# Tag: real estate

## NPV, PI, IRR, FMRR, MIRR, CpA — Stirring the Alphabet Soup of Real Estate Investing, Part 2

#### IRR – Internal Rate of Return

Internal Rate of Return (IRR) seems to befuddle many investors, but if you understand Discounted Cash Flow and Net Present Value, then you already understand IRR. That’s because it is really the same process, but one where you are solving for a different unknown.

In DCF, you believe you know what the future cash flows will be, and you believe you know the rate at which those cash flows should be discounted. Your mission is to figure the Present Value of the cash flows.

With IRR, you still believe you know what the future cash flows will be, but now you know the Present Value and want to find the discount rate. How is it that you know the Present Value? This is a deal happening in the real world. The PV is the amount of cash you are paying for those future cash flows.

When you solve for the IRR, you are looking for the discount rate that accurately describes the relationship between those future cash flows and the money you put on the table on Day One.

When you’ve found the discount rate that makes the PVs of the future cash flow equal to your initial investment, you’ve found the IRR. You can express this another way: When you’ve found the discount rate that makes the NPV equal zero, you’ve found the IRR.

Admittedly, the math to find the IRR is ugly, but if you’re reading this then you probably have a computer (or a highly sensitive gold filling that also picks up the BBC on the Internet); there are plenty of tools, including Microsoft Excel and our own RealData software that will do the job for you.

IRR is the measurement of choice for many investors because it take into account both the timing and the magnitude of your cash flows. Consider this example:

You still have that \$300,000 to invest, and you can invest it in the property you saw in the first example, yielding these cash flows and IRR:

 Year 0 Initial Investment: (300,000) Year 1 Cash Flow: 10,000 Year 2 Cash Flow: 20,000 Year 3 Cash Flow: 25,000 Year 4 Cash Flow: 30,000 Year 5 Cash Flow: 385,000 (includes the proceeds of sale) IRR = 10.32%

Or you can acquire this property:

 Year 0 Initial Investment: (300,000) Year 1 Cash Flow: 80,000 Year 2 Cash Flow: 50,000 Year 3 Cash Flow: 30,000 Year 4 Cash Flow: 10,000 Year 5 Cash Flow: 300,000 (includes the proceeds of sale) IRR = 12.97%

If you add up the cash inflows and outflows for both properties, you will find that each has \$300,000 going out in Year 0, and a total of \$470,000 coming in over the next five years. However, the second property shows a significantly higher IRR. Both properties have the same total number of dollars going out and coming in over five years, but the second property shows a greater return on investment. Why?

Because IRR is indeed sensitive to both the timing and amount of cash flow. The first property has a big payday, but you have to wait five years to get the money. In the meantime, annual cash flows are relatively modest.

In the sale year the second property returns combined cash from operation and resale that is only as much as you originally invested to acquire the property. However, the intervening cash flows are much larger, especially the earlier ones. The early cash flows are especially valuable because you don’t have to wait long to receive them and therefore you don’t have to discount their values so greatly.

But Wait…

This sounds terrific; we’ve found the perfect way to measure our investment’s return. But wait – on closer inspection, IRR has a few warts. Sometimes its results are imperfect, sometimes even misleading. In the third installment of this series, we will look at the problems with IRR and at some potential solutions. We’ll examine FMRR and Modified IRR, and how they provide us with a means of dealing with the shortcomings.

—Frank Gallinelli

####

Your time and your investment capital are too valuable to risk on a do-it-yourself investment spreadsheet. For more than 30 years, RealData has provided the best and most reliable real estate investment software to help you make intelligent investment decisions and to create presentations you can confidently show to lenders, clients, and equity partners. Learn more at www.realdata.com.

## NPV, PI, IRR, FMRR, MIRR, CpA – Stirring the Alphabet Soup of Real Estate Investing, Part 1

NPV, PI, IRR, FMRR, MIRR, CpA–It may seem like a witch’s brew of random letters, but truly, it’s just real estate investing. You can handle it. Any or all of these measures can be useful to you, if you understand what they mean and when to use them.

#### NPV – Net Present Value

NPV, or Net Present Value, is connected to what all good real estate investors and appraisers do, namely discounted cash flow analysis (aka DCF, if you’d like some more initials).

