Tree Appraisal: What is the Trunk Formula Method (9th Edition)?

© 1997, 1998, 2000 Scott Cullen.

[See Acknowledgments and Explanations below.]

Introduction

The Trunk Formula Method (CTLA 2000, 70-75; CTLA 1992, 57-63) may be the most widely employed method of appraising landscape or amenity trees. But there are frequent questions about proper application of its various adjustment factors (CTLA 2000, 25-55; CTLA 1992, 13-42). The Location factor, for example, was treated in detail at ASCA's 1996 annual conference in Seattle. And there is continuing debate about the inherent logic of the Trunk Formula Method and its strengths or weaknesses vis-a-vis other methods. "Trunk Formula vs. Cost of Cure" was on the program of ASCA's 1997 annual conference in Orlando and the Guide for Plant Appraisal, 9th Edition has expanded treatment of Cost of Cure (CTLA 2000).

The purpose of this article is to explain (not critique) what the Trunk Formula Method is and to ground it in an appraisal or valuation [i] context. This may help tree appraisers to better: A) understand and address real or perceived weaknesses in the method; B) understand when or when not to select it and how to apply it; and C) defend or explain their selection and application of it.

1) The Trunk Formula Method is a tool selected by the appraiser using professional judgment (CTLA 2000, xiv; CTLA 1992, vi ¶5). It is not the source of value. It is not the only method available to the appraiser. It is, in the abstract, neither inferior nor superior to other methods. It is, simply, a tool with certain advantages and certain limitations. Its appropriateness and reliability in any particular situation can only be judged in light of the definition of the appraisal problem. [ii]

2) The Trunk Formula Method is an appraisal model for estimating a defined value. Value is broadly defined as "the current worth of future benefits" (Appr.Inst. 1993, 384). This definition considers that value is derived from utility (Appr.Inst. 1993, 383; Appr.Inst. 1992, 24; Black 1990, 1551), the "ability of a product to satisfy human wants, needs or desires," that is to provide benefits. In actual practice, the benefits which are considered or how their worth is estimated will vary depending on a more specific definition of value (Appr. Inst. 1992, 18-24; Black 1990, 1551 ¶3 et seq). [iii] The appraiser must specify [iv] the definition which applies and the appraisal model must be selected and applied accordingly.

These first two characteristics are not unique to the Trunk Formula Method, but common to all appraisal methods.

3) The Trunk Formula Method is a surrogate or substitute. It may substitute for data which are not available. It may substitute for time or budget which are not available, within the scope of an assignment, to collect other data or apply other methods. It may substitute for methods which are not appropriate or warranted for a particular assignment, even if data and/or time/budget required for such other methods would otherwise be available. This surrogate characteristic may be considered a limitation if other, more reliable methods can be applied; or an advantage if other methods cannot be applied, if reliability is less important than other considerations or if it can be applied in addition to other methods.

4) The Trunk Formula Method is a depreciated replacement cost approach to value. The cost [v] approach considers that the utility or benefits inherent in an object are replaced or reproduced by replacing or reproducing the object. The cost of replacement or reproduction, therefor, provides an indication of value. [vi] This replacement cost is depreciated (Appr. Inst. 1993, 96; Appr.Inst. 1992, 343-365; CTLA 2000, 21 ¶1), that is reduced, to reflect any difference in the benefits that would flow from a new, idealized [vii] replacement as compared to an older or otherwise imperfect appraised object in a particular situation.

In applying the Trunk Formula Method (CTLA 2000, 70-75), the appraiser starts with the cost to buy and install the largest reasonably available replacement tree (Installed Tree Cost [viii]). The appraiser then calculates a cost per unit area (Unit Tree Cost [ix]) for such a tree and applies it to the difference in size (trunk area increase) between the replacement and appraised trees. The result is added to Installed Tree Cost to obtain Basic Tree Cost. [x] The surrogate characteristic of the method is demonstrated in these steps as the available replacement cost data are extrapolated out to the trunk area increase, for which replacement cost data are not available. [xi]

The Basic Tree Cost is then reduced by Species, Condition and Location factors to reflect the difference, if any, between the cost to produce an idealized replacement for the appraised tree and the benefits the appraised tree is (or was) likely to provide.

The Species adjustment can be understood as functional depreciation [xii] which considers species related attributes such as growth characteristics, maintenance requirements and aesthetics.

The Condition adjustment can best be understood as physical depreciation[xiii] which considers condition related factors in the broad categories of structural integrity and plant health.

