Explain IRR one more time

Internal Rate of Return (IRR) is a common metric for comparing investment opportunities. It shows up everywhere and is a critical concept for aspiring investors to grasp.

It wasn't sinking in for me and I was feeling quite dense until I took the time to experiment with some examples and play around with numbers in a spreadsheet. This post captures the steps that led me to a better understanding of IRR. Hopefully it can help you too!

What is IRR?

IRR is a measure of the return on an investment, weighted by the time value of money.

Imagine that two distinct investments offer the opportunity to double your money in 10 years, therefore they both offer a 100% cash-on-cash return. Investment A returns a portion of your profits at the end of each year, while Investment B returns all profits in a single lump sum at the end of the 10 year period. Investment A will have a higher IRR because IRR gives more weight to earlier returns. The money returned at the end of year 1 in Investment A could be deployed for 9 more years in another deal to produce additional gains. By having all your money tied up for 10 years with Investment B, you may lose out on another investment opportunity of which you could have taken advantage of by getting money out of Investment A sooner. This is called Opportunity Cost and you'll often hear Opportunity Cost mentioned as a justification for the value of the IRR.

Breaking down an example

In this example, we purchase a property for an initial cash investment of $100,000 and sell it five years later for $204,200. The property yields an annual cash flow of $6,000 each year we hold it.

If we enter this information into a spreadsheet it looks like this:

A few things to note: The initial investment is represented as a negative value because it's money going out, whereas the other values are money coming in. The year 5 cash flow is $6,000 + the sale price of $204,200 = $210,200.

Calculating IRR

The IRR for this investment is 20%. We calculate it using the IRR function (under the Insert -> Function -> Financial menu) in Excel or Google sheets.

The above example investment could be thought of as a series of cash flows. Each cashflow in the series matures at a different rate (1, 2, 3, 4 and 5 years). The IRR is the compounding rate of return for each cash flow in the series. You can unwind the IRR calculation by determining the present value (PV) of each cash flow, discounted at the IRR.

What!?

Reverse engineering IRR

Let's reverse engineer our IRR example above. We have to reverse engineer each of the five cash flows. Luckily, there's a formula we can use, Present Value (PV). PV backs into the present value of a future cash flow based on the interest rate, the length of time and the future cash flow value.

Our first cash flow was $6,000 that matured over one interest period (1 year). If the IRR function determined the compounding interest rate of each cash flow to be 20%, then that $6,000 cash flow must have started out as $5,000 and compounded at 20% for one year to become $6,000. The second cash flow of $6,000 compounded for two interest periods (2 years), so it started out as $4,166,67. Using the PV function, we've calculated the present value of each of the five cash flows:

The sum of present values of all future cash flows equals ~$100,000. This illustrates how our initial investment of $100,000 can be viewed as five initial investments that compound at 20% for different lengths of time to produce our future cash flows. That's the magic of the IRR!

Why didn't the sum of discounted cash flows equal exactly $100,000? That's because IRR isn't a simple formula, it's a heuristic that uses trial and error to find the return rate that most closely discounts your cash flows back to your present value!

IRR vs CoC return

Now let's introduce another common metric used to evaluate the return on an investment, annualized cash-on-cash (CoC) return. Annualized CoC return is the non-time-value-weighted equivalent to IRR. Let's go back to our example to see how they differ.

The sum of all our cash flows equals $234,200 ($6,000 * 4 + $210,200). That's $134,200 profit on our $100,000 initial investment, or a 134.2% cash-on-cash return. If we divide that by five years, we get 26.84% annualized CoC return.

Two different methods of evaluating the performance of the same investment yield significantly different results (20% IRR and 26.84% annualized cash-on-cash return). Our example investment provides a great return, but you get most of that return at the end of the five year period. Another 5 year investment may have a lower annualized return, like 24%, but a higher IRR, like 22%, because you're receiving larger annual cash flows in years 1-4.

That's the power of the IRR. It's a sophisticated measure of investment performance that's widely used throughout the industry as a means of comparing apples-to-oranges investments. So far, the apples-to-oranges analogy applies to comparing investments of the same length of time, but with different distributions of cash in that time. Does IRR help compare investments that are even less similar?

Bonus: investments with different time horizons

What if we add another year into our example (a $30,000 cash flow in year five).

If we recalculate our annualized CoC return, it now yields 27.367%. That's up from 26.84% in our previous five-year investment. Wow! This six-year investment is a better deal!

Not so fast...our new IRR is 19.54%, down from 20%.

What does this mean?

In the six-year investment, we're delaying our big cash out event by a year. IRR takes into account the time value of that money and tells us it's better to get that payout a year earlier and get our money working for us in another deal sooner. Annualized CoC favors the longer-term investment because that year 5 cash flow is just above the average cash flow if you distributed distributions equally over all six years.

Recap

• IRR and CoC return are both useful metrics for evaluating investments, but IRR takes into account more information, such as time value of money and mismatching time horizons.
• Computing an IRR requires evaluating all cash flows separately and computing a single compounding interest rate that explains how each cash flow compounds from a portion of your initial investment to the ultimate cash flow that goes into your pocket.