We have covered Internal Rate of Return in a previous article. Now it is time to cover Modified Internal Rate of Return (MIRR). The goal of MIRR is to fix some of the common limitations with IRR, of which there are plenty. If you have a solid understanding of IRR, this won’t be too complex of a lesson to get through. If you don’t have a solid understanding, I encourage you to check out our IRR article linked above.
What is MIRR?
MIRR is IRR’s overachieving younger brother. It makes up for all of the mistakes of IRR. It is an annual return that assumes funds are reinvested at a specified rate, and that future cash outlays use present-day funds invested at a specified financing rate. It’s difficult to grasp the concept just by seeing the definition, so let’s go through the formula and show an example.
Below are the cash flows for an investment with a time horizon of five years. It has an initial cash outflow in year zero, and an additional one in year one. After that, the investment has cash inflows for the remainder of the investment.
The MIRR equation below is what we will be using to calculate the MIRR for the example above. At first glance, it looks a fair bit easier than the IRR formula, but it’s actually a bit more complex.
Let’s start with the numerator, FVPCF, which stands for Future Value of Positive Cash Flows. The future value of every positive cash flow is added together to get the total FVPCF. The equation below shows how this is calculated.
Where:
n = # of periods
t = time period
PCF = positive cash flow
r = required return
We see that we have positive cash flows in years two through five, so let’s show the calculation. We’re going to assume our required return is 10%, as that is our typical return for the rest of our portfolio.
When you add up all of these values, you find that the sum of the positive cash flows in year five is equal to $1,692,300. Now that we have our numerator, let’s move on to PVNCF, which stands for Present Value of Negative Cash Flows. Below is the equation we will use to find the PVNCF.
Where:
n = # of periods
t = time period
NCF = negative cash flow
f = financing rate
Our negative cash flows are in years zero and one, so let’s show the calculation for those two periods. We’re going to assume our financing rate is 5%, as that is the rate we can invest our capital at until it is needed for the investment.
When you add these values together, you find that the sum of the negative cash flows in year zero is equal to $976,190. We now have everything we need to calculate our MIRR for this project.
The MIRR as shown in the equation above is 11.63%. We calculated that all cash inflows grown at the reinvestment rate of 10% to Year 5 are equal to $1,692,300, and all cash outflows discounted at the financing rate of 5% to Year 0 are equal to $976,190. Once we found this, we were able to calculate the annual growth rate required for the present value to equal the value of future cash flows over the five year investment period.
MIRR Returns vs. IRR Returns
So, we’ve seen an example of how MIRR is calculated, we know how it corrects some limitations of IRR, and now it is time to see how its returns compare to IRR. This isn’t too difficult to understand. We have discussed how IRR and MIRR are different, and it should be easy to tell why the returns shown by each vary. Let’s go through a few examples below.
No Financing Examples
In the example below, we are assuming a reinvestment rate of 8.00% for the MIRR formula, as that is our required rate of return. The calculated MIRR is lower than the IRR. All of those incremental cash flows of $70,000 are assumed to be reinvested at 8% for the MIRR equation and 10.26% for IRR, which explains the difference in values for these two metrics. All else being equal, the metric that assumes the higher reinvestment rate is going to have the highest return.
In the below example, we have the same cash flows as the investment we just discussed. As you can see, the IRR is the same, but the MIRR is now higher than the IRR. This is because we have adjusted the reinvestment rate from 8%, which is lower than the IRR, to 12%, which is higher than the IRR.
Financing Example
Now that we understand how MIRR returns compare to IRR with different reinvestment rates, it is time to see how different financing rates will affect the MIRR in relation to the IRR. Keep in mind that IRR does not have a separate rate for cash outflows because all cash flows, no matter if they are positive or negative, are discounted by the IRR.
We know that a required return rate higher than the IRR gives you an MIRR that is higher than the IRR. Now we need to see if the same is true for financing rate. In the examples below, we have set the required return equal to the IRR so that the only differences between the IRR and MIRR are caused by our financing rate assumptions.
