Passive Investor Series Part 8: Misconceptions of The Rule of 72

When evaluating different real estate deals, there are common returns discussed, including AAR, IRR, Cap Rate, and Equity Multiple. It is not uncommon to see a deal sponsor use AAR and IRR to show investors the type of returns they can expect. Every once-in-a-while, however, I do see the misuse of AAR and IRR when a deal sponsor is showing the return on their proposed investment. While in the long-run this is not a huge deal, having the understanding of the difference between the AAR and IRR is something every deal sponsor should understand. As a passive investor, this will help you be more informed and understand what your true returns are.

AVERAGE ANNUALIZED RETURN (AAR)This is also known as the Annualized Rate of Return (ARR). To calculate the AAR, you will add up all of the cash received from cash flow and any capital event(s), including refinances and sale. Next, subtract the capital invested from the total, then divide this number by the capital invested. This will give you the return on investment (ROI) as a percentage. From here, divide this percentage by the number of years invested and the result is the AAR.

Example: An investor who invests $100,000 and receives $40,000 in cash flow and $150,000 when the property sells after 5 years.

Step 1: $150,000 + $40,000 = $190,000 (Add up all cash flow and proceeds)
Step 2: $190,000 - $100,000 = $90,000 (Subtract total from the capital invested)
Step 3: $90,000 / $100,000 = .9 or 90% (Divide by capital invested)
Step 4: 90% / 5 years = 18% (Divide by years invested)
AAR = 18%

AAR is a useful measure because it helps give a general understanding of how the investment performs annually on average. The above example does not mean the investor will return 18% every year, but over the life of the investment they will average 18%. There may be little payout at the beginning of the investment, but a larger payout at the end or vice versa.

Another positive of this measure is its ease to calculate. You just need a few numbers and it can be done on the back of an envelope.

INTERNAL RATE OF RETURN (IRR)The technical definition is the “discount rate that makes the net present value of an investment zero”. In more simple terms, it is the expected compound annual rate of return that will be earned on an investment. IRR incorporates the concept of time value of money (TVM), which means that it adjusts returns based on the fact that money received today is more valuable than money received in the future. So, the sooner you receive capital back in the investment, the more it is worth. The big assumption is you are reinvesting the funds you get back and are receiving the same return as the rest of the investment.

This is one of the most common returns used in real estate for the fact that the timing of returns are taken into consideration. However, calculating IRR is very complicated and is not easily done by hand. Excel has a very handy formula that will quickly calculate it for you.

IRR’s advantage is the timing of the returns, but does it really matter to an investor if these funds are not reinvested?

THE MISUSED “COMPOUND ANNUAL GROWTH RATE (CAGR)”In real estate, the term IRR and AAR are often used to discuss returns on a property. There is another calculation investors often misuse when discussing real estate called CAGR. No, this is not a party you went to during college. CAGR (Compound Annual Growth Rate) is used frequently when discussing stock investment returns and is often confused with IRR and AAR.

CAGR “is the rate of return (RoR) that would be required for an investment to grow from its beginning balance to its ending balance, assuming the profits were reinvested at the end of each period of the investment’s life span.

CAGR measures the return on an investment over a certain period of time. IRR also measures investment performance. While CAGR is easier to calculate, IRR can cope with more complicated situations.

The most important distinction between CAGR and IRR is that CAGR is straightforward enough that it can be calculated by hand. In contrast, more complicated investments and projects, or those that have many different cash inflows and outflows, are best evaluated using IRR.” (Investopedia)

Three numbers are needed to calculate the CAGR: 1) beginning balance, 2) ending balance, and 3) years invested. These are similar to what is needed to calculate AAR; hence, why investors easily confuse the two calculations.

When the stock market averages a 7% return over the last 50 years (fact!), this is the compound annual growth rate. This is different from a flat percentage return on your capital. Let’s look at an example:

From 2000 to 2020, the S&P 500 and DOW averaged approximately 7.5% to 8% annual returns. During this same period, if you received a flat 7.5% return on capital, then it’s return equaled what the stock market did without all the ups and downs in the market. In addition, if an investor received a 4.75% compounded return, it also equaled the stocks returns. This compound interest is what led Albert Einsten to say, “[c]ompound interest is the eighth wonder of the world. He who understands it, earns it … he who doesn’t … pays it.”

CAGR is an investment return compounded over a specified time period. This is also where I often hear real estate investors incorrectly say their investment will double in five years with a 15% AAR.

What this investor is using is the Rule of 72. This rule is not really a rule, but a generalized formula to estimate when an investment will double based on a fixed return. To use the Rule of 72, take a fixed rate of return and divide it by 72.

For example, an investment with a 15% return should double in 4.8 years:
72 / 15% = 4.8 years

You can also use this formula to find out what return you need for an investment to double.

For example, to find out what return is needed for an investment to double in 3 years, you will do the following calculation:

72 / 3 years = 24%

What is important to note about the Rule of 72 is the return used is the compounded return and not an average annualized return.

Going back to the earlier example, the 15% AAR is not going to double the investment because AAR is not a compounded return, so the Rule of 72 formula does not work here. Since AAR does not compound, the AAR return after 5 years will be 75% (15% x 5 years) and will not double.

Let’s show an example with the side-by-side comparisons of the returns. In this example, an investor invests $100,000 and receives various amounts of cash flow with a return of capital at the end of year 5 along with $50,000 in proceeds from the sale.

AAR: 16.2%
IRR: 13.5%
CAGR: 12.6%

In this example, the AAR is 16.2% and the CAGR is 12.6% and this investment will not double during the investment period. If we incorrectly take the AAR and apply it to the Rule of 72, the result is 4.4 years. The correct return is 81% (16.2% x 5 years). If you apply the CAGR to the rule of 72, then the result is 5.71 years (72 / 12.6%), which correctly shows the investment has not doubled.

Let’s change the above example with the side-by-side comparisons of the returns. In this example, all the cash flow returns remain the same but with $75,000 in proceeds from the sale.

AAR: 21.2%
IRR: 16.6%
CAGR: 15.6%

As can be seen here the CAGR is 15.5% while the AAR is 21.2%. This investment will double because the CAGR is above 15% and the AAR is above 20%. If you add up all the cash flow and proceeds, it equals $206,000 which shows the investment does double in value ($206,000). Adding up the AAR shows a 106% return (21.2% x 5) which is correct and a 5 year CAGR at 15.6% shows the same return.

Just for fun, what if some capital was returned earlier in the investment through a refinance? Let’s take a look:

AAR: 21.2%
IRR: 20.2%
CAGR: 15.6%

Look at how the IRR rockets up to over 20% by just returning some of the capital a few years earlier but both AAR and CAGR stay the same. As mentioned before, IRR takes into account the timing of the return of capital, so IRR will change depending on when capital is returned.

It is important to pay close attention to the returns and how they are calculated. There are operators who do not know the difference between the AAR and IRR, and many confuse it with CAGR. By understanding this calculation, you can confidently calculate the returns of potential opportunities presented to you and ensure you are receiving the returns stated.

If a sponsor says their investment will double in 5 years, then find out what they are using to calculate this return. With the knowledge you have of the different returns discussed here, you can know whether what they are saying is true.