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Adjusting overall rates and gross income multipliers: a fresh perspective.

Recently, a well-respected tax appeal attorney with a strong background in the valuation of income-producing real estate posed the question of why it is considered taboo for appraisers to make quantitative adjustments to overall capitalization (cap) rates derived through comparable sales and gross income multipliers. After all, he argued, since appraisers are able to make quantitative grid adjustments to comparable sales and rentals for a myriad of factors, why are cap rates and gross income multipliers immune from such analysis? This article is based on the contention that comparable sale-derived overall cap rates (|R.sub.0~s) and gross income multipliers (GIMs) can and should be adjusted quantitatively to a given subject property in adjustment grid analysis by segregating the income and sale price components of the comparables.


Appraisal educators emphasize that differences between comparable sales and rentals can be adjusted quantitatively through adjustment grids. Relative to |R.sub.0~s derived from comparable sales and GIMs, however, educators suggest that adjustments should be made more subjectively. As noted in The Appraisal of Real Estate, tenth edition, "If there are differences between a comparable property and the subject property that could affect the overall capitalization rate selected, an appraiser must account for these differences. In such cases an appraiser must decide whether the rate chosen for a subject property should be higher or lower than the rate in a specific sale. Appraisal judgment is also needed to determine whether the rate selected for the subject should fall within the range established by the sales or, as in certain cases, be set above or below the range."(1)

Although it does not state so directly, this quotation seems to refer to an unadjusted overall cap rate range that should be adjusted to a given subject property according to "appraisal judgment" without mentioning a more exacting, quantitative adjustment process as is used to adjust comparable sales and comparable rentals.

Appraising Residential Properties carries this subjective argument a step further, stating, "Indicated GRMs |gross rent multipliers~ are not adjusted because property differences are already reflected in the GRMs. By adjusting GRMs an appraiser would consider these differences twice. Adjustments are only made in the second step of the income capitalization approach when the market rent of the subject property is estimated."(2)

The purpose of this article is to suggest that it is in fact both logical and possible to adjust |R.sub.0~s from comparable sales and GIMs through a simple dissection of the overall cap rate and gross income multiplier formulas. Appraisers thus can better support cap rate and income multiplier conclusions and fortify more defensible valuation estimates.


To adjust |R.sub.0~s derived from comparable sales to a given subject property, it is necessary to segregate the overall rate formula components:

Overall rate (|R.sub.0~) = Net operating income (NOI)/Sale price (Value)

as well as the gross income multiplier formula components:

Gross income multiplier |(GIM).sup.3~ = Sale Price (Value)/Gross Income (GI)

In deriving an NOI estimate via the income approach for a subject property, adjustments for such elements of comparison as market conditions (time), location, and physical characteristics are generally made through a comparable rental adjustment grid. Therefore, to accurately adjust comparable sale |R.sub.0~s to a given subject property, it is imperative to hold the comparables' NOIs constant to avoid a double or compounded adjustment of the income component. This theory would also hold true of GIMs with reference to the gross income component.

Another way to view the income component of a cap rate derived from comparable sales or gross income multipliers is to consider it to be a given characteristic of the sale that was inherited through the purchase of the real estate, not unlike a given location or a given physical characteristic.

Because the goal is to determine the interrelationship between income and value relative to a subject property, the only remaining component that can be adjusted is the sale price component of the comparable sales' |R.sub.0~s and GIMs. In adjusting comparable sale |R.sub.0~s and GIMs to a particular subject, the only factor that requires adjustment is therefore the sale price component. To carry this a step further, it is logical that a comparable sales adjustment grid similar to those prepared in the sales comparison approach should be performed on the sale price component of all comparable sale |R.sub.0~s or GIMs to accurately adjust these rates and multipliers to a particular subject property.

The following example aims to illustrate how this method can be used in practice. For academic purposes, the hypothetical details of the subject property and comparables in this example have been simplified.

Assume the following conditions exist.

* The subject property consists of a 10,000-square-foot light industrial building with an average industrial location and average physical characteristics.

* Each of the comparable rentals represents leases involving single-tenant-occupied, 10,000-square-foot light industrial buildings.

* Each of the four comparable leases used in Table 1 is also used to derive |R.sub.0~s from comparable sales and potential gross income multipliers (PGIMs) in Table 2.

* Each comparable lease was signed just prior to each sale transaction.

* The net income for each of the comparables and the subject is 50% of potential gross income (PGI).

After adjustments, the comparable rentals indicate a narrow range (from $96,600 to $104,400 for PGI and from $48,300 to $52,200 for NOI). An adjusted PGI of $100,000 and an adjusted NOI of TABULAR DATA OMITTED TABULAR DATA OMITTED $50,000 is thus well supported for the subject property.

