Arboriculture & Urban Forestry 37(5): September 2011 205 Table 6. Maintenance costs example at a 5% interest rate illustrating minimum size delayed patterned terminating cash flows (MSDPTCF). Currency is in U.S. dollars. Treatment Pruning (annual) Pruning (minor) Pruning (major) Net present value (over 90 years) $160 and major pruning occurs once every 10 years for $260, then a calculation from Formula 9 should be used. Table 6 also illustrates this cash flow in a simple format. Note that major prun- ing was actually an MSDPCF of $100 occurring once every 10 years stacked onto the MSDPCF of $160 occurs every five years. DISCUSSION The types and nature of cash flows for urban tree and forest DCF or income approach valuation were described. Regular DCF formulas were described and specialized DCF formulas were developed to accommodate many of the irregular cash flows common to urban tree and forest valuation. Examples show how each formula might be used in the income approach. DCF valuation software is in common use, including urban forestry applications. Unfortunately, most of this software con- tains the standard DCF formulas and requires cash flows to be one of the regular patterns (e.g., annual, terminating, perpetual, or periodic). All standard DCF formulas have rigid assumptions on cash flow structure; especially on the timing of the first pay- ment and that payments must be uniform over time. Cash flows in urban tree and forest valuation situations often do not follow these rigid patterns, preventing appraisers and analysts from us- ing conventional software valuation packages to solve complex problems. The income approach is a valuable tool in appraisals and valuations (Cullen 2005), and the complexity of cash flows is one of the reasons it is not used more. Plus, the income ap- proach is valuable as supporting evidence when other approaches are used. For example, an appraisal based on comparable sales is stronger if a supplemental analysis of cash flows and the income approach support the estimated value (Appraisal Institute 2008). These specialized DCF formulas allowed for easier use of the income approach in urban tree and forest situations. In addition, any standard forest valuation software package could be easily expanded to include urban situations by in- cluding formulas and cash flow situations in calculation op- tions. FORVAL, for example, already includes specialized for- estry situations (Bullard et al. 2011), and its format was ideal to add the type of cash flow patterns discussed in this study. The examples were kept simple to illustrate formula use. How- ever, complex patterns could be constructed and solved with these formulas. It would not be difficult to take any of the examples and expand them into a more realistic, complex urban tree or forest sit- uation. The goal of the study authors was to present formulas and techniques that made the income approach easier to use in these situations, and so kept examples relatively simple in order to stress ease of use, rather than the complexity that could be included. The study authors presented techniques that should make DCF analysis a more practical application for urban tree and forest appraisals and valuations. These techniques will find their way into relevant appraisal and valuation software. As presented, many could be easily incorporated into existing Frequency Annual Five years Ten years Year(s) 20–90 20–90 20–90 Amount ($) (160.00) (160.00) (260.00) PV ($) (1,226.72) (271.40) (95.65) (367.05) appraisal and valuation models. For example, many models are now spreadsheet-based, and adding these formulas to a spread- sheet would be a relatively simple matter. The authors expect the methodology and specialized formulas to become part of urban tree and forest appraisal and valuation software and to pro- vide useful analytical shortcuts for these specialized situations. Acknowledgments. This research was sponsored by the USDA Forest Service National Urban and Community Forestry Advisory Council. LITERATURE CITED American Forests. 2001. Urban ecosystem analysis, Atlanta Metro Area: Calculating nature. Accessed February 2011. Appraisal Institute. 2008. The Appraisal of Real Estate. 13th Edition. The Appraisal Institute. Chicago, IL. AtlantaTreeServiceAtCost.com. 2011. Get Atlanta tree services at cost now. Accessed 01/01/2011. Bullard, S.H., and T.J. Straka. 1998. Basic Concepts in Forest Valuation and Investment Analysis. 2nd Edition. Forestry Suppliers, Inc., Jack- son, MS. Bullard, S.H., T.J. Straka, and C.B. Landrum. 2011. FORVAL. Online Forestry Investment Calculations. Mississippi State University. Accessed 01/02/2011. Burns, R.M., and B.H. Honkala. 1990. Silvics of North America: 1. Conifers; 2. Hardwoods. USDA Forest Service, Washington, D.C. Casey Trees and Davey Tree Expert Company. 2009. National Tree Benefit Calculator. Accessed 01/02/2010. Council of Tree and Landscape Appraisers. 2000. Guide for Plant Appraisal. 9th Edition. International Society of Arboriculture. Champaign, IL. Cullen, S. 2005. Tree appraisal chronology of North American industry guidance. Journal of Arboriculture 31:157–162. Gollier, C., P. Koundouri, and T. Pantelidis. 2008. Declining discount rates: Economic justifications and implications for long-run policy. Economic Policy 56:757–795. Kanniainen, J. 2009. Can properly discounted projects follow geometric Brownian motion? Mathematical Methods of Operations Research 70:435–450. Kaye, T.N., and D.A. Pyke. 2003. The effect of stochastic technique on estimates of population viability from transition matrix models. Ecol- ogy 84:1464–1476. Klemperer, W.D. 1996. Forest Economics and Finance. McGraw-Hill, Inc., New York. Martin, C.W., R.C. Maggio, and D.N. Appel. 1989. The contributory value of trees to residential property in Austin, Texas Metropolitan Area. Journal of Arboriculture 15:72–76. McPherson, E.G., and J.R. Simpson. 2002. A comparison of municipal forest benefits and costs in Modesto and Santa Monica, California, USA. Urban Forestry and Urban Greening 1:62–74. ©2011 International Society of Arboriculture
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