|<< Previous||Contents||Next >>|
Present Value (or worth): An economic concept that represents the translation of specified amounts of costs or benefits occurring in different time periods into a single amount at a single instant (usually the present). Two related considerations underlie the need for computing present values:
- the fact that money has an intrinsic capacity to earn interest over time (known as the time value of money) due to its productiveness and scarcity, and
- the need in an economic study for comparing or summing incremental outlays or savings of money in different time periods.(1)
Equivalent Uniform Annual Cost (or Benefit): A uniform annual cost (or benefit) that is the equivalent, spread over the entire period of analysis, of all incremental disbursements or costs incurred on (or benefits received from) a project. The present value of the uniform series of equivalent annual costs equals the present value of all project disbursements.(1)
Discount Rate (Interest rate, Time Value of Money): A percentage figure - usually expressed as an annual rate- representing the rate of interest money can be assumed to earn over the period of time under analysis. A governmental unit that decides to spend money improving a highway, for example, loses the opportunity to "invest" this money elsewhere. That rate at which money could be invested elsewhere is sometimes known as the "Opportunity Cost of Capital" and is the appropriate discount rate for use in economic studies. Discount factors derived as a function of the discount rate and time period relative to the present can be used to convert periodic benefits and costs for a project into present value or into equivalent uniform annual cost. However, calculating benefits in constant dollars and using market rates of interest is an error because the market rate of return includes an allowance for expected inflation. Hence, if future benefits and costs are calculated in constant dollars, only the real cost of capital should be represented in the discount rate used. The discount rate assumes annual end-of-year compounding, unless otherwise specified. The sum of $100 in cash today is equivalent, at a 10 percent discount rate, to $110 a year from now, $121 at the end of the second year, and $259.37 at the end of the tenth year. Correspondingly, a commitment to spend $259.37 in the tenth year discounted at 10 percent has a present value of $100.(1)
Residual or Salvage Value: The value of an investment or capital outlay remaining at the end of the study or analysis period.
The equation for determining the present worth or rehabilitation and maintenance costs for a given facility is as follows:
|PW = C + Mi||1||ni||+ ... Mj||1||ni||- S||1||N|
|1 + r||1 + r||1 + r|
|PW||=||Present worth or present value of all costs|
|C||=||Present cost of initial rehabilitation activity|
|Mi||=||Cost of the ith maintenance & rehabilitation (M&R) alternative in terms of constant dollars|
|ni||=||Number of years from the present to the ith M & R activity|
|S||=||Salvage value at the end of the analysis period|
|N||=||Length of the analysis period in years|
|is commonly called the single payment present worth factor.|
The present worth or present value of all costs over the analysis period can be stated in terms of EUAC by multiplying PW by the uniform series capital recovery factor:
|=||PWX||r (1 + r )N|
|( 1 + r )N - 1|
|PW||=||Present Worth as before|
|crƒ(r,N)||=||The uniform series capital recovery factor for discount rate r and analysis period N|
The major initial and recurring costs that should be considered in the economic evaluation of alternative techniques include the following:(2)
- Agency Costs:
- Initial construction costs.
- Future construction or rehabilitation costs (overlays, seal coats, reconstruction, etc.)
- Maintenance costs, recurring throughout the design period.
- Salvage return or residual value at the end of the design period (which may be a "negative" cost).
- Engineering and administration costs.
- Traffic control costs if any are involved.
- User Costs:
- Travel time.
- Vehicle operation.
- Time delay and extra vehicle operating costs during resurfacing or major maintenance.
For a simplified analysis, the following costs are usually considered for life cycle analysis:
- Initial capital costs of rehabilitation.
- Future capital costs of reconstruction or rehabilitation.
- Maintenance costs.
- Salvage value.
However, certain user costs such as time delay costs during rehabilitation must be considered on certain facilities.(3) Factors that must be considered when determining these costs include:
- Will the roadway be closed over a lengthy period of time?
- Are alternate roadways available?
- Can operations be moved to a different facility?
- What are the costs of traffic delays associated with closing the facility?
For present worth calculation, a discount rate of four percent is suggested.(4) It is recommended that because the results of present worth analyses are sensitive to the discount rate, economic calculations at two or three discount rates of 4, 7, and 10 percent be made for a sensitivity analysis(3). Alternatives with large initial costs and low maintenance or user costs are favored by low rates of return. On the other hand, high discount rates favor strategies that combine low initial costs and higher maintenance and user costs.
