200 Peterson and Straka: Cash Flow Analysis Formulas for Urban Trees and Forests Arboriculture & Urban Forestry 2011. 37(5): 200–206 Specialized Discounted Cash Flow Analysis Formulas for Valuation of Benefits and Costs of Urban Trees and Forests Kristin S. Peterson and Thomas J. Straka Abstract. Urban trees and forests have distinct benefits and costs that can be evaluated financially. While there are appraisal methods commonly used to value individual trees and urban forests, one method that is difficult to use in practice is a discounted cash flow (DCF) analysis. This is the appraisal method that best accounts for the time value of money and allows for a temporal comparison of benefits and costs. Current timber appraisal methods are discussed for urban situations and DCF analysis is presented as a viable supplemental appraisal method for valuation of the urban trees. Simple models are presented that allow for the solution of DCF-type urban forestry valuations using conventional software valuation packages. Examples are provided of typical urban tree benefit and cost scenarios, with DCF calculations of present value (PV) and net present value using the specialized DCF formulas. Key Words. Appraisal; Discount Rate; Discounted Cash Flow Analysis; Financial; Net Present Value; Present Value; Urban Forestry; Valuation. Discounted cash flow (DCF) analysis is a method of valuation often used in forests managed for timber production objectives, to obtain the present value (PV) of cash flows or the value in current day currency (e.g., U.S. dollars) considering interest (Bullard and Straka 1998). Several conventional forestry valuation software packages use DCF as a method for financial decision-making be- cause it accounts for the time value of money and represents the dynamic financial nature of a timber stand. Early forest valuation models, such as Faustmann’s formula, rely on the principles of DCF analysis to determine important forestry investment financial criteria, such as land expectation value, and financial optima, like rotation length (Tietenberg and Lewis 2008). DCF analysis pro- duces reliable monetary valuations for natural resources, includ- ing forests (Gollier et al. 2008; Kanniainen 2009). DCF is often used over long spans of time with good results; however, its use to value long-life assets, like trees, may produce concerns, such as fairness to future generations and inflation estimates (Price 2005). Despite its accepted use in forestry for timber production, DCF analysis, or the income approach in general, has not been fre- quently used in urban forestry and arboriculture. Cash flows for the benefits and costs of single trees or urban forests are difficult to determine, and the mathematical structure of DCF analysis is somewhat complicated (Council of Tree and Landscape Apprais- ers 2000; Straka and Bullard 2006). Negative cash flows or ex- penditures (both capital and operating) are called “costs” in tradi- tional forestry investment analysis, but they are more likely to be labeled as “expenses” in an appraisal income approach. Conven- tional forestry valuation software packages (such as Forest Valua- tion—forestry investment calculations, or FORVAL) can be used for DCF calculations, but they require that cash flows be input in one of a few standard structures (e.g., single sum, terminating an- nuity, perpetual annuity, or perpetual periodic series) (Straka and Bullard 2002). These standard structures have rigid assumptions about the cash flow sequences; for example, a cash flow occurring ©2011 International Society of Arboriculture each year and beginning at year 1, or a cash flow occurring period- ically every X years and beginning at year X (Straka and Bullard 2002). Benefits (i.e., income) and costs in urban forest and tree valuation situations do not always occur in these structured pat- terns. Standard DCF formulas do not handle irregular cash flows well. This is another primary reason the income approach is often difficult to apply in these situations (Bullard and Straka 2006). STUDY METHODS The study authors identified a series of specialized discounting formulas that were well-suited for solving valuation problems that follow typical cash flow patterns occurring in the benefit and cost structures of urban tree and forest situations. That is to clarify, valuation problems that do not follow standard structured cash flow patterns and, thus, would be difficult to value using many conventional DCF formulas (McPherson and Simpson 2002; McPherson 2003; McPherson 2007). Using the standard DCF formulas common to forest valuation (Appraisal Institute 2008, Bullard and Straka 1998) as a foundation, a series of new or “special” DCF formulas that will allow these benefit and cost sit- uations to be evaluated were constructed using conventional DCF valuation software packages. Simple hypothetical examples of the individual benefit and cost valuations were developed. The study authors also reviewed the basic, standard DCF formulas as they are the basis of these specialized formulas. Most formulas could be utilized as part of a standard DCF valuation software mod- els, like FORVAL (Straka and Bullard 2006; Bullard et al. 2011). First, for the current study, three fairly standard formu- las were presented. Next, a few unusual, but standard formu- las were described that have application to urban situations. Finally, some unique DCF formulas were derived for typical urban tree and forest situations that usually don’t allow for di- rect PV calculations using traditional DCF valuation software
September 2011
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