Case study: an alternative technique to the land residual method.
Land valuation problems vary from being straightforward to highly complex. The many tasks involved in complex land analyses include attaining a complete understanding of the physical and legal constraints applicable to the subject property; reaching a determination of whether the land can be immediately developed or is likely to be held for future development; and forecasting the timing of expected development for speculative land parcels. Land appraisal assignments of easily understood subject properties can also become problematic when there are no directly comparable sales in the neighborhood.
This article considers those situations where the direct sales comparison approach is difficult to apply, even to immediately developable properties, because of a lack of directly comparable data. First, a traditional alternative valuation method, the land residual technique, is evaluated from a critical perspective, and then the idea of selecting land sales from other locations and making allowances for differences in location by studying variations in rent is explored.
During the course of an actual appraisal assignment completed by the author, the two methods were considered in the process of completing the property valuation. The appraisal problem involved an infill, multifamily land parcel. It was literally the last vacant site in its neighborhood, and comparable, developed sites in the neighborhood were so mature that their land acquisition costs were dated and not applicable to the valuation date. Though there were no new apartment projects in the neighborhood, existing properties were well maintained and fully occupied at rents that were higher than average for the community. It was evident that the subject site's market price would reflect the feasibility of immediate development.
LAND RESIDUAL METHOD
According to The Appraisal of Real Estate, tenth edition, value "represents the monetary worth of property, goods, or services to buyers and sellers."(1) For income properties, "investors ... give up current purchasing power for some promised future benefits...."(2) The expected future benefits are the property cash flows over the ownership period.
To derive cash flow from an apartment site, however, the site must be improved with an apartment building. For this reason, land residual analysis starts with the improved property. The land residual method has at least two variations; both versions derive a land value estimate by initially analyzing hypothetical improvements representing the highest and best use of the site. The cost analysis version of the method involves estimating value for the hypothetically improved property and then deducting creation costs (i.e., labor, capital, and entrepreneurship) to derive an estimate of the value of the land. The band of investment version of the method consists of estimating the expected net operating income (NOI) to be derived from the hypothetically improved property, calculating the portion of the NOI attributable to the improvements, and then subtracting the improvement NOI from the property NOI to estimate the land NOI. Once the NOI attributable to the land is known, it is capitalized at an appropriate rate to estimate land value.
CRITICISM OF THE LAND RESIDUAL METHOD
Use of the land residual technique was first considered as a way of estimating value for the subject apartment site because it is generally taught as the method of choice when sale data are not available.(3) When faced with the task of actually employing this valuation method in practice, however, its shortcomings became quite evident. Some of the questions that arose are discussed in the following sections.
What specifications define the hypothetical improvements?
It was not difficult to flesh out an image of a building that satisfied the general requirements of the highest and best use of the vacant site. The local zoning code, in this instance, determined site density, building setback and height, parking requirements, and landscaped area. Market information was available to bring probable unit mix, apartment floor area, and room count into reasonable focus. Also, site layout could be anticipated to some extent because of access constraints imposed by existing curb cuts and street frontage.
The finer details of the hypothetical improvements that represented the highest and best use of the vacant site were, however, much more difficult to determine with precision. How does an appraiser go about specifying the improvements that market participants are most likely to develop on the site? Will the improved site incorporate an interior courtyard? Should it include a swimming pool? Will parking be open, covered, or enclosed? Will the roof be pitched or flat? Are heat pumps the best choice for air conditioning? Will the exterior design include patios and balconies? Will the designer consider shading of windows during summer months to save on energy consumption, or will energy efficiency be sacrificed to cut initial cost? Will low-cost, low-water-use desert landscaping be employed, or will lush, attractive landscaping be used to enhance the property's curb appeal?
The list of specific questions could go on indefinitely, and different appraisers would undoubtedly compose different lists. While some of the listed specifications can be quantified with a good deal of confidence by observing market norms, others are difficult to quantify because there is no consistent pattern in the marketplace. The critical issue is that the market value of, and market rent for, the hypothetical improvements cannot be estimated with certainty if the improvements cannot be described with certainty. Further, creation costs for the improvements cannot be accurately estimated when the improvements are not adequately described.
How much should be allowed for improvement value?
In the cost analysis version of the land residual method, the appraiser subtracts creation cost. As stated above, estimation of hard construction cost is less than a straightforward procedure. In addition, it is necessary to estimate all soft costs to obtain a true measure of the residual land value. Financing, design, engineering, survey, building permit, and plan review costs must be estimated. Further, the appraiser must estimate an allowance for profit (the cost of entrepreneurship). This version of the land residual method becomes the cost approach in reverse, except that there is no building or architectural plan to work from.