The 4 percent discount rate must be used with constant dollar costs at the time the analysis is conducted and must remain fixed for the analysis period. For example, if an asphalt concrete pavement is to be constructed, the cost of asphalt concrete at the time of an overlay 20 years after construction should be the same as at the time of initial construction.
The following reasons against inclusion of inflation rates in economic studies have been advanced:(3)
- Difficulties in predicting future inflation rates.
- The acceptance of inflation as a norm may be counter to the government's responsibility for price stabilization.
- Federal programs, if justified in part by inflating benefits, may contribute to inflation.
- Debtor's gains through repaying outstanding debts with inflated dollars are offset by creditors' losses.
- Future dollars to pay for future expenses will likewise be inflated and therefore there is no net change.
An important factor in identifying and performing economic analyses of alternatives in the design of new pavement construction and/or the repair and rehabilitation of existing pavement is the life cycle of the alternative under consideration. The life cycle is the period of time of actual use before replacement, reconstruction, or extensive rehabilitation is required. Obviously, there is a time variation of specific service lives between project sites for a given pavement alternative. Therefore, the life cycle is an overall average of service lives of the specific service lives for identical pavement alternatives experienced at various project sites. The designer may use the generally accepted life cycle for a particular alternative, such as 40 years with maintenance for new PCC pavement, or he/she may elect to use a different life cycle for the same alternative, such as 30 years with little or no maintenance. Table A-1(3) shows typical life cycles for new pavement construction and pavement overlays.
|Pavement Type||Representative Ranges*|
|New PCC||15 - 25|
|PCC Overlay||7 - 14|
|New AC||12 - 20|
|AC Overlay||8 - 12|
- * Varies depending on location, traffic, thickness, existing pavement condition, etc.
- PCC - Portland Cement Concrete,
- AC - Asphalt Concrete.
Pavement repair, maintenance, and rehabilitation life cycles were derived from responses to a questionnaire in 1985 from more than 40 Air Force bases.(3) Respective maintenance activity lives were averaged for all locations in the survey and rounded to the nearest year to arrive at the life cycle for the particular alternative, and are listed in table A-2.(4)
|Maintenance Activity||Life Cycle (Years)|
|Crack Sealing (flexible)||4|
|Chip Seal (flexible)||5|
|Shallow Patch (flexible)||3|
|Deep Patch (flexible)||6|
|Slurry Seal (flexible)||6|
|Cold Milling (flexible)||10|
|Heater Planing (flexible)||6|
|Crack Sealing (rigid)||5|
|Joint Sealing (rigid)||7|
|Shallow Patch (rigid)||5|
|Deep Patch (rigid)||8|
|Slab Replacement (rigid)||19|
|Mud Jacking (rigid)||16|
In performing economic studies of projects under consideration an economic life, service life and analysis life must be established. The service life is the time period of actual use. The economic life is the time period over which a project is economically profitable, or until the service by the project can be provided by another facility at lower costs. The economic life may be less than the service life. Lack of capital may extend a project service life beyond the end of its economic life. Economic life usually ends when the physical deterioration of a pavement proceeds to the point where reduced service and increased maintenance costs justify replacement with an alternative having expected lower life-cycle costs.
Analysis life may not be the same as the service life or economic life of a project, but it is a realistic estimate for use in an economic analysis. The analysis life period selected should be long enough to include the time between major rehabilitation actions for the various alternatives under study, but not so long as to make the analysis uncertain. Suggested values to use for analysis life are shown in table A-3.(3)
|Activity||Pavement Surface Type||Recommended Analysis Life, Years|
|New construction, reconstruction or thick overlays||PCC and AC|
- PCC - portland cement concrete.
- AC - asphalt concrete.
The salvage value of a pavement structure is the residual value at the end of the analysis period. If at the end of this analysis period, it is expected that the facility will be abandoned, the salvage value is any value that the materials may have if removed and reused. In general, it is practical to assume that the salvage value is zero unless specific data are available to calculate otherwise. However, the facility may possess useful life after the analysis period, and if so, the salvage value should be included in the life-cycle cost analysis. The residual value of the last rehabilitation action based on its anticipated remaining life appears to be the best method for determining salvage value. A simplified, but adequate, method for estimating the salvage value can be calculated with the following equation:
|SV = 1 -||LA||C|
|SV||=||salvage value (or residual value) of rehabilitation alternative|
|LA||=||analysis life of rehabilitation alternative in years, i.e., difference between the year of construction and the year of termination of the life cycle analysis|
|LE||=||expected life of the rehabilitation alternative|
|C||=||cost of the rehabilitation alternative|
Use of this simplified approach in estimating salvage value is justified by the fact that there are several uncertainties associated with the service lives and costs for the different pavement component layers, and the relatively small impact that salvage value actually has on life cycle comparisons.
