If you have ever analyzed an investment opportunity, you are probably aware of the concept of Internal Rate of Return (IRR). The beauty of this return metric is that you don’t have to do much studying to understand what it’s telling you. If you’re looking at an investment that has a projected IRR higher than your required rate of return, you are generally safe in assuming it is a solid investment.
Still, if you’re going to be a top investment analyst, you need to have a complete understanding of the calculation and what it is actually telling you. This lesson is going to give you a complete understanding of the concept and how you can use it to analyze deals.
What is IRR?
Let’s begin with an explanation of what IRR actually measures. IRR is the discount rate at which the net present value of an investment is equal to zero. It is a metric that measures the overall return of your investment as a percentage. Let’s go through a quick and easy example below.
Each investment has an initial cash outflow that is put towards the project. Let’s say you are investing in a stock that you are planning on selling in one year. You invest $10,000 into your shares, which is your initial cash outflow. After a year, the value of your shares is $11,000 and you close your position for a net gain of $1,000.
Cash Outflow: $10,000
Cash Inflow: $11,000
Net Profit: $1,000
So, what is the IRR of this project? Going back to the definition of IRR above, we need to find the discount rate that makes the net present value (NPV) equal to zero. Net Present Value is the value of all future cash flows divided by a discount rate minus the initial investment.
Where:
n = # of periods
t = time period
CF = cash flow
i = discount rate
In order to get an NPV of zero, you need to adjust the discount rate so all future cash flows are equal to the initial investment. In our example above, we need to divide the cash inflow of $11,000 by this rate to equal our initial investment of $10,000. Let’s take a look.
A discount rate of 10% discounts our future cash flow back to the amount of our initial investment, so this means that our IRR is 10%.
Detailed Analysis
We have the basics down, but each investment is different, so we need to show how IRR works in some different scenarios.
Multiperiod Scenario
Let’s use the same example we used earlier. You purchase shares of a company for $10,000 but now plan to sell them two years from now instead of one year from now. At the end of the two years, the shares are valued at $12,000. What is the IRR?
We use the same NPV calculation above and solve for x. When you do this, you get an IRR of 9.54%. If you look back to the previous example, you’ll see that the IRR was 10.00%. In that scenario we profited $1,000 in one year, and in this one we profited $1,000 per year, so what exactly is the difference?
Let’s look to the denominator of the equation above. In our first scenario, we had 1 in the exponent because the investment ended in one year. In this scenario, we have 2 because our investment ends in year two.
If the IRR was 10%, our denominator would be: (1 + 10%) x (1 + 10%) = 1.21. This is saying that an IRR of 10% would require a 21% overall return. Where did the extra 1% come from? It comes from the compounding of the IRR. When you’re calculating the return for a one year period, you’re not finding the return over your initial value, you’re finding the return over the previous year.
Let’s take our present value of $10,000 and show the compounding taking place so we can see the future value we would need to achieve the 10% IRR in the first scenario.
Year One
$10,000 x (1 + 10%) = $11,000
Year Two
$11,000 x (1 + 10%) = $12,100
From this, you can see that you would need $12,100 in year two in order to achieve an IRR of 10%. Since we only had a return of $12,000 in our example above, we had a lower IRR.
Now that we’ve covered IRR in a multiperiod scenario, we are close to having the full picture of IRR. However, we need to also take a look at IRR in a scenario where there are incremental cash flows.
Multiperiod Incremental Cash Flow Scenario
No Growth Scenario
The previous example is a helpful look at an investment like a stock that doesn’t pay any dividends. You have an initial investment, and the only way to get any returns is to sell your shares. Many investments, such as bonds, dividend paying stocks, and real estate, will have incremental cash flows returned to you before the close of the investment.
We need to make sure we understand the IRR calculation in these scenarios as well. The equation is the same as the one we showed above, but we need to go over each component. So, let’s say we invest $1,000,000 into a four-unit apartment complex that returns $50,000 annually. After three years, we sell it for $1,000,000. What is the IRR? Let’s build out our equation.
There’s no way to calculate this other than trial and error. When you plug these cashflows into a calculator or into Excel using the IRR function, it is just changing the value of x until an NPV of zero is hit. In this case, you will get an IRR of 5.00%.
Does this make sense? At first glance it definitely does. You invest $1 million and get $50,000 each year, which is 5.00% of $1 million. But hang on, in the last section we were discussing how IRR compounds each year. If this is the case, wouldn’t the $50,000 we receive in year 3 be worth less than what we receive in year one? And if this is the case, how can our IRR still be 5.00% if the 5.00% return we receive later on is worth less than the 5.00% return we get in year one?
These are the most difficult questions to answer when dealing with IRR. If you can understand this, you basically have a complete understanding of the topic. First, let’s make sure we aren’t going crazy and overthinking everything. We are already comfortable with the concept of multiperiod IRR with one cash outflow and one cash inflow, so let’s see what a 5.00% IRR would look like in that scenario.
In the equation above, x is equal to $1,000,000 x (1 + 5%)3 which is $1,157,625. When you subtract the initial investment of $1 million, you get a profit of $157,625. In our incremental cash flow example, our profit was only $150,000 and we achieved the same IRR. How can this be?