The following assumptions are applicable to Table 2:

* Each of the comparables represents a transaction involving a fully leased, single-tenant-occupied, 10,000-square-foot light industrial building.

* The fee simple interest of the subject property is to be valued.

* Adjustments for property rights conveyed in sales 2 and 3 were derived by taking the difference between adjusted NOI for each sale ($52,200 and $48,300, respectively) and market-derived NOI ($50,000) ascertained through Table 1 and capitalizing the difference by a market-estimated 10% rate as indicated by the grid.(4) Sale 2 requires an upward adjustment for this factor since contract rent exceeds market rent; conversely, sale 3 requires a downward adjustment.

Prior to adjustment, the sale and capitalization grid indicates a wide range (|R.sub.0~s range from 8.96% to 11.05%; PGIMs range from 4.52 to 5.58; both ranges are in excess of 23% from low to high) from which a market-derived rate and multiplier could be estimated.(5) It is quite difficult to subjectively reach a defensible cap rate and income multiplier conclusion with a significant degree of certainty or credibility in light of such a variance. While any subjective argument may be perfectly valid,(6) in the absence of quantitative support any conclusion drawn from such a wide range may be considered quite speculative.

After adjustments are made to the sale price component as illustrated in Table 2, the adjusted cap rate and income multiplier ranges narrow significantly to within approximately 1%. A conclusion of an overall rate of 10% and a PGIM of 5 is clearly well supported and quite defensible under such a method.

Applying the market-derived NOI and PGI developed through Table 1 to the market-derived PGIM and |R.sub.0~ developed through Table 2 renders value indications via each capitalization method as shown in Table 3.


As an aid in proving this method, sale 1 can be used as an example. As indicated earlier, subjectively it is clear that the unadjusted |R.sub.0~ in sale 1 requires an upward adjustment and the unadjusted PGIM requires a downward adjustment. It is clear that these |R.sub.0~s and GIMs should be adjusted in this way because there is less TABULAR DATA OMITTED perceived risk in a property with above-average physical characteristics than in a property with average physical characteristics.

Another way to view this scenario is to reasonably assume that with all else being equal (including income), a purchaser would be willing to pay a little more for the sale 1 property since its physical characteristics are superior to those of the subject. The result is that this property has a slightly lower |R.sub.0~ (as price increases while income remains steady, |R.sub.0~ decreases) and a slightly higher GIM (as price increases while income remains steady, GIM increases) compared with a property with average physical characteristics. To measure this quantitatively, it is appropriate to hold income constant and to isolate and solely adjust the sale price component as shown in Table 2. Table 4 summarizes the simple formula involved in this process.

In adjusting comparable sales' |R.sub.0~s and GIMs to a given subject property, it is imperative to consistently apply the appropriate sequence of adjustments(7) when using percentage adjustments. Failure to do so will often result in incorrect estimates.


If, for example, both the income and sale price components are adjusted, the indicated cap rate and income multiplier do not change, as shown in Table 5.

The reason the |R.sub.0~ and PGIM do not change is mathematically obvious. Because the goal of deriving the |R.sub.0~ from comparable sales and GIMs is to study the relationship between a given income and a negotiated price based on that income as it relates to the subject, the income component must be held constant to measure this relationship. After that relationship (i.e., the reconciled |R.sub.0~ and GIM) is defined, the subject's income can then be entered into the |R.sub.0~ and GIM formulas to generate a value estimate.

For a number of reasons, it would be inappropriate to adjust |R.sub.0~s based on comparable sales on a "macro" percentage basis without segregating the cap rate components. The most fundamental reason is that to do so would be to consider adjustments to the income component (numerator x 5% in Table 7) of the equation twice, since income has already been adjusted in the estimation of market rent. The denominator (sale price) is held constant under this scenario.

The result of adjusting in this incorrect fashion is that |R.sub.0~s in need of net upward adjustments are adjusted too little, and |R.sub.0~s in need of net downward adjustments are adjusted too much.

At first blush, it appears that since multipliers are factors, macro-adjustments may work when GIMs are concerned, because the sale price component in the numerator is adjusted. This is only true, however, provided that percentage adjustments are applied to each element of comparison requiring adjustment and that the integrity of the sequence of adjustments is maintained.

For example, assume a situation in which a comparable sale requires both a -5% market conditions (time) adjustment and a +10% adjustment for location. As Table 8 illustrates, if the proper sequence of adjustments is adhered to (as reflected in Table 2), more accurate conclusions can be drawn from the market.

