204 Peterson and Straka: Cash Flow Analysis Formulas for Urban Trees and Forests Windbreak Savings (MSDPCF Calculation) The presence of a large oak on the lawn may stop the removal of shingles from a windstorm that occurs once every 10 years (Table 4). An approximation of cost savings (per 10 years) in this situation was $150. This represented the cost (in time, labor, and materials) of replacing the shingles on the home. The study authors thus assumed the first windstorm occurred in year 15, then every 10 years thereafter until year 85. Again, tree plant- ing and tree removal are single sums and Formula 1 was used to obtain a present value. Wind savings were trickier. The present value of a terminating periodic series of $150 every 10 years, for 80 years, is $233.70. The standard period annuity would have a first payment at year 10, instead of year 15, so the $233.70 needed to be discounted for five years to obtain the correct PV of $183.11. The same value can be calculated using Formula 7; the annuity occurs for 80 years, the length of the time period is 10 years, and the first payment is delayed by five years. Using those same three variable values, Formula 7 provides a PV of $183.11. Soil Enhancement (PTPS Calculation) On lots without trees, treatments for soil, such as aeration, sod, and fertilization, are used to keep the soil lush. Sodding, aera- tion, and fertilization costs can be significant (Ocone 2000). As- sume the soil (without trees) needs annual fertilization, sodding, and aeration once every 10 years and that the cost savings on sod and aeration, as well as fertilizer, were calculated as benefits (Table 5). Because fertilizer cost is stacked onto the base cost of sod and aeration, this was a patterned terminating series and Formula 8 can be used. Note that the fertilizer cost was stacked onto the base cost of sod and aeration. The pattern was illus- trated in detail to better show how the formula could be used to solve for a present value (Table 5). Fertilization, sod, and aera- tion benefits were increased after year 30 to show an increase as the tree matures, which illustrates the formula’s complexity. Maintenance Costs (MSDPTCF Calculation) There were costs to maintain trees on a site. For example, a crew works for five hours with three men (paid $10 per hour) prun- ing a crapemyrtle (Lagerstroemia indicate) once every year. Transportation cost to the site and back is $10. This occurred at the beginning of year 20 until year 90. The PV was shown to be $1,226.72 (Table 6). In some cases, this pruning cost will not be as easy to calculate. If one supposes this tree is the white oak and a minor pruning occurs once every five years for a cost of Table 3. Energy savings model at a 5% interest rate illustrating minimum size delayed annual cash flows (MSDACF). Currency is in U.S. dollars. Treatment Plant tree Annual savings Remove tree Net present value (over 90 years) UTSV (in perpetuity) Frequency Single time Annual Single time Year(s) 0 10–90 90 Amount ($) (70.00) 13.67 (406.00) PV ($) (70.00) 172.84 (5.03) 97.81 99.04 Table 4. Windbreak model at a 5% interest rate illustrating minimum size delayed periodic cash flows (MSDPCF). Currency is in U.S. dollars. Treatment Plant tree Wind savings Remove tree Net present value (over 90 Years) UTSV (in perpetuity) Frequency Single time Every ten years Single time Year 0 15, 25, 35... 90 Amount ($) (70.00) 150.00 (406.00) PV ($) (70.00) 183.11 (5.03) 108.08 109.44 Table 5. Soil enhancement model at a 5% interest rate illustrating patterned terminating periodic series (PTPS). Currency is in U.S. dollars. Treatment Plant Fertilization Sod/aeration Sod/aeration Sod/aeration Fertilization Sod/aeration Sod/aeration Sod/aeration Sod/aeration Sod/aeration Remove tree Net present value (over 90 years) UTSV (in perpetuity) ©2011 International Society of Arboriculture Frequency Single Annual Single Single Single Annual Single Single Single Single Single Single Year(s) 0 10–30 10 20 30 30–90 40 50 60 70 80 90 Amount ($) (70.00) 25.00 1,100.00 1,100.00 1,100.00 50.00 2,200.00 2,200.00 2,200.00 2,200.00 2,200.00 (406.00) PV ($) (70.00) 206.61 675.30 414.58 254.52 230.55 312.50 191.85 117.78 72.35 44.40 (5.70) 2,445.41 2,476.08
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