Parcel Size, Location and Commercial Land Values

Parcel Size, Location and Commercial Land Values Authors Karl L. Guntermann and Gareth Thomas Abstract The concept of a peak in value or a 100% location is so well established in real estate that there is no reference to the term in recent real estate principles and appraisal texts. However, the land value section in appraisals of a regional shopping center did not apply the concept when adjusting comparables for location, which resulted in a substantial underestimation of site value. A regression model that included a distance variable to control for location produced a value estimate that was more than double the values in the appraisals. The empirical results illustrate that the subject site represented a distinct peak in land value as well as reemphasizing the importance of making careful location adjustments in situations where there is a distinct peak in land value. Introduction The 100% location is a term that dates back at least to the 1930s. It was used to describe the land value peak associated with the Central Business District (CBD) in older industrial cities that grew dramatically in the nineteenth and early twentieth centuries. Competition between firms for the most central location, which provided access to the greatest number of consumers and workers, led to a land value gradient that increased, sometimes very dramatically, with small changes in distance around the peak. The concept of a peak or 100% location became well established in the appraisal literature and appraisers routinely made location adjustments, aware of the sensitivity of value to small changes in distance from prime locations. In addition to a peak in the CBD, there can be other subpeaks in land or site value throughout the metropolitan area corresponding to important, secondary nodes of economic activity. Parcels might require location adjustments relative to these local or sub-peaks in value or to a range of other micro location-related factors. While appraisers are aware that they must examine comparable sales data to determine if a location adjustment is needed, data limitations or other factors may mean that appropriate adjustments are not always made. This can be a serious problem if there is a particularly valuable location that is influencing surrounding JRER Vol. 27 No. 3 2005

344 Guntermann and Thomas land values. In that case, the failure to recognize the sensitivity of per unit land values to relatively small changes in distance from the peak can lead to incorrect location adjustments and significant site value errors. This paper reviews the site value sections of two appraisals of an upscale department store that was affiliating with a regional mall in downtown Scottsdale, Arizona. In one of the appraisals, the location of site comparables relative to the subject site was ignored, while distance from the subject site received only cursory analysis and discussion in the second appraisal. The failure to properly adjust for location resulted in land value estimates that were less than 50% of the correct value. The paper is organized as follows: First, background information on downtown Scottsdale is provided and a brief summary of the site valuation sections of the two appraisals is presented. Next, the literature on value as it relates to distance is reviewed, followed by a section discussing the econometric methodology and data used in the empirical tests. The final two sections contain the results and concluding comments. Scottsdale Commercial Land Market Background Scottsdale has a reputation as an upscale community and is both a renowned retirement community and resort/convention center. Like many older cities, Scottsdale would like to see significant redevelopment of its downtown. While there are upscale shops and art galleries in and around the city center, there are also areas with considerable redevelopment potential, including numerous vacant parcels, some of which are fairly large. The opening of the Galleria, a distinct specialty retail center in the early 1990s, was intended to stimulate surrounding redevelopment but it ended in foreclosure after only a few years. The clearing of an old high school and other structures resulted in several parcels of vacant land, some of which were redeveloped into office buildings and hotels in the late 1990s. At about the same time, a planned waterfront development using land adjacent to an irrigation canal caused excitement because it was expected to be the catalyst for large-scale private redevelopment. However, the waterfront project had not moved forward as of the valuation date on the appraisals. While private redevelopment has occurred, there is still considerable uncertainty about when and how the redevelopment of downtown Scottsdale will proceed. One of the high-end super regional shopping centers in the Phoenix metropolitan area, Scottsdale Fashion Square, is located close to the center of Scottsdale and very near the canal. The owners of the mall and Nordstrom, Inc. entered into negotiations in the mid-1990s to bring a Nordstrom s department store to the mall. Nordstrom desired to enter the growing Phoenix market and Scottsdale Fashion Square believed that a destination department store like Nordstrom would be a