In the band of investment version, an appraiser must know not only the value of the improvements but also the appropriate capitalization rate to apply to derive the improvement NOI. This version relies on the relation [V.sub.O] = [V.sub.I] + [V.sub.L] where [V.sub.O] = Improved property value, [V.sub.I] = Value of the improvements [V.sub.L] = Value of the land
Because V = I/R, it follows that [I.sub.L] = NOI - ([V.sub.I] X [R.sub.I]),(4) where [V.sub.I] X [R.sub.I] = [I.sub.I], or improvement NOI.
Therefore, if property NOI, [V.sub.I], and [R.sub.I] are known, then land NOI, or [I.sub.L] can be calculated. Once [I.sub.L] is known, land value can be calculated by [V.sub.L] = [I.sub.L]/[R.sub.L].
Assuming an appraiser is able to derive a fairly precise estimate of the cost of the improvements, and that cost equals value because the appraiser is valuing a hypothetical building that perfectly fits the highest and best use of the site; how does an analyst derive precise estimates of [R.sub.I] and [R.sub.L]? If [R.sub.L] is known, it is possible to derive [R.sub.I] from improved sales if an appraiser has reliable data on expected [R.sub.O] for each improved sale and if it is possible to estimate land value for each improved sale with a degree of certainty. A difficulty arises, however, from the lack of available information on current ground leases for apartment land. Without current apartment ground lease data, the question becomes whether land capitalization rates derived from ground leased for other uses are applicable to an apartment site.
Is the land residual method reliable?
The illustration of the land residual method found in The Appraisal of Real Estate, tenth edition, makes a key assumption: that a developer engages an appraiser. Carrying this idea a step further, presume that the developer has an improvement plan in mind. In this case, if the plan is detailed enough to facilitate an accurate cost estimate, the appraiser can estimate value for the property as if improved, deduct creation costs, and obtain a residual land value. If the developer's plan fully represents the highest and best use of the property and all creation costs are accounted for, then the residual land value is probably a good estimate of market value for the site. Conversely, if the developer's plan does not fully represent the highest and best use of the site, then the residual land value represents an estimate of the investment value of the land (to the developer).
The land residual method's reliability depends initially on the confidence placed in the valuation of the hypothetical improvements. If the improvements are well specified and they fully conform to the highest and best use of the site, then the cost analysis version of the land residual method, properly done, may well be reliable as an estimator of the site's market value. Further, this version of the land residual method appears to apply to cases where investment value is sought.
The reliability of the band of investment version of the land residual method depends not only on the accuracy of the valuation of the improved property but also on the accuracy of the NOI estimate and the veracity of the estimates of [R.sub.L] and [R.sub.I]. Thus, this version of the land residual method is probably universally less reliable than the cost analysis version.
In the case of the particular appraisal assignment at issue here, both versions of the land residual method were discarded because of their inherent weakness. As a result, an alternative valuation technique was conceived and employed.
ALTERNATIVE VALUATION METHOD
To an extent, the alternative method represented a reconsideration of the direct sales comparison approach despite the lack of comparable land sales in the neighborhood. The alternative method relied on land sales from outside of the neighborhood that were purchased for immediate apartment development. Except for location and density, the land sales used were quite similar to the subject property. As shown in Table 1, there was considerable variance in price. The analytical problem consisted of how to adjust the sales for location when no sales were available in the subject vicinity to facilitate the paired sales method.
TABLE 1 Comparable Sales
Comparable No. Price/SF Density (dwelling units/acre) Price/Unit 1 $2.66 22.00 $ 5,267 2 $3.53 11.83 $12,998 3 $4.23 28.00 $ 6,581 4 $5.69 23.40 $10,592 5 $6.45 19.53 $14,386 Subject -- 14.50 --
The alternative method depended on the assumption that there was a correlation between the price paid for apartment land and market rent at the various sale locations. To eliminate density variations, apartment land prices were dealt with on a price-per-dwelling-unit basis. It should be noted that additional adjustments for time, terrain, shape, and other factors would further refine the process, and price per dwelling unit may not provide a complete adjustment for density.(5)
Rental data and rental indices
Market rent was estimated at each sale location by survey. Two criteria were used to determine which properties to include in each rent survey. First, each apartment in a particular survey had to be in the vicinity of the respective comparable sale. Second, each property had to be similar to, and directly competitive with, the project planned at each comparable sale. The goal was to estimate competitive effective gross rent (EGR) per square foot for the new apartment project intended to be constructed at each comparable site. The EGR per square foot was used as an index to account for variations in unit mix and occupancy among projects and locations.