The Location adjustment considers whether or how physical characteristics of the appraised tree are (or were) likely to be enjoyed or experienced. The appraiser must remember that value is derived from the satisfaction of human wants, needs and desires (Appr.Inst. 1993, 383; Appr.Inst. 1992, 24; Black 1990, 1551). Stated another way, there must be a beneficiary, not just the ability to provide benefits. [xiv] This notion of experienced benefits is why the Location factor was incorporated into the Trunk Formula Method (Neely 1975, 5). The location adjustment can be understood as functional or economic depreciation. [xv]

The location adjustment might be considered a surrogate A) by an explicit consideration through its Site factor of the value of the real estate [xvi] where the tree is located, for a complete sales comparable approach to market value, or B) through its Placement and Contribution factors, for a more direct or explicit consideration of benefits through an income approach to value. [xvii] The reliability of any such substitution is, of course, limited by the fact that the method explicitly relies on replacement cost data. Replacement cost approaches are most reliable when value is defined as replacement cost. If value is defined as Fair Market Value (FMV) or the Value of Benefits, cost approaches may be less reliable than approaches which consider market or benefits data.

An inherent limitation of any [xviii] replacement cost approach is an assumption that its indication of value equals replacement cost. [xix] The appraiser must consider whether value might exceed or be less than replacement cost. To the extent that this is likely, the appraiser must consider [xx] any available non-cost data such as comparable sales prices or quantifiable benefits. This may be through A) implementation by the appraiser of sales comparable or income approaches to value, or B) through data from other sources. [xxi] Since depreciation adjustments can only be downward, any increase in value above replacement cost must be made as a separate, additional adjustment. A decrease in value below replacement cost may be made as a separate additional adjustment or in revised depreciation adjustments.

Conversely, an inherent advantage of a replacement cost approach is that it may be sensitive to elements of value which are not reflected by other approaches. Value in use, for example, may exceed value in exchange. [xxii]

Conclusion

The Trunk Formula Method is a familiar and useful tree appraisal tool. Understanding its theoretical basis in an appraisal context will enable tree appraisers to apply it more skillfully, to continue to improve it and to understand its place in a complete tree appraisal framework or model (Cullen 1996; Duke 1995).


Notes

[i] A) In this article "appraisal" and "valuation" are intended to be interchangeable and are not intended to have the specific, separate meanings defined in ASCA's Code of Ethics and Standards of Professional Practice.

B) This article relies on the field of real estate appraisal to establish context since: it is highly developed with a large and readily available literature; it is widely accepted, practiced and understood; and irreplaceably large trees are normally considered a component of real estate. This is not to suggest that tree value must always be estimated as or limited to a portion of real estate value nor that other fields of appraisal such as natural resource valuation might not also be applied.

[ii] Definition of the appraisal problem is the first step in the appraisal or valuation process. It includes consideration of (among other things): the purpose, use and scope of the appraisal; the definition of value; and limiting conditions such as the nature of available data and legal or regulatory constraints (Appr. Inst. 1992, 73 fig. 4.1).

[iii] See note ii.

[iv] An appropriate value definition might be selected by the appraiser or might be imposed by: the assignment; the client; or a court, law or regulation.

[v] Appraisers distinguish cost, expense, price and value. Cost is the amount required to bring something into existence and is related to production, rather than obtaining it in exchange ready to use or enjoy. In the case of a replacement tree this would include the nursery cost plus the costs of transportation, planting and so forth (CTLA 2000, 61). In an appraisal context "cost" refers to current replacement cost or "cost new" and is distinguished from historical cost or "book cost." Expense is an expenditure to operate or maintain an existing product or good. Price is an amount actually accepted or paid for an existing product or good and is related to exchange. It is historic fact. Value is the worth of a product or good which may or may not equal cost or price, depending on the definition of value and the facts. It is the figure which appraisers attempt to estimate or predict.

[vi] Contrast the other traditional approaches to value (CTLA 2000, 19=23):

A) the sales comparable approach considers the prices in actual exchanges of comparable objects as indications of the value -- usually market value -- of the object and its inherent benefits.

B) the income capitalization approach directly considers the worth of benefits which flow from an object as an indication of the value of the object.

