Estimating Terminal Cap Rates

[Curtis West]

Why is there a rate of decrease in NOI?

Perhaps I should have been a little more particular in the wording of the statement. Please let me rephrase.

If the rate of relative decrease in NOI is greater than the relative rate of decrease in value the terminal rate will be higher. Otherwise there will be a different relationship.

For example: If both NOI and Value are changing (in the same direction) at the same rate, the going-in rate and the terminal rate will be equal.

 

[Fred]

While you are free to perform your analysis however you choose, based upon my experience with institutional investors, you value conclusions will be approximtely 5% - 7% higher than those of most institutional participants. Concequently, would this then truely reflect "market value"?

You make it sound like buyers set the market by themselves. I know you don't mean to.

I also think, as my prior calculations show, that on a 10-year hold, you'd have to get a dump truck to load the terminal rate with approximately 250 basis points in order to lower model results by 7%. Any institutional investors loading it that much?

In any case, I don't think your point about systematic bias would hold up in a practical test. I don’t know whether to call it a fundamental principle of capitalization or the laws of arithmetic, but as long as you treat the comps and subject the same, you will extract every iota of consistency the market has to offer. For example, extract from rates from comps with no reserves, get a 10% Ro, and apply to subject with no reserves. Then take 5% reserves from the comps and subject and get the same value with a 9.5% Ro.

Same thing would happen with DCF. In your market, where they load the Rn enough to lower values by 7%, you’ll be extracting Yo’s of 10%, and the other analysts will be extracting Yo’s of about 9.2% and getting the same subject value. There would be no systematic bias.

 

[Curtis West]

For investment grade properties, the reported Korpacz survey data usually show that the yield rate is greater than the cap going-in rate (I don’t recall seeing any instance where the reported yield rate is lower than the going-in cap rate). This indicates a relative increase (or an expected relative increase) in property value over the holding period (or projected holding period). Given this indicated relationship; it is logical (in my opinion) to conclude that if the relative value of the investment property actually decreased over the holding period, then the relative NOI decreased at a greater rate (or amount) than the rate (or amount) of decrease in value. If not, why wouldn’t the reported data would show a yield rate that is lower than the cap rate?

 

[CBBoston]

Let’s think about this for a second. The value of any financial asset is the present value of the future cash flows discounted by the risk adjusted return. In simple direct cap we are using a shortcut method of discounting the NOI rather than running a DCF for perpetuity. In the DCF method we are discounting individual cash flows for the holding period but know there is still value being created by the cash flows after that point in time. We need the going-out cap rate is to calculate that terminal value. Cap rates is very similar to the weighted average cost of capital (WACC) that Wall Street would use to calculate value of, say, a stock. The formula for calculating WACC and cap rate are very similar except that WACC doesn’t include a factor for equity build-up. Given the prevalence of interest only loans an argument can be made that it should be omitted from the BOI. In finance we use the Gordon Growth Model to calculate WACC if dividends will increase at a constant rate in perpetuity. So they two are really identical.

Now thinking about the cap rate (or WACC) debt usually accounts for a sizable portion of the capital structure. If mortgage rates are historically low, like today (some of us can still remember double digit rates) the cap rate will be relatively low. Equity rates are usually some spread above debt rates to reflect the additional risk in holding an equity position. Therefore in low interest rate environments going-in cap rates should be relatively low. Interest rates in general are a reflection of expected inflation. So if inflation expectations are low, interest rates will be low. The low inflation expectations in part explain why cap rates have been historically low the last several years. Also competition among investors and high expected growth rates of NOI may have driven down cap rates.

Knowing the conditions under which the going-in rate was determined will guide us in estimating the going-out rate. Is inflation expected to increase over the holding period? Currently all indications are that expected inflation will increase. Therefore mortgage rates will increase which will cause the cap rates to increase. At the same time equity rates will have to increase to compensate investors for additional risk causing the going-out cap rate to increase by even more. Under these conditions the going-out rate should be higher than the going-in rate. Just the opposite would be expected if the current interest rate environment is high and expected inflation is expected to decrease, the going-out rate could be lower than the going-in rate.

