Arboriculture & Urban Forestry 37(5): September 2011 packages. Later, examples of urban tree and forest valuation situations representing applications of each formula were illus- trated via detailed calculations as to their use in DCF analyses. The use of each formula was illustrated using arboriculture and urban forestry examples, like carbon sequestration, energy savings, windbreak savings, windbreaks, soil enhancement, and maintenance costs. The examples were developed from actual ur- ban forest and single tree benefits and costs identified in the liter- ature. Many of the benefit estimates from the current study came from the National Tree Benefit Calculator (Casey Trees and Davey Tree Expert Company 2009) and many of the costs from Atlanta Tree Service at Cost (ATSC 2011). The consumer price index (or the inflation rate) was used to adjust costs or benefits from previ- ous studies to current levels (U.S. Dept. of Labor 2011). How- ever, the goal of the study authors was not to provide real world, current estimates of urban tree and forest benefits and costs. Rather, to provide simplified situations to better explain their us- age. The study authors included calculations of both the PV and the urban tree site value (UTSV) to show the application of both. Single-sum Discounting (SSD) The basic formula used in DCF analysis is the formula for discount- ing a single sum. Costs of tree removal, for example, occur only once in the lifecycle of a tree and are, thus, single sums and dis- counted with the SSD formula. It discounts a cash flow to year zero on a cash flow timeline. Year zero represents the current point in time or the beginning of year one or time period one. This formula is [1] where g is the percentage rate of growth of the annuity (expressed as a decimal) and the remaining variables are as previously defined. ue at year n, i is the interest rate (expressed as a deci- mal), and n is the number of years being evaluated. where V0 is the value at year zero, Vn Present Value of a Terminating Annuity (TA) Sometimes cash flows of the same magnitude occur annually. An example may be annual maintenance costs for a popula- tion of trees with a constant mix of age classes. A basic formula calculates the present value of a terminating annual series as [2] where a is the annual cash flow and the re- maining variables are as previously defined. Present Value of a Perpetual Annuity (PA) In some urban forestry situations (such as the creation of a conservation easement that generates perpetual uniform ben- efits over time), the value of an annual cash flow occurs for- ever. The calculation of a perpetual annuity is as follows [3] where a is the annual cash flow and the re- maining variables are as previously defined. Present Value of Minimum Size Delayed Periodic Cash Flows (MSDPCF) Similar to the MSDACF, the MSDPCF calculates the pres- ent value of benefits (or costs) incurred periodically that are ©2011 International Society of Arboriculture is the val- Present Value of Minimum Size Delayed Annual Cash Flows (MSDACF) In some urban trees, annual cash flows may not occur until the tree reaches a certain minimum size. For example, electricity savings in summer from the shade of a large tree do not begin until the tree reaches a certain size. Other examples might be privacy benefits, sound barrier benefits, air quality, health, and recreation benefits (Ulrich 1984; Martin et al. 1989; Novak et al. 2002; Wolf 2004). In fact, MSDACF valuation is common in urban forestry applica- tions, as many urban forest benefits rely on a certain crown size or structure more than a particular age or diameter at breast height. These crown assets only occur once the tree has reached a mini- mum age for developing a mature crown. The MSDACF formula is [6] is the number of years for which the annuity occurs and nv is the number of years the annuity is delayed from the standard an- where na nuity. The study authors note that this formula also applies to costs with similar financial scheduling, like periodic costs for pruning. 201 Present Value of a Terminating Periodic Series (TPS) The prior valuation formulas were basic DCF analysis tools. Most valuation software packages include an automatic com- putation of these values. The TPS formula is not a basic DCF formula. Terminating periodic refers to a situation where ben- efits or costs have a regular, uniform magnitude, but occur on a periodic, not an annual basis. An example would be storm- water or flood mitigation every 20 years, starting at year 20 and ending at year 140. The formula could easily be adapt- ed to time periods shorter than a year. The TPS formula is [4] where t is the length of each period in years, n is the number of compounding periods, and the re- maining variables are as previously defined. Present Value of a Fixed Rate Increasing Annuity (FRIA) In other situations, benefits or costs may occur annually but have a magnitude that increases at an exponential rate. For example, a tree’s ability to sequester carbon may increase a given rate per year. In this case, an arborist can use a formula for the pres- ent value of a growing annuity. The calculation of the FRIA is: [5]
September 2011
| Title Name |
Pages |
Delete |
Url |
| Empty |
Ai generated response may be inaccurate.
Search Text Block
Page #page_num
#doc_title
Hi $receivername|$receiveremail,
$sendername|$senderemail wrote these comments for you:
$message
$sendername|$senderemail would like for you to view the following digital edition.
Please click on the page below to be directed to the digital edition:
$thumbnail$pagenum
$link$pagenum
Your form submission was a success.
Downloading PDF
Generating your PDF, please wait...
This process might take longer please wait
