I wrote these documents many years ago when I was working on a mortgage originations system. The first one called 'mortgage handout' is a handout for a high level presentation about the basics of loan calculations. But if you really want to get into the mathemathical details you will want to read the mortgage calculation library document.

## Mortgage Calculations

## Cap Rate Versus IRR

What is the cap rate?

The cap rate or capitalization rate is a simple ratio that is determined by dividing the net operating income or NOI by the property’s purchase price or current market value, with the final number expressed as a percentage.

For example, a property that’s valued at $1 million and has an NOI of $100,000 would have a cap rate of 10%. A property that’s valued at $500,000 with an NOI of $25,000 would have a cap rate of 20%. A higher cap rate usually indicates a greater degree of risk and, typically, a higher expected return.

The net operating income refers to the property’s annual return, minus any operating costs such as taxes or maintenance. Expenses related to capital improvements and depreciation are not a part of NOI, so are not factored into the tally.

NOI can be expressed in a number of ways: current NOI, projected NOI after stabilization (that is, after improvements are made to the property to increase rents or raise occupancy levels), or forecast NOI (in the case of new development). It is critical for prospective investors to understand the specific assumptions that are built into the NOI figures as presented.

What cap rate tells investors

The cap rate is a point-in-time snapshot that investors can use to compare different investments at a given moment. Specifically, it offers the investor one measure of how much risk they’re taking on with a particular property, how the property stacks up against similar properties in the same market and what kind of current income they can reasonably expect if all of the assumptions are born out in reality.

It’s also possible to use the cap rate to make an educated guess about an investment’s payback period. This is the length of time required for a property to yield enough profit to recover the initial cash outflow. To get a rough estimate of the payback period, express the cap rate as a whole number and divide it into 100.

For example, if an investment has a cap rate of 10% the formula would look like this:

100/10 = 10 years

Obviosly, the payback period isn’t set in stone. There are a myriad of reasons why operating income (the OI in NOI) might change, for better or worse. If the cap rate increases or decreases over time, the payback period would be correspondingly shorter or longer.

What is IRR?

Like the cap rate, IRR is also expressed as a percentage but it offers one measure of the investment’s value over the entire holding period. In simpler terms, the internal rate of return is the percentage rate earned on the investment during the specific time frame in which it’s invested, assuming a reinvestment of cash flows at the IRR.

For example, an investor who holds a property for five years would earn interest on the income received during the first year for the remaining four years. Income received during the second year would earn interest for the next three years and so on. But interest received in the 2nd year is worth less than the interest earned today because of the time value of money or TVM. oWe will not get into the actual calculation here, but taken together, the interest earned on each year’s income (after discounting future earnings) would represent the IRR.

Another way of evaluating an investment is to consider the Net Present Value or NPV of the investment. The NPV tells investors whether they’ll be able to achieve their target rate of return, based on the present value of cash inflows and outflows. The IRR reflects the rate of return at which the Net Present Value becomes zero. For financial professionals, NPV is the preferred method of evaluating the economics of a particular investment.

Why IRR is important?

When compared to the cap rate, it’s clear that the IRR uses a more multi-dimensional approach to estimating returns. Instead of zeroing in on a single moment in time, the IRR projects returns over the entire ownership period based on more than just the NOI and purchase price. IRR and NPV analysis is also more robust in allowing investors to consider changing NOI assumptions over time, or changing assumptions about liquidation value.

While the IRR is used to estimate potential returns, it provides more than just a detailed picture of how much an investor stands to gain. For example, the IRR can be calculated with and without taxes factored in. By crunching the numbers both ways, it’s possible for an investor to determine his effective tax rate for the year.

When to use cap rate vs. IRR

Cap rate is often used as a “quick and dirty” way to estimate value when buying or selling a property and it’s especially useful when working up an offer. For example, if a seller lists the cap rate at a percentage point that’s below the average for similar properties in that same location, the investor might use it to scale their purchase price down.

Investors would also tend to rely more heavily on the cap rate when investing in single tenant properties with a long-term lease. In that scenario, the income is likely going to stay the same and it’s easier to calculate the annual operating expenses.

With an asset like an office building or strip mall, however, where multiple tenants may be moving in and out from one month to the next, it becomes more difficult to get an accurate picture of what the cap rate actually is. In that scenario, the IRR would be a more reliable standard for gauging returns because it looks at projected cash flow over the life of the investment.

If the property’s rents are increasing annually or the operating expenses are creeping up, the IRR will pick up on that information whereas the cap rate won’t because it’s based on the NOI and market value at a fixed point. In short, the IRR is a more comprehensive method for anticipating potential returns.

All financial professionals would agree that NPV and IRR analysis offer investors a more robust estimate of potential return, compared to NOI. As with NOI estimates, however, the assumptions used to produce IRR and NPV analysis are critically important, and an IRR calculation is only as useful as the assumptions that underlie it. It is as important to analyze the assumptions as it is to compare the mathematical results!

The bottom line

Both the cap rate and IRR are useful for assessing whether an investment is worthwhile, though neither one is without certain flaws and limitations. The cap rate, for example, doesn’t take into account financing, which would directly affect the final rate calculation. With the IRR, it’s impossible to predict with 100% certainty what a property may eventually sell for, at what pace income from rents will grow, or the rate at which cash flows can be reinvested. Unforeseen expenses, changes in vacancy rates, and other factors also affect investment returns and are difficult to predict with accuracy.

Ultimately, both measures play an important part when making investment decisions. Just remember that as with anything, the cap rate and IRR are only as accurate as the information that’s used to calculate them. That’s why it’s crucial for investors to make sure they have the complete picture on a property before crunching the numbers.