The 1.5% used by the AI might make sense in a stable interest rate environment. However, like others have mentioned I doubt that an additional 10 years in age of a commercial property will have too much impact on its riskiness. Other factors such as space market conditions may have a much bigger impact on equity return expectations.

The bottom line here is that in all likelihood whatever you use for the going-out rate will be wrong. It’s more important that you use sound financial theortical logic to come up with the rate.

 

[Fred]

Let’s think about this for a second. The value of any financial asset is the present value of the future cash flows discounted by the risk adjusted return. In simple direct cap we are using a shortcut method of discounting the NOI rather than running a DCF for perpetuity.

I agree direct cap is a short cut. I think this discussion shows we know what we are short cutting and that is not going to be true in discussions found in other parts of the forum. And since Denis is here for advice, he should take note at this point that if you have a "perpetual" interest and a stablized property, the type of situation discussed in these last few threads, a DCF isn't really needed, because we know how to adjust the shortcut to get the same result.

That means that if you do this with and without the shortcut you should get the same result or know exactly why they are different. This is simply is a matter of math, as there is only one income stream.

As you say, let's take a second to think, Using a holding period and developing a reversionary value, rather than taking projections out to 50 years is a type of shortcut too. However, market value of stabilized property doesn't vary with the length of the holding period. If your model results change every time you change the holding period, then you just built in error above what the market itself generates. That is, your holding period models will vary, while your direct cap doesn't move or your 50-year DCF doesn't move. The only way to keep the length of the holding period from moving affecting the results, is to keep Rn equal to Ro.

The bottom line here is that in all likelihood whatever you use for the going-out rate will be wrong. It’s more important that you use sound financial theortical logic to come up with the rate

With emphasis on theoretical and wrong. It seems to me that what you mean by theoretical is coming up with some hypothesis that rationalizes moving the Rn. It would always be anecdotal, and there would always be a countering anecdote. I would say that is exactly what makes an Rn "wrong." On the other hand, recognizing that using a holding period is a shortcut, part of a formula, and making sure the shortcut itself (length of the holding period) doesn't affect results is exactly what makes it "not wrong." My Rn is not a forecast. It's a safety pin.

The bottom line for me is why would I want to make a rote procedural change that lowers value by 5%, versus consciously and explicity lowering value 5% and being able to explain why it's not 10%.

 

[hastalavista]

For investment grade properties, the reported Korpacz survey data usually show that the yield rate is greater than the cap going-in rate (I don’t recall seeing any instance where the reported yield rate is lower than the going-in cap rate).

Curtis-

I will now attempt to apply what I have allegedly learned and see if it sticks to the wall! :new_smile-l:

Your part in bold is consistent with what I believe is called the General Model, that is the overall capitalization rate (Ro) is equal to the overall yield rate (Yo) minus any change in value (designated by "∆a") so that
Ro = Yo - ∆a. Value can be a change in the income stream or a change in the property's value (reversion).

Therefore, the overall yield rate must be greater than the going-in (overall) cap rate if there is a positive change in value. I assume that Korpacz (and any other surveys) would always have a Yo > Ro because to have it the other way around, the change in value would need to be negative for the yield to be less than the overall cap rate. While this does happen in the real world, my assumption is that no one plans to purchase a property and lose money.

And since Denis is here for advice, he should take note at this point that if you have a "perpetual" interest and a stabilized property, the type of situation discussed in these last few threads, a DCF isn't really needed, because we know how to adjust the shortcut to get the same result.

Steven-

I am taking note and this discussion is valuable to me. To be sure that I am in-sync with your post, in the case where there is no change in value (∆a = 0), then Ro = Yo, which would be similar to an interest bearing account (or a bond).

The changes that can occur in value were described in my courses as:
a. A change income.
b. A change in the value of the property (reversion).
c. A combination of the two.

When the change is irregular in the income, a DCF is necessary.
When the change is regular in the income (constant) a shortcut formula can be used. Ditto when the income is level and there is a change in the value of the property.
When income and property value are changing at the same compounded rate, the shortcut is really easy (Ro = Yo - CR(compounded rate)).

Did I get it correct?

 

[Fred]

Denis

Because…no one plans to purchase a property and lose money.