This can be explained by the reinvestment assumption in the IRR calculation. The reinvestment assumption assumes that any incremental cash flow you receive is going to be reinvested and achieve a return equal to the IRR. Let’s go through this below.
In year one, we receive $50,000. We likely aren’t just going to sit on that $50,000 for the next two years as the investment continues. We’re going to put it to use, and IRR assumes that we’re going to put it to use at the same rate of our current investment. The formulas below show how this will look.
$50,000 x (1 + 5%) x (1 + 5%) = $55,125
So, at the end of year three, if you invest these funds at the IRR rate, you will get a profit of $5,125 from that incremental cash flow. Let’s do the same for year 2.
$50,000 x (1 + 5%) = $52,500
The cash flow from year two grows by 5% for one year to get to the future value in year three, and we get a profit of $2,500 from it.
From our two years of incremental cash flow, if invested at the IRR rate of 5%, we would achieve an additional profit of $7,625. This is the exact difference in profit between the multiperiod scenario and incremental multiperiod scenarios we discussed above ($157,625 – $150,000 = $7,625). This proves that IRR is assuming incremental cash flow is being reinvested at the IRR rate and explains why we can achieve the same IRR with less profit when we have incremental cash flows.
Growth Scenario
I want to cover one more example with incremental cashflow. This is an example that will be useful for real estate professionals, where cash flows are typically growing every year due to inflation or market conditions.
Let’s use the example above, except cash flows increase by 5% each year, and the value of the property also increases by 5% annually. What would our IRR be? First, let’s find our cash flow in each year.
Year 1
$50,000
Year 2
$50,000 x (1 + 5%) = $52,500
Year 3
$50,000 x (1 + 5%)2 + $1,000,000 x (1 + 5%)3 = $1,212,750
When you calculate the IRR based on these calculations, you get a value of 10.00%. The example with no growth had an IRR of 5.00% which was tied directly to the annual return of 5%. From this example, you can see that IRR is equal to the base return (5%) plus the growth rate of cash flows and investment value (5%).
Most of the value created through this is from the appreciation in the value of the property rather than the growth in annual net income, but you do still need to grow both by 5% in order to hit the 10.00% IRR. Let’s go through a quick comparison to show the logic of IRR being equal to the base return plus the growth rate. We will do this by comparing this example to one where there are no incremental cash flows and the investment value increases by 10% each year.
Year 1
Incremental CF Value
$1,000,000 x (1 + 5%) + $50,000 = $1,100,000
No Incremental CF Value
$1,000,000 x (1 + 10%) = $1,100,000
Year 2
Incremental CF Value
$1,000,000 x (1 + 5%)2 + $50,000 x (1 + 10%) + $50,000 x (1 + 5%) = $1,210,000
No Incremental CF Value
$1,000,000 x (1 + 10%)2 = $1,210,000
Below is a quick breakdown of what happens in the incremental cash flow scenario in year two.
$1,000,000 x (1 + 5%)2: This is the investment value growing at a rate of 5% for two years
$50,000 x (1 + 10%): This is the year one cash flow being reinvested at IRR of 10%
$50,000 x (1 + 5%): This is our year two cash flow, which is the year one cash flow grown at 5%
Year 3
Incremental CF Value
$1,000,000 x (1 + 5%)3 + $50,000 x (1 + 10%)2 + $52,500 x (1 + 10%) + $50,000 x (1 + 5%)2 = $1,331,000
No Incremental CF Value
$1,000,000 x (1 + 10%)3 = $1,331,000
Below is a quick breakdown of what happens in the incremental cash flow scenario in year three.
$1,000,000 x (1 + 5%)3: This is the investment value growing at a rate of 5% for three years
$50,000 x (1 + 10%)2: This is the year one cash flow being reinvested at IRR of 10% for two years
$52,500 x (1 + 10%): This is the year two cash flow being reinvested at IRR of 10%
$50,000 x (1 + 5%)2: This is our year three cash flow, which is the year one cash flow grown at 5% for two years
As you can see, in each year the value in both scenarios was equal. This shows that growth and base return are both important factors to the IRR.
Limitations of IRR
We’ve now spent a lot of time gaining a thorough understanding of internal rate of return. Now it’s time to tell you that in many ways it is a flawed metric…sorry.
No investment metric is perfect. You should include several different metrics in your analysis of investment opportunities in order to get the full picture. As long as you understand the limitations, you can still use it to evaluate investment opportunities. Let’s go over some of the drawbacks.
Multiple IRR Scenario
If you have an investment with bizarre cash flows, there can actually be multiple discount rates that get you an NPV of zero. Let’s say you invest $100,000 into a stock. Next year, the value of this stock is $600,000 and you cash out.
You’re pumped. You’re the next Warren Buffett and you found your Coca Cola. The next year you decide to invest another $1,000,000 into the project. However, your luck has run out and the stock dips 50%, so you panic and sell your shares for $500,000. In total, you invested $1.1 million and got $1.1 million out of it, so you broke even. Won’t your IRR just be 0%. It will be 0%, but it won’t just be 0%.