Discounted Cash Flow is a pretty straightforward undertaking. You project the cash flows that you think your investment property will achieve over the next 5, 10, even 20 years. Then you pause to remind yourself that money received in the future is less valuable than money received in the present. So, you discount each of those future cash flows by a rate equal to the “opportunity cost” of your capital investment. The opportunity cost is the rate you might have earned on your money if you didn’t spend it to buy this particular property.

Consider this example, where you invest \$300,000 in cash to earn the
following cash flows:

 Year 1 Cash Flow: 10,000 Year 2 Cash Flow: 20,000 Year 3 Cash Flow: 25,000 Year 4 Cash Flow: 30,000 Year 5 Cash Flow: 385,000 (includes the proceeds of sale)

If you discount each of these cash flows at 10%, then add up their discounted values, you’ll get 303,948:

 Year 1, Discounted: 9,091 Year 1, Discounted: 16,529 Year 1, Discounted: 18,783 Year 1, Discounted: 20,490 Year 1, Discounted: 239,055 Total PV of Cash Flows: 303,948

Now you have the Present Value of all the future cash flows. However, you also had a cash flow when you initially purchased the property (call that Day 1 or Year 0) – a cash outflow of \$300,000, your initial investment. To get the Net Present Value, you find the difference between the discounted value of the future cash flows (303,948) and what you paid to get those cash flows (300,000).

 NPV = PV of future Cash Flows less Initial Investment NPV = 303,948 – 300,000 = 3,948

What does that mean to you as an investor? If the NPV is positive, it suggests that the investment may be a good one. That’s because a positive NPV means the property’s rate of return is greater than the rate you identified as your opportunity cost. The more positive it is in relation to the initial investment, the more inclined you’ll be to look favorably on this investment. Your result here is not stellar, but it is at least positive.

If the NPV is negative, the property returns at a rate that is less than your opportunity cost, so you should probably reject this investment and put your money elsewhere.

That’s all fine, to the extent that you’re confident about that discount rate, your opportunity rate. You estimated 10% in the example above. What if you adjust that estimate by one-half of one percent either way?

 NPV @ 9.5% = 10,284 NPV @ 10.0% = 3,948 NPV @ 10.5% = (2,244)

 NPV @ 9.0% = 16,789 NPV @ 10.0% = 3,948 NPV @ 11.0% = (8,238)

Clearly, the NPV here is very sensitive to changes in the discount rate. If you revise your thinking just slightly about the appropriate discount rate, then the conclusion you draw may likewise need to be revised. As little as a half-point difference could change your attitude from luke-warm to hot or cold. The prudent investor will test a range of reasonable discount rates to get a sense of the range of possible results.

While we’re beating up on NPV, let’s also note that it doesn’t do you much good if your goal is to compare alternative investments. To have some kind of meaningful comparison, you need at least to keep the holding period for both properties the same. But what if one property requires that \$300,000 cash investment, but the alternative investment requires \$400,000?

PI – Profitability Index

Fortunately, NPV has a cousin that can help you with that problem: Profitability Index. While the NPV is the difference between the Present Value of future cash flows and the amount you invested to acquire them, Profitability Index is the ratio. It doesn’t tell you the number of dollars; it tells you how big the return is in proportion to the size of the  investment.

So where the NPV in the example above was equal to 303,948 minus 300,000, the Profitability Index looks like this:

 PI = 303,948 / 300,000 = 1.013

If, quite improbably, you expected exactly the same cash flows from the property that required a 400,000 investment, you would expect your Profitability Index to be much worse, and it is.

 PI = 303,948 /400,000: = 0.760

A Profitability Index of exactly 1.00 means the same as an NPV of zero. You’re looking at two identical amounts, in one case divided by each other so they give a result of 1.00 and in the other case subtracted one from the other, equaling zero.

An Index greater than 1.00 is a good thing, the investment is expected to be profitable; an Index less than 1.00 is a loser. When you compare two investments, you expect the one with the greater Index to show the greater profit.

There is a good deal more stirring about in our alphabet soup, so join us for the next installment when we look at IRR – Internal Rate of Return.

—Frank Gallinelli

####

Your time and your investment capital are too valuable to risk on a do-it-yourself investment spreadsheet. For more than 30 years, RealData has provided the best and most reliable real estate investment software to help you make intelligent investment decisions and to create presentations you can confidently show to lenders, clients, and equity partners. Learn more at www.realdata.com.

## Estimating the Value of a Real Estate Investment Using Cap Rate

Why do you invest in income-producing real estate? Perhaps you are looking for cash flow. Possibly you anticipate some tax benefits. Almost certainly, you expect to realize a capital gain, selling the property at some future time for a profit.