For the example below, we are going to assume a financing rate of 5.00%. This is lower than the IRR percentage, and you can see that because of this, the MIRR is lower than the IRR. The reason is simple. By discounting the $100,000 in Year 1 by a lower rate, it means that we require more money today in order to achieve this value by Year 1. This increases the present value of our cash outflows and in turn lowers our MIRR.
Let’s do one more example to confirm that we are thinking about this correctly. The below example assumes a financing rate of 12.00%, which is higher than the IRR. As you can see, the MIRR is now higher than the IRR because the financing rate is higher than the IRR. We are discounting the Year 1 cash outflow by a higher amount in the MIRR formula, which means that we will need less money today in order to have $100,000 a year from now.
We’ve discussed that the financing rate represents lower risk investments that companies would put funds into until they are ready to be used. In the example above, we set it to 12% and then invested it into a project getting a lower return. Does this make sense? No, not at all. If a lower risk investment gets you a higher return, you shouldn’t invest in this project. I just wanted to show you all how the assumption affects the MIRR.
What IRR Limitations Does It Correct?
Multiple IRR Scenario
The multiple IRR scenario is an issue when there are multiple changes between positive and negative cash flows during your investment period. Occasionally there are two or more IRRs that can be used to achieve a net present value of zero.
This problem isn’t an issue for MIRR because we are setting the required rate of return ourselves. Any cash flows being reinvested must be done at the rate we set, so there can only be one MIRR because of this.
Unrealistic Reinvestment Rate
One of the biggest complaints about the IRR metric is the assumption that cash flows will be reinvested at the IRR. This isn’t usually an accurate depiction of how things will work out for a company’s investment.
The cash flows from an investment will be reinvested at the rate of return of a typical investment in the portfolio. There is no guarantee that the IRR for this individual investment represents a typical return.
The MIRR equation allows you to set the exact rate of return you want for cash flows depending on the return you would expect to receive in your typical portfolio.
Not Accounting for Financing
The IRR calculation does not account for the financing of cash outflows. Whether the cash flow is positive or negative, it is discounted by the internal rate of return. This doesn’t make a lot of sense, though, because that isn’t how most companies should be looking at money they contribute to an investment.
If a company is planning on putting $5 million into a project a year from now, they need to make sure they have that money available, so they will probably have funds set aside gathering interest in a security that is either low-risk or risk-free.
How Often is it Used?
So, MIRR clearly has a lot of benefits. It must be used by quite a few investment professionals, right? Well, in my entire investing career, I don’t believe I have ever seen it used. That’s not to say that you won’t, but in private equity it is not a metric that sees much use.
There are a couple reasons for this. First, private equity funds typically aren’t reinvesting funds after an investment is completed. Instead, these funds usually get returned to investors and they are free to do whatever they wish with their returns. Each investor will have a different rate of return so there isn’t a uniform way to represent MIRR to all investors.
More importantly, if you’re doing your job right, MIRR is going to be lower than IRR because your IRR is going to be higher than your required rate of return. Nobody ever wants to report a lower number when showing results to investors, so no general partner would ever want to show the MIRR.
Portfolio management teams can benefit from MIRR because they need to look at an entire portfolio of investments and not just a single one. Therefore, they need to see how each individual deal contributes to the entire portfolio. Essentially, it’s a great internal measure of projected performance but shouldn’t really be used as an external measure.
Conclusion
Even though MIRR isn’t used in every area of investing, it is still a great metric and will help you better understand some of the flaws of its more popular counterpart, IRR. If you find yourself in a portfolio management or corporate finance role, this can be a valuable metric to use in order to see the overall effect the investment has on your overall portfolio.
I hope you have enjoyed learning a bit more about the modified internal rate of return. If you would like to learn more, I encourage you to head over to our Learning page for more real estate and finance lessons. Also, be sure to check out our Internal Rate of Return lesson if you haven’t yet.