The following is an example situation(3) in which the above equation can be used to calculate the estimated salvage value: If an analysis period of 20 years is used on a project where a rehabilitation alternative has a life cycle of nine years, the residual or salvage value of the second rehabilitation action is equal to the straight-line depreciated value of the alternative at the end of the analysis period as follows:
|SV =||1 -||2||$3.12 ($2.50) = $2.43 ($1.94)|
(Assuming cost of the rehabilitation alternative is 3.12 per square meter, $2.50 per square yard). A more detailed discussion of salvage value and other terms used in this section is contained in Reference2.
Price data are needed for construction, rehabilitation and maintenance operations. Sources of these data include:
- Local records.
- State records.
- Bid summaries.
Price data for recycling and other rehabilitation operations are discussed further in chapter 6: Summary and Cost Data.
Example of Life Cycle Cost Analysis
A simplified example of a life cycle cost analysis is shown in tables A-4 to A-7.(3) Table A-4 shows cost data for rehabilitation alternatives considered for a project in the southwestern United States. A typical calculation sheet for determining present worth and equal uniform annual cost is shown in table A-5. Table A-6 shows costs associated with seven rehabilitation alternatives. A summary of first costs and life cycle costs is shown in table A-7.
|Rehabilitation Alternative||Costs $/m2 ($/yd2)|
|Asphalt cement chip seal||1.08 (0.86)|
|Asphalt-rubber chip seal or interlayer||1.56 (1.25)|
|Fabric interlayer||1.50 (1.20)|
|Heater scarification||1.12 (0.90)|
|Asphalt concrete - 25 mm (one in)||2.06 (1.65)|
|Asphalt rubber interlayer with 36 mm (1.4 in) asphalt concrete||4.66 (3.73)|
|Fabric interlayer with 38 mm (1.5 in) asphalt concrete||4.60 (3.68)|
|Heater scarification with 38 mm (1.5 in) asphalt concrete||2.79 (2.23)|
|Cold recycle 152 mm + 50 mm (6 in + 2 in) asphalt concrete||8.25 (6.60)|
|Hot recycle 177.8 mm (7 in)||10.12 (8.10)|
|Year||Cost, Dollars per sq m (sq yd)||Present Worth Factor, 4%||Present Worth, Dollars|
|Initial Cost||1.56 (1.25) A-R Chip Seal||1.0000||1.56 (1.25)|
|3||0.31 (0.25) maintenance||0.8890||0.27 (0.22)|
|4||6.19 (4.9) 76 mm AC ( 3") AC||0.8548||5.29 (4.23)|
|10||0.12 (0.10) maintenance||0.6756||0.08 (0.07)|
|11||0.12 (0.10) maintenance||0.6496||0.08 (0.06)|
|12||0.12 (0.10) maintenance||0.6246||0.07 (0.06)|
|13||0.19 (0.15) maintenance||0.6006||0.11 (0.09)|
|14||0.31 (0.25) maintenance||0.5775||0.18 (0.14)|
|15||3.12 (2.50) 38 mm AC (1-1/2") AC||0.5553||1.73 (1.39)|
|19||0.12 (0.10) maintenance||0.4746||0.06 (0.05)|
|20||0.19 (0.15) maintenance||0.4564||0.09 (0.07)|
|Salvage Value||0.89 (0.71)||0.4564||-0.41 (-0.32)|
|Total||11.49 (9.19)||Total||9.14 (7.31)|
|Uniform Annual Cost||=||Present Worth x Capital Recovery Factor|
|=||9.14 x (7.31) x 0.07358|
|1 AR Chip Seal||2 76 mm|
|3 HS + 50 mm|
|4 A-R + 50 mm|
|5 Fabric: + 50 mm|
|6 Cold Recycle||7 Hot Recycle|
|Initial||1.56 (1.25)||6.19 (4.95)||5.25 (4.20)||3.64 (4.55)||5.62 (4.50)||6.60||8.10|
|3||0.31 (0.25)||0.19 (0.15)|
