From: Subject: Circular No. A-94 -- Guidelines and Discount Rates for Benefit-Cost Analysis of Federal Programs Date: Wed, 19 Mar 2003 11:36:41 -0800 MIME-Version: 1.0 Content-Type: multipart/related; boundary="----=_NextPart_000_003C_01C2EE0B.CF99A880"; type="text/html" X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2600.0000 This is a multi-part message in MIME format. ------=_NextPart_000_003C_01C2EE0B.CF99A880 Content-Type: text/html; charset="Windows-1252" Content-Transfer-Encoding: quoted-printable Content-Location: file://C:\Temp\Circular%20No_%20A-94%20--%20Guidelines%20and%20Discount%20Rates%20for%20Benefit-Cost%20Analysis%20of%20Federal%20Programs.htm Circular No. A-94 -- Guidelines and Discount = Rates for Benefit-Cost Analysis of Federal Programs Original url for document:=20 http://www.whitehouse.gov/omb/circulars/a094/print/a094.html

3D"Office

Circular No.=20 A-94
Revised
(Transmittal Memo No. 64)

October 29,=20 1992

MEMORANDUM FOR=20 HEADS OF EXECUTIVE DEPARTMENTS AND ESTABLISHMENTS

SUBJECT:  Guidelines and Discount Rates for=20 Benefit-Cost Analysis of=20 =       
     &nb= sp;           &nbs= p; =20  Federal Programs

Table of = Contents

  1. P= urpose=20
  2. R= escission=20
  3. A= uthority=20
  4. S= cope=20
  5. G= eneral=20 Principles=20
    1. Net = Present=20 Value and Related Outcome Measures
    2. Cost-Effectiveness Analysis
    3. Elements of=20 Benefit-Cost or Cost-Effectiveness Analysis
  6. I= dentifying=20 and Measuring Benefits and Costs=20
    1. Identifying=20 Benefits and Costs=20
    2. b. = Measuring=20 Benefits and Costs
  7. T= reatment=20 of Inflation=20
    1. Real = or Nominal=20 Values=20
    2. Recommended=20 Inflation Assumption
  8. D= iscount=20 Rate Policy=20
    1. Real = versus=20 Nominal Discount Rates=20
    2. Public=20 Investment and Regulatory Analyses=20
    3. Cost-Effectiveness, Lease-Purchase,Internal = Government=20 Investment, and Asset Sale Analyses
  9. T= reatment=20 of Uncertainty=20
    1. Characterizing=20 Uncertainty=20
    2. Expected Values=20
    3. Sensitivity=20 Analysis=20
    4. Other=20 Adjustments for Uncertainty
  10. = Incidence=20 and Distributional Effects=20
    1. Alternative=20 Classifications=20
    2. Economic=20 Incidence
  11. = Special=20 Guidance for Public Investment Analysis=20
    1. Analysis of=20 Excess Burdens=20
    2. Exceptions
  12. = Special=20 Guidance for Regulatory Impact Analysis=20
  13. = Special=20 Guidance for Lease-Purchase Analysis=20
    1. Coverage=20
    2. Required=20 Justification for Leases=20
    3. Analytical=20 Requirements and Definitions
  14. = Related=20 Guidance=20
  15. = Implementation=20
  16. = Effective=20 Date=20
  17. = Interpretation=20

Appendix=20 A: Definitions of Terms
Appendix=20 B: Additional Guidance for Discounting
Appendix=20 C: Discount Rates for Cost-Effectiveness, Lease-Purchase, and = Related=20 Analyses

Other=20 Documents

1.=20 Purpose. The goal of this Circular is to promote efficient = resource=20 allocation through well-informed decision-making by the Federal=20 Government. It provides general guidance for conducting = benefit-cost and=20 cost-effectiveness analyses. It also provides specific guidance on = the=20 discount rates to be used in evaluating Federal programs whose = benefits=20 and costs are distributed over time. The general guidance will = serve as a=20 checklist of whether an agency has considered and properly dealt = with all=20 the elements for sound benefit-cost and cost-effectiveness=20 analyses.