The above picture is taken from Excel. The IRR formula in Excel asks you to input the cash flows and you have the option to enter in a guess for the IRR. The guess isn’t required, but is beneficial in cases where you believe there may be more than one IRR. When you enter a guess, Excel will look for the IRR closest to that guess. If there is only one IRR, it will just show that IRR no matter what you guess.
In the example above, I entered in three different guesses, and each produced a different IRR. This means that you can discount the cash flows above by any of those three IRRs and you will get an NPV of zero. The multiple IRR scenario occurs when there are multiple sign flips for cash flows. After our initial contributions we have a large positive inflow, followed by an outflow, and then followed by another inflow.
In a situation with multiple IRRs, it doesn’t make sense to report this metric. The information is pretty much meaningless, though I’m sure many investment managers wouldn’t mind reporting a 261% IRR. Metrics like equity multiple and compound annual growth rate would do a better job of showing that you came out even on this project.
Reinvestment Assumption
The aspect of IRR that people seem to struggle with the most is the reinvestment assumption. We commonly look at IRR only at the deal level. But do most investors only have one deal? Of course not. Investors have an entire portfolio of deals they need to take into account. The reinvestment assumption with IRR is that any cash flow you receive from the investment can be reinvested into other projects at the project-level IRR.
This isn’t always a great assumption. As an example, say you invest in multifamily properties. You were able to purchase an apartment complex from an investor in need of cash to paydown loans on other properties. This complex is in need of repairs and renovations, but it’s located in an area with homeowners who are known to fight against zoning for apartment complexes.
Because of this, there isn’t enough supply to meet the demand, and rents can be bumped up quite a bit. After renovations, you increase the rents and value of the property enough to achieve a projected 25% IRR. That’s an incredible return! The rest of your portfolio is around a 12% IRR. Here’s the issue. All of the cash flow you’re getting from that great returning investment is most likely going to be reinvested into projects similar to the 12% IRR investments.
Keep in mind, the project is still good, and you want to include projects with higher returns, but the returns to your overall portfolio are not going to be as good as the IRR leads you to believe. There is a way to modify IRR to account for the expected reinvestment rate, appropriately named Modified Internal Rate of Return (MIRR). This calculation will find the IRR of the project under the assumption that cash flow is reinvested at your typical return level.
Comparing Investments
IRR & NPV Mismatch
IRR is not a great tool for comparing two different investments. Many investment professionals think you can look at two projects and that the project with the higher IRR is always the best option. This isn’t always true, though. There are times when the project with a higher IRR than another project will have a lower NPV. Let’s take a look at the example below.
Project 1 has a higher IRR than Project 2, but Project 2 achieves a higher NPV. Both NPVs were calculated using a 5% discount rate. This means that the return the investor expects to return on their portfolio is 5%. Project 1 receives cash flows each year, and IRR assumes those cash flows are reinvested at the IRR return.
This is a bad assumption because the portfolio only expects a 5% return, so you can’t assume those cash flows will be reinvested at the higher IRR rate. The NPV calculation accounts for this issue and discounts all cash flows at the expected 5% return. The difference in assumed returns between the IRR and NPV formulas causes the mismatch.
If you are comparing two investments, and there is a mismatch between IRR and NPV, you should choose the project that has the higher NPV as long as it is above zero. Your focus should be how an investment adds value to your portfolio. IRR is a good measure for looking at a single investment, but not for looking at the impact on an entire portfolio.
Size and Duration of Investments
These issues are a bit more easy to see than the other ones so I will just give a quick explanation below. We’re close to the finish line and I don’t want to add another couple of miles. IRR doesn’t account for the size of different investments, so it isn’t useful for comparing two investments of different sizes.
For example, say you have to choose between two investments. One investment is $10,000 and returns a 50% IRR after one year, and the other is $1,000,000 and returns a 20% IRR over five years. It doesn’t matter that the $10k returns a 50% IRR because that’s such a small percent of your portfolio.
The same issue arises with duration. When two investments have different durations it can be difficult to evaluate which to use based solely on IRR for the same reasons. In the example above, say that first investment is $1,000,000 instead of $10,000. Now both of your options require equal investments. Can you safely say you should go with the 50% IRR option?
Nope. It would require further analysis. After the one year, if your assumed rate of return is 5%, the value of this project over five years could still be less than if you chose the 20% IRR option. You won’t know until you perform additional calculations.
In general, you shouldn’t be using IRR comparisons for two different investments. If you are going to use IRR to compare investments, it is best to only do it when the investments are of similar sizes and durations.
Conclusion
IRR is a fantastic return metric for analyzing individual investments, however, as we have discussed, it certainly has its drawbacks. If you become an investment professional, you are going to see that IRR is the most common metric used to evaluate investments and portfolios, even with its drawbacks. Now that you have a full picture, you will be able to understand when this may cause problems.
I hope you enjoyed learning about IRR. We will be adding more lessons as time goes on, including lessons on NPV and MIRR so you can get a better picture on how these metrics relate to one another.