Your projection of the future worth of the property, therefore, can be a vital element in your investment decision.

#### APPRECIATION

A fairly simple approach to this issue is the use of an appreciation rate. You bought the property today for X dollars. You make a conservative estimate as to the rate of appreciation, apply that rate to your original cost and improvements and come up with presumed future value.

The use of appreciation as a predictor of future value typically makes sense when the desirability of the subject property is based on something other than its rental income. The most common example, of course, is the single-family residence. Consider also a single-user rental property such as a small retail building on a main thoroughfare. The owner of a business operating as a tenant in such a location is probably willing to spend more for the building than an investor would pay. In general, rate of appreciation as a predictor of future value may be appropriate when comparable sales work well as a measure of present value (i.e., “Commercial buildings on Main Street are selling for \$200 per square foot by next year they will be up to \$225.”).

#### INCOME CAPITALIZATION

With most other types of income-producing real estate, what you paid for the property is not likely to make much of an impression on a new buyer. Witness the rapid run-up and even faster collapse of prices in the late ‘80s, and again in 2008. The typical investor will be interested in the income that the property can generate now and into the future. He or she is not buying a building, but rather its income stream.

That investor is likely to use capitalization of income as one method of estimating value. You have probably heard this referred to as a “Cap Rate” method. It assumes that an investment property’s value bears a direct relation to the property’s ability to throw off net income.

Mathematically, a property’s simple capitalization rate is the ratio between its net operating income (NOI) and its present value:

#### Cap. Rate = NOI/Present Value

Net operating income is the gross scheduled income less vacancy and credit loss and less operating expenses. Mortgage payments and depreciation are not considered operating expenses, so the NOI is essentially the net income that you might realize if you bought the property for all cash. If you purchase a property for \$100,000 and have a NOI of \$10,000, then your simple capitalization rate is 10%.

To use capitalization to predict value requires just a transposition of the formula:

#### Present Value = NOI/Cap. Rate

The projected value in any given year is equal to the expected NOI divided by the investor’s required capitalization rate.

To use capitalization rate as a predictor of future value, in short, is to use this logic: “I am buying this property with the expectation that its net operating income will represent a return on my investment. It is reasonable to assume that whoever buys the property from me in the future will have a similar expectation. That new investor will probably be willing to purchase the property at a price that allows it to yield his or her desired rate of return (i.e., capitalization rate).”

If you project that the property will yield a NOI of \$27,000, and that a new buyer will require a 9% rate of return (capitalization rate), then you will estimate a resale price of \$300,000.

You must never forget that, while the algebra involved here is simple, the judgments you need to make in order to achieve an accurate prediction of value are more complex. Your assumptions as to future years’ income and expenses have to be realistic.

The same is true of your estimate of a new buyer’s required cap rate. Look at the investment from the new buyer’s point of view and remember that there are other opportunities competing for his dollar. Would you buy an office building with a projected cap rate of 9% if you could buy a bond that yields 7%? What if mutual funds are rocking and rolling at 15% and more? To attract a buyer, your property may need to be priced so that its cap rate is competitive with alternative investment options. The higher the cap rate, the lower the price. In our example above, the property with the \$27,000 NOI capitalized at 12% might attract an offer of \$225,000.

Our discussion here has been limited to simple or “market” capitalization rates. If you would like to delve further into this topic you may want to look into “band of investment” or derived cap rates. In addition, follow our blog as we go into greater depth as to how investors look at a property’s projected long-term income stream when deciding if and on what terms to purchase an income property.

—Frank Gallinelli

####

Your time and your investment capital are too valuable to risk on a do-it-yourself investment spreadsheet. For more than 30 years, RealData has provided the best and most reliable real estate investment software to help you make intelligent investment decisions and to create presentations you can confidently show to lenders, clients, and equity partners. Learn more at www.realdata.com.

## Understanding Real Estate Resale

One topic that often gets less attention than it deserves from real estate investors, however, is resale. Some tend be dismissive, looking at resale as speculation, but many others simply find it difficult to focus seriously on the matter of selling a property they haven’t yet purchased.

It may take a little extra discipline to work a consideration of resale into your investment mindset, but it is just such discipline that often separates the successful investor from the sorry.