Commercial Land Values 345 good fit with the mall and would further enhance the mall s prestige and desirability. The Nordstrom site is south of the existing mall and is connected to the mall with a two-story pedestrian walkway over Camelback Road that is integrated into the mall with upscale in-line shops. Scottsdale Fashion Square Partnership (SFSP) purchased the site used for the Nordstrom store and its parking structure in a double escrow transaction. A 14.47- acre parcel containing the Nordstrom site was sold in August 1996 for $16,489,000 or $26.16 per square foot. Simultaneously, SFSP purchased a 6.70- acre (291,852 sq. ft.) part of the larger parcel for $10,108,305 or $34.64 per square foot. SFSP then ground leased 2.122 acres (92,427 sq. ft.) to Nordstrom, Inc., which built and owns the store on the site. The remaining part of the 6.70-acre parcel was used to construct a parking structure and provide open space. The ground leased parcel would be considered the most desirable part of the larger 14.47-acre parcel because it includes considerable frontage on Camelback Road. Nordstrom opened in September 1998 and challenged the assessed value of the store and site as determined by Maricopa County. Under Arizona law, property that was put in service prior to October 1 can be taxed for the entire year, so Nordstrom s was appraised for purposes of the property tax appeal as of January 1, 1998. It is the site value portion of both appraisals that is the subject of this paper. Appraisal Reports Appraisal reports were prepared for both the plaintiff, Nordstrom, Inc. and the defendant, Maricopa County. A brief summary of selected information for the seven comparables used by the appraisers is presented in Exhibit 1. The plaintiff s appraiser used five comparables (Exhibit 2, Nos. 1 5) to estimate land value as part of the cost approach, while the defendant s appraiser used six land comparables, including a prior sale of a larger parcel that included the Nordstrom site (No. 7). 1 Both appraisers used four of the same comparables (Nos. 2 5). The plaintiff s appraiser adjusted the unit price of comparables 1 5 for market conditions (time) at the rate of 1% per month and size at the rate of $0.34 per square foot for each 10,000 square feet of difference in size between the subject site and each of the comparables. This produced a final value for the land of $24.00 per square foot and a total value of $2,500,000 (rounded). No adjustment was made for location. The defendant s appraiser used comparables 2 7 and adjusted for market conditions (6% per year), size (0.44% per acre), and location in arriving at a land value of approximately $35.00 per square foot or $3,235,000 for the Nordstrom site. A positive adjustment of 15% was made to comparables 2 6 for location (distance to the Nordstrom site) but no explanation or support was presented for the adjustment. It is interesting to note that one appraiser made no adjustment for location while the other made a flat 15% adjustment to essentially the same set of comparables (Exhibit 2), excluding No. 7. JRER Vol. 27 No. 3 2005

Exhibit 1 Plaintiff and Defendant Appraisals Land Comparables and Adjustments Subject 1 2 3 4 5 6 7 Date of Sale Feb. 1998 Nov. 1997 Aug. 1997 July 1997 April 1997 March 1998 Aug. 1996 Price $2,763,316 $2,825,000 $2,362,761 $3,750,000 $2,400,000 $3,600,000 $10,108,305 Size (sq. ft.) 92,427 1 116,595 31,603 100,000 88,615 115,434 115,434 291,852 Price/SF $23.70 $21.47 $23.63 $19.88 $20.79 $31.19 $34.64 Plaintiff Time 0.3 0.5 1.12 1.35 2.02 Size 0.48 0.99 0.09 2.93 0.44 Adjusted Price/Sq. Ft $23.95 $22.90 $24.66 $24.16 $23.25 346 Guntermann and Thomas Defendant Time 0.21 0.59 0.60 0.94 0.31 2.94 Location 3.26 3.62 3.07 3.26 4.63 Size 0.10 0.11 0.23 0.13 0.08 0.76 Adjusted Price/Sq. Ft. $25.04 $27.95 $23.78 $25.12 $35.59 $38.34 Notes: 1 Based on a survey; plaintiff s appraisal, 102,583 SF based on the assessor s map.