|4||6.19 (4.95)||0.25 (0.20)|
|5||0.25 (0.20)||0.12 (0.10)||0.12 (0.10)|
|6||0.31 (0.25)||0.12 (0.10)||0.12 (0.10)|
|7||3.12 (2.50)||0.12 (0.10)||0.12 (0.10)|
|8||0.19 (0.15)||0.12 (0.10)||0.19 (0.15)|
|9||0.12 (0.10)||0.31 (0.25)||0.12 (0.10)||0.31 (0.25)|
|10||0.12 (0.10)||0.19 (0.15)||3.12 (2.50)||0.12 (0.10)||3.12 (2.50)||0.05|
|11||0.12 (0.10)||0.25 (0.20)||0.19 (0.15)|
|12||0.12 (0.10)||0.25 (0.20)||0.31 (0.25)||0.05||0.05|
|13||0.19 (0.15)||0.31 (0.25)||3.12 (2.50)|
|14||0.31 (0.25)||3.12 (2.50)||0.12 (0.10)||0.12 (0.10)||0.10||0.05|
|15||3.12 (2.50)||0.19 (0.15)||0.19 (0.15)||0.15|
|16||0.12 (0.10)||0.31 (0.25)||0.31 (0.25)||0.25||0.10|
|17||0.19 (0.15)||3.12 (2.50)||0.12 (0.10)||2.50||2.50|
|18||0.25 (0.20)||0.19 (0.15)||0.10|
|19||0.12 (0.10)||0.25 (0.20)||0.31 (0.25)||0.20|
|20||0.19 (0.15)||0.31 (0.25)||3.12 (2.50)||0.25|
|Salvage Value||0.89 (0.71)||0.45 (0.36)||1.79 (1.43)||3.12 (2.50)||1.43||1.43||0|
- A-R - Asphalt Rubber
- H-S - Heater Scarification
- AC - Asphalt Concrete
|Description of Project:|
|Location:||Southwestern United States|
|Type of Facility:||Runway, length 975.36 m (3,200 ft) - width 22.8 m (75 ft)|
|Critical Aircraft:||10.89 Mg (24,000 lbs.) gross weight|
|Type of Material||Thickness mm (in)||Condition||Equivalency Factor||Equivalent Thickness mm (in)|
|AC Surface||100 (4)||Fair||1.2||122 (4.8)|
|Untreated Base||254 (10)||Good||1.0||254 (10.0)|
|Condition of Pavement:|
|Condition Survey:||Alligator cracking, moderate 20 percent of area; transverse cracking, moderate, 1-4 per station; longitudinal cracks, moderate, 45.72 m (150 ft) per station.|
|Required Thickness of New Pavement:||457 mm (18") min. 50 mm (2") AC, 127 mm (5") base|
|Equivalent Thickness of Old Pavement:||376 mm (14.8")|
|Required Overlay Thickness:||76 mm (3") AC|
|First Cost $/m2 ($/yd2)||Life Cycle PW, $/m2 ($/yd2)||Time for Rehab.||Chance for Success|
|1. Asphalt-rubber chip seal to delay overlay||1.56 (1.25)||9.14 (7.31)||2 days||90|
|2. 75 mm (3 in) AC overlay||6.19 (4.95)||12.35 (9.88)||5 days||95|
|3. Heater scarification + 50 mm (2 in)||5.25 (4.20)||9.15 (7.32)||4 days||97|
|4. Asphalt-rubber interlayer + 50 mm (2 in) overlay||5.69 (4.55)||8.45 (6.76)||4 days||97|
|5. Fabric interlayer + 50 mm (2 in) overlay||5.62 (4.50)||9.52 (7.62)||4 days||97|
|6. Cold recycle with asphalt emulsion 152 + 50 mmAC (6" + 2"AC)||8.15 (6.60)||9.45 (7.56)||6 days||97|
|7. Hot recycle with AC 178 mm (7")||10.16 (8.10)||10.57 (8.46)||6 days||99|
- J.A. Epps, D.N. Little, R.J. Holmgreen, and R.L. Terrel. Guidelines For Recycling Pavement Materials, NCHRP Report 224, TRB, National Research Council, Washington, DC, September, 1980.
- American Association of State Highway and Transportation Officials (AASHTO). AASHTO Guide for Design and Pavement Structures, Washington, DC, 1986.
- Pavement Recycling Guidelines for Local Governments - Reference Manual, Report No. FHWA-TS-87-230, FHA, U.S. Department of Transportation, Washington, DC, 1987.
- Asphalt Recycling and Reclaiming Association. An Overview of Recycling and Reclamation Methods for Asphalt Pavement Rehabilitation, 1992.
|<< Previous||Contents||Next >>|