Table 2 shows the rent survey applicable to Sale 1 as an example of the method employed. A rental index of $.497 per square foot per month applied to this sale. The $.497 rental index was the weighted average, by unit count, of the EGR per square foot for the projects surveyed at the Sale 1 location. Rental indices for each comparable sale, shown in Table 3, were all computed in the same manner as the index derived in Table 2. It should be noted that more conventional adjustment processes are also appropriate methods for derivation of rental indices.
[TABULAR DATA OMITTED]
TABLE 3 Rental Indices for Each Comparable Sale
Comparable No. Rental Index 1 $0.497 2 $0.586 3 $0.500 4 $0.575 5 $0.609
The next step involved creating a rental index for the subject property's neighborhood. Projects were selected and surveyed in much the same manner as the surveys at each comparable sale location. Only newer, well-maintained projects were included in the survey because they would constitute the competitive market for a new project hypothetically occupying the subject site. Analysis of survey data, using the same method shown in Table 2 for Sale 1, resulted in an index of $.558 per square foot per month for the subject location.
Analysis of the data
When price per unit and the rental index for each sale's location were arrayed in ascending order it was obvious that there was a correlation. The strength of the correlation was determined by use of a simple two-variable regression analysis. Regression results were: Price/Unit = -31,795.23 + (75,460.83 X Index) [R.sup.2] = .968
Application of the regression equation to the rental index of $.558 at the subject location resulted in an estimated market value for the vacant site of $10,312 per dwelling unit. This value estimate worked out to $3.43 per square foot of site area based on a subject site density of 14.5 units per acre derived from the appraisal's highest and best use analysis. For simplicity's sake, the regression analysis appeared in the appraisal as a footnote. A graph, as shown in Figure 1, was used instead to illustrate the strong correlation between price and rent.
This article shows how a seemingly simple land appraisal can become rather complex. Ideally, comparable land sales should come from the subject property's neighborhood or from a nearby competing neighborhood. When usable sales are not available appraisers resort to alternative valuation techniques such as the land residual method.
Because an appraisal method is mentioned in a textbook, however, does not necessarily mean that the method is an effective tool for solution of a particular problem, or that it is easily applied. In most cases the land residual site valuation method requires so many assumptions regarding the nature of hypothetical improvements that the cost of the improvements cannot be estimated with acceptable precision. Further, the band of investment version of the land residual method requires an appraiser to estimate land and improvement capitalization rates as well as improvement value. Even under the best of circumstances this requirement adds more uncertainty to the appraisal process. For property types not often developed on leased land, the band of investment version may well be impossible to apply.
The alternative method employed in this case does not conflict with the theory that the value of land is a residual, with land rent paid only after payment to the other factors of production. It merely measures the residual land value indirectly by observing the correlation between expected rent and land price at various locations. When comparable, directly competitive rental properties are available for survey in the vicinity of apartment land sales and in the vicinity of the subject property, the correlation between expected apartment rent and land price should be high. In these instances, an indirect measure of land value may well produce a more reasonable outcome than traditional land residual techniques.
(1.)Appraisal Institute, The Appraisal of Real Estate, 10th ed. (Chicago: Appraisal Institute, 1992), 18.
(2.)Sherman J. Maisel, Real Estate Finance (New York: Harcourt Brace Jovanovich, 1987), 50.
(3.)The Appraisal of Real Estate, 10th ed., 307.
(4.)Most appraisal texts use [I.sub.B], [R.sub.B], and [V.sub.B] where I have denoted these variables as [I.sub.I], [R.sub.I], and [V.sub.I]. I use the [subscript.sub.I] to make the point that we should be concerned with the improvements rather than just the building.
(5.)Rental indices derived at the comparable and subject locations also reflect the impact of land use intensity (i.e., density) on market rent. Therefore, the graphic analysis developed as an alternative valuation model implicitly adjusts for variations in density as well as location. The data used were selected to avoid extreme variations in density (e.g., townhomes and patio homes at the low end and midrise apartments at high end). If variations in density were more extreme the correlation between rental index and price per unit could become worse or break down altogether.