[vii] Typically, replacement cost approaches consider new, man-made products which are presumed to be perfect, or free from deterioration or defects which tend to erode away the value in an older product. Trees are not man-made products and perfection may be impossible to define. Likewise, defects, if they are considered departures from perfection, may be difficult to distinguish from normally or commonly occurring conditions in irreplaceably large trees. And defects in trees, as natural rather than man-made products, are difficult to relate to units of replacement cost. (Except for curable items as discussed at note xiii).

It is most useful, then, for the tree appraiser to consider A) depreciation in terms of a tree's reduced utility or reduced ability to provide benefits, and B) the reduction as compared to a "...'high quality' specimen (CTLA 2000, 25; CTLA 1992, 13)."

[viii] Formerly Replacement Cost (CTLA 1992).

[ix] This replacement unit cost may be wholesale, retail or installed (CTLA 2000, 71). Formerly Basic Price (CTLA 1992).

[x] Formerly Basic Value (CTLA 1992).

[xi] The Trunk Formula Method is specifically recommended for appraising trees beyond reasonably replaceable size (CTLA 2000, 70; CTLA 1992, 5, 13, 48, 57) since by definition replacement cost data do not often exist for such large trees.

It should be noted that there is increasing availability of actual experience data for obtaining, transporting, planting and establishing large trees and that appraisals using these data are more common than they once were. These actual data might be considered superior to the surrogate data used in the Trunk Formula Method, but the appraiser must remember that their applicability might be limited (CTLA 2000, 66), that if applied depreciation must also be applied to reflect actual benefits and that they may involve more appraisal time and expense to apply.

[xii] Also known as functional obsolescence (Appr. Inst. 1993, 154), it considers deficiencies (Appr.Inst. 1993, 92; Appr.Inst. 1992, 355-356; CTLA 2000, pp. 26 & 27 Tables 4.1 & 4.2; CTLA 1992, 43 Table 7-1) or inadequacies, elements of capacity or quality , which are reflected in cost but not present and cannot provide benefits. A tree of a given species may be deficient (as compared to an idealized species) for a given setting or growth environment and require a Species rating of less than 100%.

Functional attributes, such as weak branch attachments or pest problems that are related to a Species rather than to a particular specimen should be reflected in this adjustment (CTLA 2000, 28 ¶3). The tree appraiser must be cautious not deduct from replacement cost in both the Condition and Species ratings for the same functional item (Harris n.d).

Formerly (CTLA 1992), the Species adjustment was applied only to the trunk area increase portion of Basic Tree Cost (formerly Basic Value) and not to the Installed Tree Cost (formerly Replacement Cost) portion.

[xiii] Since it is concerned with the physical condition or physical deterioration (Appr.Inst. 1993, 98, 265) of the tree.

Items reflected in the Condition adjustment should be incurable (Appr.Inst. 1993, 179-180; Appr. Inst. 1992, 350, 355). Curable (Appr.Inst. 1993, 86) items, in trees which are not destroyed, are more properly addressed by estimating a Cost of Repair (CTLA 2000, 57 & 76; CTLA, 68) and making a separate (dollar rather than percentage) deduction from the cost indication of value resulting from the formula. This additional adjustment reflects that, as of the date of appraisal, the unrepaired or uncured condition reduces the utility of the tree and thus reduces the replacement cost indication of value by the cost of the needed repair. The appraiser must recognize that once the repair is completed its cost would be added back to appraised value. Other approaches might even indicate an increase in value greater than the cost of repair (Appr.Inst. 1992, 348).

[xiv] "Value is extrinsic to the [object] to which it is ascribed ; it is created in the minds of the individuals [to whom it provides utility] (Appr.Inst. 1992, 24)."

[xv] Also known as functional or economic/external obsolescence (Appr. Inst. 1993, 154, 112, 128), either of which can be used to explain the location adjustment.

Functional obsolescence considers super adequacies (Appr.Inst. 1993, 357; Appr.Inst. 1992, 355-356) or excesses in capacity or quality which are present and reflected in costs but which will not be experienced as benefits or recognized as value. A tree of given size, species and condition may be super adequate for a given setting and require Site or Placement ratings of less than 100%.

Functional obsolescence also considers deficiencies (Appr.Inst. 1993, 92; Appr.Inst. 1992, 355-356; CTLA, 43 Table 7-1) or inadequacies, elements of capacity or quality which are reflected in replacement cost but not present and cannot provide benefits. A tree of given size, species and condition may be deficient for a given setting and require a Contribution rating of less than 100%. (The tree appraiser must be cautious not to deduct from replacement cost in both the Condition and Contribution ratings for the same item (Harris n.d.)).