Commercial Land Values 347 Exhibit 2 Comparable Land Sales in Downtown Scottsdale JRER Vol. 27 No. 3 2005

348 Guntermann and Thomas The plaintiff s appraiser apparently decided that there was no distinct competitive advantage to any particular location in downtown Scottsdale and that the relatively small differences in the per-acre price of comparables 1 5 could be adequately explained with the time and size adjustments. The fact that the subject site is in close proximity to a major destination mall, while the comparables are at least one-third mile away, suggests that a substantial location adjustment might be required. The second appraiser realized that a location adjustment was needed, based on the unit price of No. 7, but did not take into consideration the variation in distance between each of the comparables and the subject site when making the adjustment. The transactions involving the Nordstrom site raise several interesting questions about their use as comparables and the location adjustment that should be made to them. The 14.47-acre parcel sold for $26.16 per square foot compared to $34.64 per square foot for the northern 6.7-acre portion of the parcel with frontage on Camelback Road. While the sale of the 6.7-acre parcel (No. 7) is included as a comparable, the 14.47-acre sale is not used even though it too may contain useful information. The actual Nordstrom site (2.122 acres) is essentially the northern one-third of the 6.7-acre parcel and it may be considerably more valuable than the average price of $34.64. This is because the Nordstrom site contains the desirable commercial frontage on Camelback Road. An adjustment was made to comparable 7 for size but not for location on the basis that the Nordstrom site was part of comparable 7. However, the location of the two parcels is not the same. The Nordstrom parcel is more desirable but to properly value it, all of the comparables, including No. 7 should have been adjusted for location relative to the Nordstrom site. However, to do so would have meant gathering additional sales data and analyzing it within the context of a peak or 100% location. A highend department store such as Nordstrom s may provide the greatest residual value to the land on a per square foot basis, making its site the 100% location. Because of the value of Scottsdale Fashion Square, it is also possible that the mall site would represent the 100% location. Distance and Size To properly adjust comparable sales where it is likely that there is a distinct peak in per-unit land value at or close to the subject site, it is necessary to understand how distance and size are related to value. In empirical studies, land value usually is modeled as a negative exponential function of distance and other factors. Value would decline at a decreasing rate from a central point, which could be the CBD or other pronounced sub-peaks of value within the metropolitan area. However, parcel size tends to increase with distance, while price per acre declines as parcel size increases, primarily because of subdivision costs reflected in the price of smaller parcels. Colwell and Munneke (1997) present evidence that the distance coefficient is biased in models specified with price per acre as the dependent

Commercial Land Values 349 variable because that specification imposes a proportional requirement on the price-size relationship. In the model estimated here, price is the dependent variable and size is one of the explanatory variables, which avoids the misspecification problem that could bias the distance coefficient. If a portion of the commercial land market has a distinct peak in value, per-unit values may decline very rapidly over relatively short distances as competition for prime locations decreases. In the case of Scottsdale, a possible peak in value at the Nordstrom or regional mall site may represent a very small portion of the downtown Scottsdale commercial market. Outside of the prime competitive area, the reduced demand for land is likely to result in a more gradual decline in value as distance from the peak increases. If the pattern of land values that results from the change in demand is pronounced, the negative exponential specification may not be the best way to model the value-distance relationship. Instead, the specification of the distance function should allow for the possibility that distinctly different slopes characterize different portions of the curve. Colwell (1998) presents piecewise parabolic multiple regression analysis as a technique for estimating the structure of the spatial price function in the Chicago CBD. The technique has the potential to detect distinct changes in shape, such as what might exist in the Scottsdale data. Colwell and Munneke (1999) use the same technique to develop contour maps for much of the Chicago metropolitan area. However, while the technique is appealing, the data requirements far exceed that which is available in this study. Colwell and Guntermann (1984) used a simple kinked distance function to estimate the point at which negative externalities associated with proximity to primary schools (noise, trampled lawns, etc.) declined to zero. The externality variable was included in a hedonic model along with an accessibility variable, the reciprocal of distance from each house to its primary school, which measured the benefit of accessibility. The accessibility effect would be expected to decline with distance. The externality variable was assigned the value, d* d (distance) up to the distance, d*, where the externality declined to zero or could not be measured, and had the value zero beyond d*. The kink would be expected to occur at d*, leaving only a diminishing accessibility effect beyond d*. The distance where external costs declined to zero was determined by estimating a series of regressions for various values of d* and selecting the d* that produced the highest R-square value. A more recent use of a kinked function can be found in Colwell and Ramsland (2003) where functional obsolescence is estimated as a piecewise exponential function of age. The critical age, equivalent to d*, is where observable functional obsolescence essentially stops... even though functional obsolescence or technological change does not cease. 2 Due to advances in econometric techniques, the critical age was determined by nonlinear regression instead of a trial-and-error procedure. In this paper, we take the same approach as Colwell and JRER Vol. 27 No. 3 2005

