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16 Initial Const $$ Rehab $$ Rehab $$ Rehab $$ Maint Maint Maint Maint Maint Maint Maint $$ $$ $$ $$ $$ $$ $$ Time, years t1 t2 t3 t4 0 Salvage $$ Figure 10. Example expenditure-stream diagram. For economic analysis, only the differential user costs In deterministic analysis, computing life-cycle costs involves incurred from the use of one alternative over another are con- a simple application of NPV. In probabilistic analysis, the NPV sidered. The suggested practice is to consider only the time is calculated after each iteration to generate an array of fore- delay and vehicle operating cost components associated with casted costs. These costs are then analyzed and compared with work zones. These components can be estimated reasonably the forecasted costs of other alternatives to identify the most well and constitute a large portion of the total user costs. Other cost-effective strategy. Probabilistic simulation requires the use user cost components are difficult to collect and quantify of a computerized spreadsheet program equipped with the accurately. necessary probabilistic distribution functions, such as FHWA's More detailed discussion on user costs can be found in the RealCost (Office of Assett Management 2004), or a stand-alone FHWA's guidance on the LCCA. computer program to perform the simulation. When performing a probabilistic simulation, it is important to make sure that each iteration represents a scenario that can 4.3.3 Develop Expenditure-Stream actually occur. Two modeling errors with the potential to cre- Diagrams ate unreal scenarios are as follows (Walls and Smith 1998): Expenditure-stream diagrams are graphical or tabular repre- sentations of direct-agency expenditures over time. These dia- Lack of appropriate predefined relationships between grams help the designer/analyst visualize the magnitudes and input parameters. Although each randomly selected value timings of all expenditures projected for the analysis period for for a given iteration may be legitimate on its own, reality each alternative. As illustrated in Figure 10, an expenditure- may dictate that certain relationships exist between the stream diagram shows the costs and benefits associated with input parameters. For example, since higher traffic volume various activities of an alternative's pavement life cycle on a generally is linked with shorter pavement life for a given time scale. Costs normally are depicted using upward arrows, design cross section, it is important to establish an appro- and benefits (e.g., salvage value) are depicted using downward priate sampling correlation between these two inputs. Such arrows. a correlation would ensure that, for each iteration, a sam- ple from the high side of the traffic probability distribution is countered with a sample on the low side of the pavement 4.4 Compute Life-Cycle Costs life probability distribution, and vice versa. Once the expenditure-stream diagram for each alternative Lack of fixed limits on input sampling distributions. pavement strategy has been developed, the task of computing For some types of sampling distributions, the limits for projected life-cycle costs is undertaken. This step combines ini- sampling are not among the criteria used to define the dis- tial and future agency costs that are projected to occur at dif- tribution (e.g., in defining a normal sampling distribu- ferent points in time on a comparable scale. Considering the tion, only the mean and standard deviation are needed). time value of money, all future costs are converted to present However, it is important to know the minimum and max- values using a specified discount rate. The initial costs and all imum values for sampling so that reasonable values are discounted future costs are then summed together to produce used in the simulation. Misleading simulation results can the NPV of agency costs. The user costs are not combined with be expected, for instance, if the distribution for a cost or the agency costs but are evaluated separately using the process pavement service-life parameter allows negative values to discussed in Chapter 5. be selected.