate the IRR through an equation, so you use the Net Present Value formula, and plug in rates until you find the rate that gets the net present value as close to zero as possible. This video shows a very good example of how you use the Net Present Value Formula for determining internal rates of return. If, like me, you don't want to sit there and plug in rates over and over until you find the IRR, you can also use a financial calculator, or a function within Excel.

## Example of IRR

Let's look at a simple example of IRR in a business situation. Say someone comes to you for a $2,000 investment. They will use your investment for some form of business venture, and will pay you $500 a year for 10 years in return for your investment today.

NPV=(-$2,000)+$500/(1+r)^1 + $500/1+r)^2 + $500/1+r)^3 + $500/1+r)^4 + $500/1+r)^5 + $500/1+r)^6.... And so on and so on until you have included 10 years.

I'll tell you right up front, I used a calculator, rather than working this out by hand with "trial and error." The internal rate of return bringing the net present value close to zero is 21.4%.

You can use this information when gauging an investment. Do you have the money up front? Or do you need to borrow in order to make the investment? If so, you need your own borrowing rates to be below 21.4% in order for the investment to be sensible for you. You call this your required rate of return (RRR). You could also view it as your cost of capital. If your cost of capital is lower than the internal rate of return on investment, the investment has merit. If the IRR is below your RRR, then it's a poor investment, as you'd technically be losing value.

**Pros and Cons of Using IRR**

First off, using NPV and IRR involve estimates. To get this right, you have to be correct in your estimates. If you're wrong, or if real life events alter outcomes, the IRR changes, or was never accurate to begin with. Furthermore, it's sort of an overly mathematical view. What about other points, such as the merit of the investment in terms of your grand strategy? What about the time constraints? Maybe you don't want to wait that long for the investment, despite the merits of the IRR. There is also the idea that an investment involving more capital with a lower internal rate of return, will still produce larger cash flow than a small investment with a higher internal rate of return. From that standpoint, you might look at allocating your capital differently, based on your tactics and point of view. IRR's also assume reinvestment of cash flows. That doesn't always happen.

As I said though, it's very useful for trying to gauge investments where you have capital costs involved, such as loans. You could also use it to gauge two separate investments, where your "capital cost" would be the difference between the investments IRRs.

**IRR vs. Compound Annual Growth Rate**

The compound annual growth rate is simpler than the internal rate of return, in that it only looks at the beginning values and end values, allowing you to gauge the return on that investment through that time. When looking at CAGR, you're simply saying "I invested $2,000 at this point, and the final value was $5,000 after five years."

[(Final Value) / (Initial Value)] ^ (1/n) - 1

[$5,000/$2,000]^(1/5)-1

So the Compound Annual Growth Rate would be 20.1%.

You can see it's a much simpler concept, and doesn't take into account the variables year to year like the NPV formula that is used for IRRs takes into account. Because of this, the IRR can be used for more complicated issues, like varying cash flows, or multiple investment installments made at different times, etc.

**IRR vs. Return on Investment**

The difference between internal rate of return, and return on investment is pretty straightforward. Your internal rate of return that we put together earlier, is showing us what we're making per year on our investment over time, along with helping with discounting cash flows to present values. A return on investment is simply what you made from beginning to end.

ROI: I invested $2,000. I ended up with $5,000. My return was $3,000.

[($5,000-$2,000)/$2,000]x100=150.

So my return on investment was 150%. It's my total return from the entire venture.

The hiccup here as compared to IRR is based primarily around time. If you're making a simple investment, with a short time horizon, or very few variables, ROI is a common and useful tool. But it's tough to estimate it ahead of time, unless the variables, cash flows, and costs are very straightforward.

**Do Your Homework**

While IRR can be a very useful tool in trying to gauge an investment's value based on your capital costs, and or comparing various investments in making decisions about how to allocate your current capital, these sorts of calculations always miss out on some piece of the unforeseeable real world. To that end, they're a nice complementary tool, but can't give you the whole story. Do your homework on investments. Know the management, know the business, know the industry.

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