Alternatively, the Location adjustment can be understood as Economic or External obsolescence which considers "...diminished utility of [an object] due to negative influences emanating from outside [the object]...(Appr. Inst. 1992, 358)." When all factors relating to the tree itself (including functional deficiencies) are considered in size and in the species and condition adjustments, then factors external to the tree can be considered in the Location adjustment. The Contribution rating would be 100% and the Site and Placement ratings would be assigned as appropriate.

[xvi] Which must be obtained from a competent source.

[xvii] "The [replacement] cost approach is particularly important when a lack of market activity limits the usefulness of the sales comparison approach and when the [objects] to be appraised are not amenable to valuation by the income capitalization approach" (Appr. Inst. 1992, 316).

The great appeal of the Trunk Formula Method has been that as a replacement cost approach it provides a straightforward surrogate for the other approaches.

With regard to the sales comparable approach: irreplaceably large trees are not market goods in and of themselves; there are few model surveys in the literature which attempt to isolate tree values as a component of real estate fair market values; and such surveys are beyond the reasonable scope of the appraisal of an individual tree.

With regard to the income capitalization approach: the income or benefits provided by a tree are seldom explicitly quantified in dollars; application models which attempt to do so are just emerging; and such models have not been designed as appraisal tools and are intended for other purposes. (City-GreenTM, Aunan ; Moll 1995, 22-27, 70)and QuantiTreeTM (Davey 1993; Jones 1995)are "urban forest" models intended to quantify the environmental benefits of large groups of trees. The National Arborist Foundation's large tree model (NAA 1994; NAA 1995; NAA 1995) is designed to consider single trees but is intended to demonstrate the benefits of maintenance.)

[xviii] A) The Replacement Cost Method and the Cost of Cure Method are also depreciated replacement cost approaches to value (CTLA 2000, 57ff).

B) The Cost of Repair Method and the Compounded Replacement Cost technique (CTLA 2000, 125) are replacement cost approaches to value which may also involve depreciation steps to reflect pre-casualty conditions.

C) These methods may also identify additional tree removal, site cleanup, restoration and preparation expenditures and additional maintenance expenditures and so may result in value indications which exceed the cost of the replacement tree alone. Any such excess may be related to additional damages rather than to a tree value in excess of replacement tree costs.

[xix] The replacement cost approach is classically rooted in the supply-side theory of economics which recognized only the factors of production and considered that the cost of production must equal value.

The demand-side theory of economics, by contrast, recognized utility as the factor which determines value.

Modern value theory recognizes elements of both the supply and demand-side theories and that replacement cost is one way to approach value rather than being necessarily equal to value (Smith & Belloit 1987; 22-26). In the appraisal process indications of value from various approaches are reconciled (Appr. Inst. 1993, 296) to reach an opinion of value.

[xx] To the extent allowed by the scope of the appraisal.

[xxi] E.g., the qualified opinion of a real estate appraiser or other expert, or specific benefit data from the client (CTLA 9, ¶3).

[xxii] Value in exchange, or market value, requires the economic characteristics of scarcity, utility and transferability. Value in use requires only utility and may exist in the absence of a market (Smith & Belloit 1987, 5, 23).


Bibliography


Acknowledgements and Explanations

This copyrighted article was first printed in Arboricultural Consultant (the newsletter of the American Society of Consulting Arborists) September-October, 1997, 30(5):3ff. It was reprinted (with the permission of the author who retains all rights) in 1998 and in 2000 on the Tree-Tech Consulting web site (http://www.tree-tech.com/).

The 1998 printing was revised to employ the (Author-Date) form of citation as set forth in the Chicago Manual of Style, 14th Edition. Formatting in this printing was revised to facilitate electronic file access and transfer, most notably: substantive note numbers are presented in hard brackets [i] rather than super-scripted. The content of text and substantive notes were unchanged from the first printing.

The content of text and substantive notes were revised in 2000 to reflect changes in methodology and terminology in the Trunk Formula Method in the 2000 Guide for Plant Appraisal, 9th Edition and to make certain terminology consistent with companion articles. Certain concepts presented in first printing of this article but not in the 8th Edition Guide (CTLA 1992) are now reflected in the 9th Edition and citations have been added.

The author is grateful to Steve Day for insightful comments on drafts of the first printing and to Russell Carlson for making the original text available to a wider, on-line audience.

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