You care about the potential cash flow, the financing, the operating costs and the tax benefits. You had better care also about whether the property will be saleable after you buy it. Often one hears, “Yes, but I plan to keep it for 15 years, or until my toddlers graduate from med school, or until the Federal Reserve Board dances figure-eights on ice with the devil.”

That’s fine; may all your plans go without a hitch. But what if you need to sell this property next year? What if a better opportunity comes along in five years, and you want to cash out? Recite this mantra whenever you consider purchasing an income property: If it’s not worth selling, then it’s not worth buying.

The world may not be perfect, but at least it’s flat – flat, as in “level playing field.” You can reasonably assume that if you would scrutinize a property’s income, operating expenses, financing and various measures of return before you purchase, then tomorrow some equally astute investor will apply a similarly jaundiced eye to your numbers if you choose to sell. It pays, therefore, to run tomorrow’s numbers today, and to see just what this investment will look like to a future buyer.

So, what are the numbers that should concern you when you analyze the potential resale of an income property? The most obvious, and the most important, is the selling price. If you have followed some of our other articles, you know that with most income properties, you can estimate the value by applying a reasonable capitalization rate to the net operating income. (If you have not read the articles, you will get probably get more out of this discussion if you go back and read them first. Their links are Understanding Net Operating Income and How to Estimate Resale Value – Using “Cap” Rates.)

In brief, you first determine the property’s Net Operating Income (NOI). Next you must estimate the capitalization rate (i.e., the rate of return) that the buyer would reasonably expect. The NOI is the amount of the return and the cap rate is the rate of return. Hence, if the market expects a 10% return and your property produces a NOI of \$12,000, your estimate of its selling price would be \$120,000. Another way of articulating the algebra involved is to say, “\$12,000 represents 10% of what?”

A curious phenomenon exists in the real world. Buyers and sellers can look at the same information and see different meanings. This, I suspect, is the closest that commercial real estate will ever come to poetry. Not only might you have a different notion of “reasonable rate of return” as a seller, you might also change your perspective on NOI. It is common for a buyer to estimate value by capitalizing the current year’s NOI, and for a seller to capitalize next year’s expected NOI. The buyer typically takes the position, “I am buying the income stream that just happened, and the property’s value is based on that income stream. If the income goes up next year, that’s my business.” The seller, as a rule, will assert, “You didn’t own the building last year. You’re buying next year’s higher income stream. The value of what you’re buying should be based on that.”

You decide.

Once you develop your estimate of the resale price, the rest of the analysis of resale is fairly straightforward. You will need to calculate the estimated tax liability at the time of sale. Then, with that number in hand you can project the sales proceeds and the overall rate of return for the holding period.

If you use RealData®’s Real Estate Investment Analysis software, you will have all of these calculations done for you. Equally important, the program will test a potential resale each year, allowing you to identify an optimum holding period. Let’s look at just the first four years of such an analysis.

Our first task is to figure the gain. We do this by taking the selling price and subtracting from it the property’s Adjusted Basis.

What is the Adjusted Basis? It is the property’s original cost, plus capital improvements, plus closing costs and costs of sale, less accumulated depreciation. Essentially the Adjusted Basis is what you spent to purchase, improve and sell the property, less the amount you have already written off. If you sell the property for more than this amount, you have a taxable gain.

In calculating your tax liability at the time of sale, there are certain deductions that may come into play. For example, you may have had operating losses in prior years that you were not allowed to take because they exceeded your “passive loss allowance.” If you could not deduct them earlier, you can deduct them at the time of sale. You may also have had loan points and leasing commissions that you were amortizing (i.e., deducting over time). If you have an unamortized balance on these items, you can deduct it when you sell.

Now you have enough information to compute the tax liability due on sale.

No doubt your greatest concern is the amount of cash you will realize from the sale. To determine that figure you must take the selling price, subtract the costs of sale (such as legal fees and sales commissions), subtract the outstanding balances of all mortgages and add back any unused funds left over in your reserve account. Now you have your Before-Tax Sale Proceeds. Subtract the Federal tax liability and you have the After-Tax Sale Proceeds.

The timing as well as the amount of your resale are important to your overall return. In this example, the software is computing that overall return for different holding periods and you can see that the timing can make a substantial difference.

Internal Rate of Return (IRR) is one of the most commonly used methods of measuring the quality of a real estate investment. Others include Present Value, Return on Equity, Cash-on-Cash Return and Debt Coverage Ratio. Some of these measures are fairly sophisticated, while others are quite simple. Check the “articles” section of our blog for more about these topics.