350 Guntermann and Thomas Ramsland but we estimate distance instead of age and use a different estimating procedure. Econometric Methodology Since either Scottsdale Fashion Square or the Nordstrom site could be possible peaks in land value, distances could be included in the database from each possible peak to each of the parcels. In an ideal situation, the sales would be distributed around both possible peaks and distance variables for Scottsdale Fashion Square and Nordstrom could be included in the model. However, there is very little distance between the two possible peaks (Exhibit 2). Because of the topography in the area, there are very few commercial properties to the north and west of the Nordstrom and Scottsdale Fashion Square sites. Most sales fall into a wedge from east of the Nordstrom site clockwise to the south. This pattern is generally similar but somewhat wider than the distribution of the appraiser s comparables in Exhibit 2. Because of the high correlation that would exist if both distance variables were included in a model and the fact that Nordstrom is the subject site, the Nordstrom distance variable will be tested in the models with the center of the Nordstrom site as the hypothesized peak in land value. X* is used to test the kinked relationship between price and distance in the models. X* has a value that is either related to DistNord or is equal to zero. With the data ordered from the smallest to largest distance, each observation is assigned a rank, k i th and rank is used to determine the value of X*. X* is equal to (Distnord K 0 DistNord) ifk i k 0 and X* is equal to zero if k i k 0, where k 0 is the point of the kink. The value of k 0 is estimated through the use of a technique suggested by Bai (1997): est k o arg min S N(k). (1) 1kN where S N (k) is the sum of squared residuals from a least squares regression with a set value of k. If there is no kink in the price-distance relationship, X* will be statistically insignificant and DistNord will measure the decline in value with distance in the usual way, as a negative exponential function. Since the sample size in these regressions is relatively small, (n 48), tests of normality were undertaken to ensure that inferences based upon normality assumptions were valid. A Shapiro-Wilk test was unable to reject the null hypothesis of normality for either model. The data are forty-eight commercial land sales from 1992 through 2000, which are from the Costar/Comps, Inc. database. Costar/Comps begin with the assessor s monthly data tape and then verify important facts with the principals to the transactions, as well as adding additional information. Each observation

