Arboriculture & Urban Forestry 39(4): July 2013 169 Figure 4. Range of Outcomes Using QTRA (Norris 2007). 2005). In principle, this risk acceptance criterion has much merit, but may be viewed as prescriptive. There is much evidence that annual fatality risks that exceed 1 in 1,000 are unacceptable, and that risks between 1 in 1,000 and 1 in 1 million may be acceptable to government and asset owners if the benefits outweigh the risks (Stewart and Melchers 1997) (Figure 5). There is no clear consensus about at precisely what level risks become unacceptable, so any prescribed safety goal needs to be interpreted with some flexibility. Ellison (2005) notes that “the hazard could confer benefits that might be set against the risk of harm.” This implies a cost-benefit assessment, but the QTRA process does not offer guidance on how a cost-benefit analysis should be under- taken. The two cost-benefit examples to follow are provid- ed to illustrate some key cost-benefit assessment concepts. Example 1: Net benefit of tree removal First, assume that tree removal is the recommended decision and that this will cost $10,000 per tree. If this cost is spread over years (T), then the annual cost discounted to present values is [8] annualized over T = 10 years at r = 3%, then this gives a present value of approximately $1,200 per year. This might be viewed as a direct cost. However, an opportunity cost might also be associated with loss of amenity (e.g., shade, viewpoints, prop- erty value), which might amount to $1,000 or $5,000 per year. The benefit of tree removal is that it will remove all risk, and so ∆R = 100%. Another benefit of tree remov- al is that it may eliminate root damage to pavement and services, producing maintenance savings of $250 per year. If a tree were to fail, the losses would be damage to adjacent property and loss of life totaling $5 million. All costs are converted to annual costs to ensure consis- where CT tency of units. All values are illustrative only to help explain parameters and tradeoffs between costs and benefits. The NPV or net benefit for tree removal (Equation 7) is as follows: ©2013 International Society of Arboriculture CA = T t CT ∑ ( )t 1 =1 1+ r is the total cost and r is the discount rate. If costs are Figure 5. Generally agreed risk acceptance criteria for annual fatality risks (Stewart and Melchers 1997). [9] NPV = E(B) + ∆R (ROH × Closs) – C∆R where ROH = annual risk of harm per tree, E(B) = $250 per year (no root damage to infrastructure), ∆R = 100% (tree removal eliminates all risk), Closs of tree failure), and C∆R = $5 million (consequences of tree removal and $1,000 loss of amenity), and C∆R removal and no loss of amenity), C∆R = $1,200 per year (cost of tree = $2,200 per year (cost = $6,200 per year (cost of tree removal and $5,000 loss of amenity). Figure 6 and Table 2 show that net benefit varies as a function of ROH for losses of amenity of $0, $1,000, and $5,000 per year. If ROH is 1/100 then net benefit of tree removal is $44,000–$49,000, with net benefit highest when there is no loss of amenity. When ROH = 1/1,000 then the net benefit of tree removal reduces to $4,050 and $3,050 for loss of amenity of $0 and $1,000, respectively. However, when ROH = 1/1,000 and loss of amenity is $5,000 per year, then there is not a net benefit of tree removal, but a net loss of $950 per year. A lower ROH of 1/10,000 produces net losses irrespective of level of loss of amenity. To be sure, more detailed analyses are possible, but this example shows that even if ROH exceeds the prescribed QTRA safety goal of 1/10,000, there can still be a net benefit to retaining a tree once all costs and benefits of tree removal are considered.
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