Part A in the example shown in Table 8 is incorrect because all the adjustments are treated as additive and are improperly netted out. Part B is correct because the time adjustment is made first (-5%) and then adjustment is made for location. The result of adjusting in this incorrect fashion is that GIMs in need of net upward adjustments are adjusted too much, and GIMs in need of net downward adjustments are adjusted too little.


One of the additional benefits of a capitalization adjustment grid is that it can serve as an effective tool in the reconciliation process. It should be noted that the net adjusted sale price range shown in Table 2 is quite wide (from a low of $417,450 or $41.75 per square foot to a high of $577,800 or $57.78 per square foot). This indicates that to use the sale-price-per-square-foot unit of comparison to derive a value conclusion is subjective to a large degree.

In such an instance, significantly more weight should be given to the PGIMs in reconciling the sales comparison approach because adjusted rental and PGIM ranges are tight and therefore better explain how the market operates with regard to a particular subject based on the given market data. Overall, more weight should be given to the income approach in this example since the adjusted rental and |R.sub.0~ ranges are tight, resulting in a more convincing and defensible valuation conclusion.

Conversely, if the adjusted PGIM range and |R.sub.0~ range or the adjusted rental range diverge more from the adjusted sale-price-per-square-foot range, more weight should be given to that unit of comparison in the sales comparison approach and more weight should be given to the sales comparison approach overall.


In the spirit of developing more supportable valuations, professional appraisers continually strive to better justify the conclusions derived through the valuation process. This article suggests a method through which appraisers can increase support for their valuation conclusions via overall rates derived through comparable sales and gross income multipliers. Through the proper segmentation and consideration of the |R.sub.0~ and GIM formulas and components, quantitative analysis through a grid adjustment process can add a significant degree of objective support to |R.sub.0~ and GIM capitalization techniques that in the past have generally been considered more subjective.

TABLE 4 Proper Adjustment Sale 1

NOI $52,632/Price $555,000 - 5% = 9.98% (|R.sub.0~)

Price $555,000 - 5%/Gross income $105,293 = 5.01 (PGIM)

TABLE 5 Constant Ratio Change Adjustment Sale 1

NOI $52,632 - 5%/Price $555,000 - 5% = 9.48% (|R.sub.0~)

Price $555,000 - 5%/Gross income $105,293 - 5% = 5.27 (PGIM)

TABLE 6 |R.sub.0~ Macro Adjustment Sale 1

NOI $52,632/Price $555,000 = 9.48% unadjusted |R.sub.0~

NOI $52,632/Price $555,000 x 5% = 9.96% adjusted |R.sub.0~

TABLE 7 PGIM Macro Adjustment

Price $500,000/Gross income $100,000 = 5.00% unadjusted PGIM

A. Price $500,000/Gross income $100,000 x +5% = 5.25% (adj. PGIM) (incorrect)

B. Price $500,000/Gross income $100,000 x -5% = 4.75 x +10% = 5.23% (adjusted PGIM) (correct)

1. Appraisal Institute, The Appraisal of Real Estate, 10th ed. (Chicago: Appraisal Institute, 1992), 468.

2. American Inst. of Real Estate Appraisers, Appraising Residential Properties, 1st ed. (Chicago: American Inst. of Real Estate Appraisers, 1988), 353.

3. The sale price can be divided by either the potential or the effective gross income resulting in either a potential gross income multiplier (PGIM) or an effective gross income multiplier (EGIM), respectively.

4. Although the 10% rate is effectively an unknown at this point in the grid, it can reasonably be estimated by considering the adjusted |R.sub.0~s of sales 1 and 4, which do not require adjustment for property rights conveyed. For this reason, appraisers should ideally seek out sales that do not require adjustment for property rights conveyed.

5. As experienced appraisers know, such a wide range in cap rate and income multiplier parameters is not atypical in many markets, even when excellent market data are available to the appraiser.

6. For example, most weight may be given to the unadjusted |R.sub.0~ and PGIM indicated by sale 1 since it is comparable to the subject in every regard with the exception of physical characteristics. Because this comparable is superior to the subject in terms of physical characteristics, an upward |R.sub.0~ adjustment and conversely a downward PGIM adjustment would be warranted since superior properties generally reflect lower |R.sub.0~s and higher GIMs.

7. The Appraisal of Real Estate, 10th ed., 390-392.

K. Sean Cooney, MAI, is president of Cooney Valuation Group, Inc., in Jersey City, New Jersey. He received a BA in business administration from the University of Notre Dame.
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Copyright 1993 Gale, Cengage Learning. All rights reserved.

Article Details
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Author:Cooney, K. Sean
Publication:Appraisal Journal
Date:Oct 1, 1993
Previous Article:Market value: does one size really fit all?
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