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2.=20 Rescission. This Circular replaces and rescinds Office of=20 Management and Budget (OMB) Circular No. A-94, "Discount Rates to = Be Used=20 in Evaluating Time-Distributed Costs and Benefits," dated March = 27, 1972,=20 and Circular No. A-104, "Evaluating Leases of Capital Assets," = dated June=20 1, 1986, which has been rescinded. Lease-purchase analysis is only = appropriate after a decision has been made to acquire the services = of an=20 asset. Guidance for lease-purchase analysis is provided in Section = 8.c.(2)=20 and Section 13.


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3.=20 Authority. This Circular is issued under the authority of = 31 U.S.C.=20 Section 1111 and the Budget and Accounting Act of 1921, as = amended.=20


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4. = Scope.=20 This Circular does not supersede agency practices which are = prescribed by=20 or pursuant to law, Executive Order, or other relevant circulars. = The=20 Circular's guidelines are suggested for use in the internal = planning of=20 Executive Branch agencies. The guidelines must be followed in all = analyses=20 submitted to OMB in support of legislative and budget-programs in=20 compliance with OMB Circulars No. A-11, "Preparation and = Submission of=20 Annual Budget Estimates," and No. A-19, "Legislative Coordination = and=20 Clearance." These guidelines must also be followed in providing = estimates=20 submitted to OMB in compliance with Executive Order No. 12291, = "Federal=20 Regulation," and the President's April 29, 1992 memorandum = requiring=20 benefit-cost analysis for certain legislative proposals.

a. Aside = from the=20 exceptions listed below, the guidelines in this Circular apply to = any=20 analysis used to support Government decisions to initiate, renew, = or=20 expand programs or projects which would result in a series of = measurable=20 benefits or costs extending for three or more years into the = future. The=20 Circular applies specifically to:

  1. Benefit-cost or=20 cost-effectiveness analysis of Federal programs or policies. =
  2. Regulatory impact=20 analysis.
  3. Analysis of=20 decisions whether to lease or purchase.
  4. Asset = valuation=20 and sale analysis.

b. = Specifically=20 exempted from the scope of this Circular are decisions concerning: =

  1. Water = resource=20 projects (guidance for which is the approved Economic and=20 Environmental Principles and Guidelines for Water and Related = Land=20 Resources Implementation Studies).
  2. The = acquisition of=20 commercial-type services by Government or contractor operation = (guidance=20 for which is OMB Circular No. A-76).
  3. Federal energy=20 management programs (guidance for which can be found in the = Federal=20 Register of January 25, 1990, and November 20, 1990).=20

c. This = Circular=20 applies to all agencies of the Executive Branch of the Federal = Government.=20 It does not apply to the Government of the District of Columbia or = to=20 non-Federal recipients of loans, contracts or grants. Recipients = are=20 encouraged, however, to follow the guidelines provided here when = preparing=20 analyses in support of Federal activities.

d. For = small projects=20 which share similar characteristics, agencies are encouraged to = conduct=20 generic studies and to avoid duplication of effort in carrying out = economic analysis.


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5. = General=20 Principles. Benefit-cost analysis is recommended as the = technique to use in a formal economic analysis of government = programs or=20 projects. Cost-effectiveness analysis is a less = comprehensive=20 technique, but it can be appropriate when the benefits from = competing=20 alternatives are the same or where a policydecision has been made = that the=20 benefits must be provided. (Appendix A provides a glossary of = technical=20 terms used in this Circular; technical terms are italicized when = they=20 first appear.)

a. Net = Present=20 Value and Related Outcome Measures. The standard criterion for = deciding whether a government program can be justified on economic = principles is net present value -- the discounted monetized = value=20 of expected net benefits (i.e., benefits minus costs). Net present = value=20 is computed by assigning monetary values to benefits and costs,=20 discounting future benefits and costs using an appropriate = discount rate,=20 and subtracting the sum total of discounted costs from the sum = total of=20 discounted benefits. Discounting benefits and costs transforms = gains and=20 losses occurring in different time periods to a common unit of=20 measurement. Programs with positive net present value increase = social=20 resources and are generally preferred. Programs with negative net = present=20 value should generally be avoided. (Section 8 considers = discounting issues=20 in more detail.)

