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Article Excerpt
Abstract
This article describes the theory behind, and the practical concerns of working with, formulas relating the whole or overall property to its parts. The article clarifies misconceptions and misapplications pertaining to application of the three approaches to value and offers insights into a broader set of asset valuation issues, such as the valuation of personal property and business intangibles, and insights into what the three approaches to value measure in real world circumstances.
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In theory, the three approaches to value can be used to determine real, personal, or business property values. In practice, many real estate appraisers mistakenly believe that the traditional sales comparison and income capitalization approaches usually, depending on property type and complexity, produce pure real property values. Many times, the sales comparison and income capitalization approaches do not produce pure real property value.
A fundamental principle of appraisal theory is that the overall value of an asset (1) can be determined by summing the values of a complete and properly matched set of the parts of the asset. This principle is sometimes expressed as "the whole is equal to the sum of the parts," and is defined herein as the principle of summation. (2) The whole is commonly known as a combination, aggregate, or the overall asset. The parts of an overall asset are known as components or elements or partial interests? The principle of summation takes several classic mathematical forms in real estate appraisal, including the following:
[V.sub.o] = [V.sub.l] = [V.sub.b] (1)
[V.sub.o] = [V.sub.m] + [V.sub.e] (2)
[V.sub.fs] = [V.sub.lf] + [V.sub.lh] (3)
[V.su.b.o] = [V.sub.income] + [V.reversion] (4)
where:
V = market value
o = overall
l = land
b = building
m = mortgage
e = equity
fs = fee simple
lf= leased fee
lh = leasehold
Formula 1 is the basis of the cost approach to value. One can have multiple building elements, each with its own value, where together they sum to the total value of the buildings or improvements. Formula 2 is a foundation of the mortgage industry. Corollary formulas about capitalization rates form the basis of the band-of-investment formulas (also known as the weighted average cost of capital formulas) and the income capitalization approach. Formula 4 may be fully presented as [V.sub.o] = present value of income stream + present value of reversion. This formula is a pillar to the discounted cash flow analysis (DCF) income approach to value.
Business appraisers, accountants, the Internal Revenue Service ORS) and the U.S. Securities and Exchange Commission (SEC) have a different classic formula to represent the principle of summation: The value of the overall business asset, referred to as a business enterprise value (4) or a going-concern value, (5) is equal to the sum of the value of the real estate, the value of personal property, and the value of business intangibles ([V.sub.o] = [V.sub.rp] + [V.sub.pp] + [V.sub.bi]), where rp = real property, pp = personal property, and bi = business intangibles. (6) In some cases, elements of the business appraisers' overall summation formula are equal to zero, but their appraisal theory begins with the critical observation that overall value ([V.sub.o]) can include values from real, personal, and business assets.
While both groups of appraisers claim to be describing overall value, the real estate appraisers' overall value is only part of the business appraisers' overall value, because the value of the real property is only part of business value. Consequently, there can be different and incompatible summation definitions and formulas of the value of an asset. Such a relativistic view of value causes substantial problems for appraisers, clients, and the public.
Note that the principle of summation requires consistency; the items summed in one approach to value or by one appraiser must be the same items summed in the other approaches or by other appraisers, for the same appraisal subject. The Uniform Standards of Professional Appraisal Practice (USPAP) alludes to this issue and appraiser responsibility when it requires proper analysis and reporting of the market or market level of an appraisal subject. (7)
An example of the market-level concern might be a restaurant appraisal, which may be appraised at the real property level only, at the real and personal property level, or at the business enterprise level with real and personal property and business intangibles. For real estate appraisers, the classic formulas for the three approaches to value are sometimes incorrectly applied because these formulas-which are pervasive throughout the valuation industry, literature and education, law and regulation, and finance-are actually special-case formulas that often do not apply in practice, depending on the market level of valuation.
The importance of the issue increases as the complexity of the overall asset increases. Confusion about special-case formulas that do not apply in practice can result in costly property and income taxation issues, in faulty reporting to investors, and in miscollateralization in loan underwriting.
There's Only One Overall Value
If overall value ([V.sub.o]) equals the market value of a combination of assets as they are commonly bundled and sold in the market, then [V.sub.o] = [V.sub.l] + [V.sub.b] only works in special cases where the commonly bundled property is typically sold without the inclusion of any personal property or business intangibles whatsoever. If hospitals, nursing homes, theaters, golf courses, restaurants, or hotels, for example, are commonly sold with real property, personal property, and business intangibles, then the overall value ([V.sub.o]) does not equal just [V.sub.l] + [V.sub.b], but rather equals [V.sub.l] + [V.sub.b] + [V.sub.pp] + [V.sub.bi] Categorically, the classic real estate formula, [V.sub.o] = [V.sub.l] + [V.sub.b], is a special-case formula, where [V.sub.pp] and [V.sub.bi] equal zero and are hence dropped.
Overall value ([V.sub.o]) ought to be reserved to designate the market-predominate combination of asset types bundled together. It is not up to the appraiser to define overall value. Rather overall value, which represents market value, is defined by the market, and is merely discovered and accepted by the appraiser and client. An appraisal report must clearly state how overall value is defined by the market of the subject property.
To report precisely, the appraiser needs to conduct market research to determine what bundle of asset types are commonly transferred together when assets like the appraisal subject are transferred. While the purpose of an appraisal may be to find the market value of real property ([V.sub.rp]), the appraiser should not define overall value ([V.sub.o] as equal to the market value of real property, when the market defines overall value as something more than the value of real property.
If a type of real property is most commonly sold bundled with other types of assets, either personal property or business intangibles, then the market is defining overall value ([V.sub.o]) as something more than the value of real property ([V.sub.rp]). When appraisers report their real property value as an overall value and the market is defining overall value as something more than the value of real property, then the appraiser is creating confusion and may be...
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