Commercial Land Values 351 includes the sale price, size of the parcel (in square feet) and date of sale. Additional information that is included in the models as control variables are whether there was a structure on the site at the time of sale requiring demolition and whether the site has frontage on a primary or arterial street. 3 Distance was measured from the center of each parcel to the center of the Nordstrom site and ranged from 0.035 miles (approximately 184 feet) to under two miles. Parcels were included up to two miles from Nordstrom s to be able to reliably test for the existence of a kink in the distance function. Parcel size ranged from one-sixth of an acre to 14.5 acres. Exhibit 3 contains summary statistics for the data used in the regressions. Results The regression results for model 1 are presented in Exhibit 4. The R-square (.9326) and F-Statistics (36.21) are quite high, indicting that the model is well specified. The annual time dummy variables are insignificant except for Year92, which has a negative coefficient, relative to the omitted year, 2000. The Phoenix area office market began a recovery in 1993 from the poor market conditions that occurred in the late 1980s and early 1990s so it is not surprising that the coefficient for Year92 is negative and significant compared to the rest of the decade. The Frontage variable is significant and has the anticipated positive sign. Its coefficient (0.338) translates to approximately a 40% premium for commercial parcels located Exhibit 3 Summary Statistics for Model 1 Variable N Mean Std. Dev. Min. Max. Price 48 1,440,280 2,779,634 100,000 16,489,000 Size 48 82,525 109,067 7,069 630,313 Year92 48 0.0417 0.2019 0 1 Year93 48 0.1875 0.3944 0 1 Year94 48 0.1042 0.3087 0 1 Year95 48 0.1667 0.3766 0 1 Year96 48 0.1458 0.3567 0 1 Year97 48 0.2083 0.4104 0 1 Year98 48 0.8333 0.2793 0 1 Year99 48 0.0208 1.1443 0 1 Year00 48 0.0417 0.2019 0 1 DistNord 48 0.8326 0.4696 0.0348 1.8783 Frontage 48 0.4167 0.4982 0 1 Structure 48 0.3333 0.4764 0 1 JRER Vol. 27 No. 3 2005

352 Guntermann and Thomas Exhibit 4 Model 1 Regression Results Variable Coefficient Standard Error p-value Intercept 4.652 0.765 0.001 Ln(Size) 0.816 0.068 0.001 Year92 0.659 0.368 0.083 Year93 0.024 0.304 0.939 Year94 0.048 0.335 0.888 Year95 0.067 0.302 0.826 Year96 0.028 0.302 0.928 Year97 0.261 0.312 0.408 Year98 0.526 0.354 0.146 Year99 0.442 0.462 0.346 DistNord 0.568 0.204 0.009 X* 1.261 0.607 0.046 Frontage 0.338 0.156 0.037 Structure 0.148 0.138 0.293 Notes: The dependent variable is Ln(Price); R 2.9326; and F-Statistic 36.21. on main or arterial streets compared to similar commercially zoned sites. The coefficient on the Structure variable is insignificant, indicating that the demolition costs of existing structures are minor relative to the value of the parcels. The coefficient for Ln(Size) is significant and less than one, meaning that price is increasing at a decreasing rate with size, as expected. Both the DistNord and X* variables are statistically significant in model 1. Commercial land values in downtown Scottsdale decline from a peak at different rates and the rates are accurately measured through the use of a kinked distance function. For Scottsdale, the kink occurs at approximately 3,200 feet (X* 0.60 miles) with the slope of the distance function greater to the left of the kink. Since the model is in semi-log form with respect to the distance variables, the coefficients can be interpreted as percentage changes in price. For distances greater than 0.60 miles, price declines by 0.568% per mile (X* 0), while for distances less than or equal to 0.60 miles, price declines by 1.829% per mile as calculated from the DistNord and X* coefficients. 4 It is clear that the value-distance relationship needs to be considered when selecting land comparables and making adjustments to them in areas characterized by distinct peaks in value. Given the empirical results, the value of the Nordstrom site can be estimated from model 1. The Nordstrom site had a valuation date of January 1998 and a size of 92,427 square feet. There was a structure on the site requiring demolition and