A reduction in income and/or value is not losing money. This could vary on whether you are an economist (foregone income) or an accountant (cash) , but to “lose” money you would need something more like Yo less than zero. Remember, even if it takes 100 years to get you $1 back, your "cash flow" is breakeven.

When the change is irregular in the income, a DCF is necessary.

You know "it depends" right? There are degrees of irregularity. One of the things I said in the last post is that there are shortcuts around having to make a DCF model while still getting the same number. Also, you can sometimes do what I showed in the post where I showed how much loading the cap rate affects value. (That’s why I agree with CB’s idea that it’s all discounting, but there are shortcuts). However, if there is enough irregularity, you will get to a point where you have to make a DCF model.

 

[Curtis West]

Denis,

I agree with the following

Therefore, the overall yield rate must be greater than the going-in (overall) cap rate if there is a positive change in value.

But I can not agree with

Value can be a change in the income stream or a change in the property's value (reversion).

As you know, Value is the present worth of anticipated future benefits (often thought of as income, for commercial investment properties). While a change in income might cause a change in value, there are also other things might cause a change in value. If I am not mistaken, in the formula that you referred to as the General Model; Δ represents the total (lump sum) change in Value (regardless of what caused that change. It (Δ) does not represent a change in income. Since I am not familiar the label General Model, I am assuming that it refers to the formula similar to the one that you posted, but includes one additional factor (the sinking fund factor), as shown below:

RO = YO – (ΔO x 1/SN)

In this formula, the sinking fund factor (1/SN) is used to annualize ΔO (the total change in value for the overall property). In other words, the average annual income equals the average annual yield minus the average annual change in value. Here, the income rate, the yield rate, and the annual change rate, are all constant (or stabilized) amounts.

While it is true that income patterns are seldom (if ever) constant over a given holding period, it is also true that there is no provision in the above formula for change in the level of income. Likewise, there is no provision in the formula RO = I / V for a change in income. Ellwood recognized this many years ago and cautioned that the RO (developed by use of his formula) should only be applied to constant or stabilized income. He also developed formulae for calculating “J” and “K” factors that could be used to modify the RO for use in analyses involving changing income patterns. Today the “Ellwood Formula” and the “J” and “K” factors are seldom used because its easy to use spreadsheet templates or canned software programs for DCF analyses involving changing income levels.

 

[Howard Klahr]

You make it sound like buyers set the market by themselves. I know you don't mean to.

While Buyers do not set the market by themselves, Buyers do set the price of transactions.

Today the “Ellwood Formula” and the “J” and “K” factors are seldom used because its easy to use spreadsheet templates or canned software programs for DCF analyses involving changing income levels.

The reason the DCF analysis is utilized more frequently today (often over utilized) is because the availability of spreadsheets and other software programs allow a more detailed analysis which more closely reflect the actual cashflows modeled in evaluating a property. (i.e. - rollover vacancy, renewal probabilities, leasing costs/commissions/TI/etc, downtime, expense recoveries). The refinement of the cashflow to this degree is not possible with adjustments to the capitalization rate such as with J and K factors.

However, K and J factors often work great in evaluating long term ground leases as the variables in these situations are often limited compared to those of an improved property.

 

[hastalavista]

As you know, Value is the present worth of anticipated future benefits (often thought of as income, for commercial investment properties). While a change in income might cause a change in value, there are also other things might cause a change in value. If I am not mistaken, in the formula that you referred to as the General Model; Δ represents the total (lump sum) change in Value (regardless of what caused that change. It (Δ) does not represent a change in income. Since I am not familiar the label General Model, I am assuming that it refers to the formula similar to the one that you posted, but includes one additional factor (the sinking fund factor), as shown below:

RO = YO – (ΔO x 1/SN)

In this formula, the sinking fund factor (1/SN) is used to annualize ΔO (the total change in value for the overall property). In other words, the average annual income equals the average annual yield minus the average annual change in value. Here, the income rate, the yield rate, and the annual change rate, are all constant (or stabilized) amounts.

Curtis-

That is one of the "shortcut" formulas that I was referring to. There are two others- unfortunately, since I do not deal with this in practice, I have to refer to my books (at the office) to respond- and I will when I refresh myself.
It could be I am not understanding the theory properly and I know that you guys will straighten me out if that is the case. :new_smile-l:

Thanks