It is time for
this blog to take another step toward legitimacy in the ever growing world of
real estate blogs. I am now going to address the frequently used and highly
touted real estate metric of Internal Rate of Return. I remember being mesmerized
by IRR when I was first learning about commercial real estate metrics. It was
introduced to me as the magic number that could explain the true return of a
property. I have since learned to respect it as one of the many tools that can
be used to understand the return value of an investment property or ABS, while understanding
its limitations.
In the interest of
brevity, I am going to explain IRR as it pertains to investment property. I
will not get into its uses in RMBS and CMBS bonds, as I will save that for a
later post. I also will not go into detail on the iterative,
successive-approximations technique by which the IRR value is derived. I am on
the fence as to whether or not such a discussion would be helpful to this blog.
Now that I have told you what I will not do, please allow me to begin my
discussion of IRR.
The Internal Rate
of Return is such a well-respected metric in real estate valuation, because it
allows one to derive the return of a set of cash flows in a matter that: 1)
accounts for the time value of money, 2) is not sensitive to the size of the purchase
price, 3) does not require one to independently find a discount rate.
Essentially, the IRR expresses the discount rate necessary for a set of cash
flows to set their Net Present Value (NPV) equal to zero. Let’s keep in mind
that I explained in a previous post the NPV as the sum of a property’s present
and future cash flows, discounted to present value by a chosen discount rate,
minus the amount of the amount of the initial investment. If a NPV equals 0,
that is an indication that the property is cash flowing at a given discount
rate. The IRR of a property is that discount rate.
The IRR is useful,
in that it expresses a true rate of return for a set of cash flows that is
comparable across property types and even asset classes. Despite its
usefulness, however, it does have some limitations. The first of these
limitations is that it can take some time to calculate an accurate IRR without
computer software. The IRR is calculated by deriving the NPV of a property and
successively guessing at the necessary discount rate, using each previous guess
to guide the next guess. IRR’s are most easily calculated with the help of
financial modeling software, such as MS Excel. The next and most major
limitation of the IRR is that it creates “non-unique” or multiple solutions
once negative cash flows are introduced into the calculations. Multiple “correct”
results are typically not helpful when using investment metrics, which is why
adjusted forms of IRR have been developed. Finally, the IRR does not give a
true picture of the difference in value that results from comparing different
investment opportunities that have different holding periods.
In order to
address the issue of non-unique solutions yielded by IRR calculations, a number
of variations on the metric have been developed. One such modified IRR is the
Financial Management Rate of Return (FMRR). The FMRR is a modification of the
IRR that takes each negative cash flow and discounts its value at the risk free
rate (typically the 10 or 30 year US treasury bill rate) back to the nearest
positive previous cash flow, adding it to that cash flow to cancel out the
negative value. The year in which the negative cash flow appeared is then given
a value of 0 and all negative cash flows are similarly discounted and added to
previous cash flows.
The Modified
Internal Rate of Return (MIRR) is another modification of the IRR that
discounts all negative cash flows at the risk free rate back to year zero,
adding them to the initial investment. Since the initial investment is already
a negative number, it is simply increased by the value of all the discounted
negative cash flows. The MIRR is the modified IRR formula used by Excel and
other Microsoft products, making it more frequently used than FMRR.
Another limitation
of IRR is that it does not account for reinvestment, which is necessary when
comparing two or more investment opportunities that have different timeframes.
For example, if a one was deciding between buying and holding building A for 3
years and buying and holding building B for 10 years, one must take into
account the fact that the proceeds of sale for building A will have been reinvested
for 7 years at the time of the sale of building B. This reinvestment caused by
the unequal timeframes of the two holding periods must be considered in
comparing the investment opportunities. This is where Capital Accumulation
Comparison (CpA) can come into play. Although CpA is not a measure of return, it
does provide a method of comparing investment opportunities with different
initial investments and holding periods. To calculate the CpA of a group of
investments, one must discount all negative cash flows to the first pervious
positive cash flow, using the risk free rate. Next, a reinvestment rate must be
chosen. This rate can be chosen from the return rates of realistic alternatives
for reinvestment. Then, each cash flow must be compounded at the reinvestment
rate to the end of the longest holding period. Finally, the initial investment
of each property must be subtracted from the cash flows. In the example above,
the cash flows of building A in would be compound at the reinvestment rate to
year 10.
A similar process
takes place when finding the CpA for properties with differing initial
investments. The difference between the initial investments must be compounded
at the reinvestment rate over the length of the longest holding period and then
added to the value of the CpA of the property with the smaller initial
investment. This process recognizes that for each opportunity to be truly
comparable, the amount available to invest must be the same in both instances,
but the portion of the initial investment that differs from the two properties
must be reinvested. The final CpA numbers are expressed in future dollars in
the same time period and are, thus comparable.
So that is IRR,
MIRR, FMRR and CpA. I credit Frank Gallinelli’s book on Cash flow for providing
much of the info for this post.
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