Commercial Land Values 353 removal and the site had frontage on an arterial street (Camelback Road). For the Nordstrom site, distance would, of course, be zero. Using the regression coefficients from model 1, a value estimate of the Nordstrom site would be: ln(price) 4.652 0.816*ln(92427) 0.526(1) 0.568(0) 1.261(0.600) 0.388(1) 0.148(1) ln(price) 15.75. (2) This is a value of $6,919,723 or $74.87 per square foot. In contrast, the two appraisals estimated the value of the Nordstrom site at either $2,500,000 or $3,235,000. The results of this analysis and value estimate can be related to the adjustments made in the two appraisals of the Nordstrom site (Exhibit 1). Both appraisers adjusted for market conditions (time) but the insignificance of the annual time variables after 1992 suggests that such adjustments were not needed. The plaintiff s appraiser made no adjustment for location (distance) even though the five comparables ranged from approximately one-third to one mile from the subject site (Exhibit 2). The defendant s appraiser made a blanket 15% adjustment to comparables 2 6 irrespective of the location of each relative to the Nordstrom site. This amounted to an adjustment of $3.07 to $4.63 per square foot applied to comparables whose sale prices ranged from $19.88 to $34.64 per square foot. Given the dramatically higher value per square foot for the Nordstrom site based on model 1, both appraisers seriously underestimated the importance of location on land value. Neither appraiser adjusted for the lack of frontage of comparables 3 6 compared to the subject site. Based on model 1, a substantial positive adjustment should have been made to those sale prices since the Nordstrom site has frontage on Camelback Road. Conclusion These results are interesting and potentially useful to appraisers and other real estate analysts for several reasons. This paper reiterates the importance of making location adjustments if there is a distinct peak in land value in the area being analyzed, as was the case in downtown Scottsdale. The adjustment process may be complicated by the fact that the magnitude of the adjustments could depend, in part, on the slope of the distance gradient. Because the price of comparables may reflect very small differences in location, some awareness of the slope of the land value function in those situations is important to establish a logical basis for making the adjustments. Finally, these results illustrate, at least in this case, that a relatively small sample of data can produce fairly powerful results. While appraisers typically present a JRER Vol. 27 No. 3 2005

354 Guntermann and Thomas relatively small number of comparable sales in their reports, they work with or have access to a much larger database. While many transactions may not appear to be particularly relevant for a given valuation assignment, they may be useful in modeling the data to identify and quantify important, but not always apparent, characteristics of the market. Endnotes 1 The plaintiff s appraiser did not use this sale. He did not consider it to be an arms length transaction because the owners of Scottsdale Fashion Square had entered into a Letter of Intent with Nordstrom to locate in the mall prior to the date of sale and because the city of Scottsdale might use eminent domain powers to acquire the site. However, over the fifteen months prior to sale, the purchase price had been renegotiated upward several times, making it likely that the buyer and seller were knowledgeable about the value of the site. 2 Colwell and Ramsland, page 57. 3 Preliminary testing of the models included dummy variables for zoning and if a parcel was located on the intersection of primary streets. Since neither variable provided any explanatory power, they were deleted from the final models. 4 Ln(Price) 0.568 (Distance) 1.261 (X* Distance) Ln(Price) 1.829 (Distance) 1.261 (0.60) References Bai, J., Estimation of a Change Point in Multiple Regressions, Review of Economics and Statistics, 1997, 79:4, 551 63. Colwell, P., A Primer on Piecewise Parabolic Multiple Regression Analysis via Estimations of Chicago CBD Land Prices, Journal of Real Estate Finance and Economics, Special Issue on Spatial Econometrics, 1998, 17:1, 87 97. Colwell, P. and K. Guntermann, The Value of Neighborhood Schools, Economics of Education Review, 1984, 3:3, 177 82. Colwell, P. and H. Munneke, The Structure of Urban Land Prices, Journal of Urban Economics, 1997, 41, 321 36.., Land Prices and Land Assembly in the CBD, Journal of Real Estate Finance and Economics, 1999, 18:2, 163 80. Colwell, P. and M. Ramsland, Coping with Technological Change: The Case of Retail, Journal of Real Estate Finance and Economics, 2003, 26:1, 47 64. Karl L. Guntermann, Arizona State University, Tempe, AZ 85287 or Karl. Guntermann@asu.edu. Gareth Thomas, Arizona State University, Tempe, AZ 85287 or Gareth. Thomas@asu.edu