Arboriculture & Urban Forestry 38(4): July 2012 As with any model, the one presented here includes vari- ous sources of uncertainty that may affect the accuracy of, and confidence in, the outputs. For certain inputs, such as removal, replacement, and treatment costs, uncertainty can be mini- mized by obtaining quoted estimates from reputable arborists. However, other sources of uncertainty previously mentioned, such as the extended benefit and cost values of MacPherson et al. (2007) and the tree growth equations based on planta- tion data, are more challenging to reduce. Formal estimates of the uncertainty are not provided (e.g., confidence intervals), but users are reminded that uncertainty is inherent in model outputs. Sensitivity analyses, such as those presented here, can help understand the implications of these uncertainties. RESULTS AND DISCUSSION The model produces an output table that shows all costs and ben- efits through time as well as the net treatment gains/losses and equivalent annual values. Table 2 presents these outputs from a model run that was parameterized using the values provided in Table 1; a review of the derivation and interpretation of these values is as follows. The present value of treatment costs was accumulated through time (reaching $2204 by year 30) as treat- ments were applied once every two years (i.e., biennially). These costs were tied to tree DBH and thus increase as the tree grows during the simulation; however, these increases are offset by eco- nomic discounting which causes the magnitude of the biennial increments to decline over time. Multiplying the home’s potential sale price ($340,000) by the estimated contribution of a mature tree (0.5%) gives the home value benefit in the first year of the simulation ($1700); in Table 1, this value declines over time due to discounting. Under the removal/replacement scenario, there is an immediate loss in home value when the tree is cut at year two, but this value is gained back over time in proportion to the DBH of the replacement tree—so that, for example, a replacement tree with a DBH of 10 cm would contribute half of the home value benefit generated by a mature tree (20 cm). Note that, once ma- ture, the tree’s contribution to home value was capped at 0.5%; no evidence was found in the literature to support a continued increase in home value in proportion to DBH. In fact, one study reported reduced home values in relation to large trees (Orland et al. 1992). It should be stressed that home value benefits are only realized in a financial sense if a house is sold and thus may only be relevant if a homeowner is selling, or wants to consider the option of selling his/her house. The remaining benefits and costs (i.e., energy, runoff and pollution, and maintenance) in any given year of the simulation are driven by tree age (as illustrated in Figure 1) and economic discounting; note that the age of the existing ash tree is estimated from the input DBH (30 cm) by rearranging Formula 1. Treatment gain (or loss) is calculated by subtracting the summed removal-and-replacement costs and benefits from the summed treatment costs and benefits; this is then converted to the equivalent annual value using Formula 2. To assist in interpreting these results, note again that the net treatment gain/loss is the dollar amount that a homeowner would be ahead/behind by treating a tree for a given number of years. For example, to conserve the tree presented in Table 2 for 25 years, it would cost an estimated $648 more than the removal and replacement approach; alternatively, this amount could be expressed as an annual equivalent (or annuity) of ~$39/year. 125 This is the additional amount that a model user would have to be willing to pay to conserve the existing ash tree over that period of time—what has been termed the break-even existence value. The net treatment gain/loss metric and its annual equivalent are particularly useful when applied to a specific time horizon. For instance, if a homeowner is considering selling his/her home at some point in the future, these measures can provide insights on the economic attractiveness of treating a tree up to that point in time. Similarly, recent studies suggest that EAB populations may crash after available ash resources have been depleted—approxi- mately 10 years after initial infestation (Knight et al. 2008)—at which point homeowners may be able to reduce the frequency of treatments; clearly this possibility will need to be revisited in the future as research into EAB population dynamics progresses. To further illustrate the model, graphical model outputs for small (15 cm DBH), medium (30 cm) and large (45 cm) ash trees are presented (Figure 2). Using default model values (Table 1) and only the basic cost considerations (i.e., none of the extended costs and benefits), treatment gains remained positive until year 11, 7, and 7, for small, medium, and large trees, respectively (Figure 2a). Inclusion of the extended benefits and costs greatly changed these outcomes, with positive treatment gains for small, medium, and large trees persisting until years 19, 17, and 15 respectively (Figure 2b). Due to space considerations, the results published here are only for the basic cost considerations and the combined suite of extended benefits and costs; however, the online ver- sion of the model allows users to select specific extended ben- efits and costs and provides a separate graphical output for each. These results lead to the perhaps counterintuitive finding that treating a small tree can, in some circumstances, be more attrac- tive than treating a large tree (Figure 2). Relevant default param- eter values for a small tree include a removal cost of $240 and an initial treatment cost of $97.50; for a large tree, these values increase to $900 for removal and $292.50 for initial treatment. One might expect that the lower removal cost would make re- moval more appealing for smaller trees; the analysis suggests that the lower treatment cost can override this effect. This find- ing is, of course, entirely dependent on the default values out- lined above. Kovacs et al. (2010), using a dynamic-programming approach, determined that the optimal course of action was to remove trees less than 30 cm DBH and treat otherwise. These divergent conclusions result primarily from the much lower treatment costs employed in the Kovacs et al. (2010) study. A simple sensitivity analysis was employed to investigate the influence of each input variable on the duration of treatment gains [i.e., the number of years that the treatment approach is financially ahead of removal and replacement (Table 3)]. Since both benefits and costs are discounted, varying the discount rate between 2% (considered relatively low) and 10 % (considered relatively high) had very little effect on the duration for which treatment gains were projected. However, at even higher discount rates (e.g., ~15%; not shown), positive treatment gains extend be- yond the 30-year time horizon used in this analysis. This result underlines the fact that high discount rates significantly lower the present value of future costs relative to current benefits; thus, homeowners with very high time preference rates on expendi- tures should carefully consider the merits of treating their ash. Treatment costs had the largest impact on the dura- tion of positive treatment gains (Table 3). Values of $5.00, $6.50, and $8.00 per cm DBH resulted in positive treat- ©2012 International Society of Arboriculture
July 2012
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