Although = net present=20 value is not always computable (and it does not usually reflect = effects on=20 income distribution), efforts to measure it can produce useful = insights=20 even when the monetary values of some benefits or costs cannot be=20 determined. In these cases:

  1. A = comprehensive=20 enumeration of the different types of benefits and costs, = monetized=20 or not, can be helpful in identifying the full range of program = effects.=20
  2. Quantifying=20 benefits and costs is worthwhile, even when it is not feasible = to assign=20 monetary values; physical measurements may be = possible and=20 useful.

Other = summary=20 effectiveness measures can provide useful supplementary = information to=20 net present value, and analysts are encouraged to report them = also.=20 Examples include the number of injuries prevented per dollar of = cost (both=20 measured in present value terms) or a project's internal rate of = return.=20

b.=20 Cost-Effectiveness Analysis. A program is cost-effective = if, on the=20 basis of life cycle cost analysis of competing = alternatives, it is=20 determined to have the lowest costs expressed in present value = terms for a=20 given amount of benefits. Costeffectiveness analysis is = appropriate=20 whenever it is unnecessary or impractical to consider the dollar = value of=20 the benefits provided by the alternatives under consideration. = This is the=20 case whenever (i) each alternative has the same annual benefits = expressed=20 in monetary terms; or (ii) each alternative has the same annual = affects,=20 but dollar values cannot be assigned to their benefits. Analysis = of=20 alternative defense systems often falls in this category. =

Cost-effectiveness=20 analysis can also be used to compare programs with identical costs = but=20 differing benefits. In this case, the decision criterion is the = discounted=20 present value of benefits. The alternative program with the = largest=20 benefits would normally be favored.

c. = Elements of=20 Benefit-Cost or Cost-Effectiveness Analysis.

  1. Policy=20 Rationale. The rationale for the Government program being = examined=20 should be clearly stated in the analysis. Programs may be = justified on=20 efficiency grounds where they address market failure, such as = public=20 goods and externalities. They may also be justified where they = improve=20 the efficiency of the Government's internal operations, such as=20 cost-saving investments.

  2. Explicit=20 Assumptions. Analyses should be explicit about the = underlying=20 assumptions used to arrive at estimates of future benefits and = costs. In=20 the case of public health programs, for example, it may be = necessary to=20 make assumptions about the number of future beneficiaries, the = intensity=20 of service, and the rate of increase in medical prices. The = analysis=20 should include a statement of the assumptions, the rationale = behind=20 them, and a review of their strengths and weaknesses. Key data = and=20 results, such as year-by-year estimates of benefits and costs, = should be=20 reported to promote independent analysis and review.

  3. Evaluation of=20 Alternatives. Analyses should also consider alternative = means of=20 achieving program objectives by examining different program=20 scales, different methods of provision, and = different=20 degrees of government involvement. For example, in = evaluating a=20 decision to acquire a capital asset, the analysis should = generally=20 consider: (i) doing nothing; (ii) direct purchase; (iii) = upgrading,=20 renovating, sharing, or converting existing government property; = or (iv)=20 leasing or contracting for services.

  4. Verification. Retrospective studies to determine = whether=20 anticipated benefits and costs have been realized are = potentially=20 valuable. Such studies can be used to determine necessary = corrections in=20 existing programs, and to improve future estimates of benefits = and costs=20 in these programs or related ones.

    Agencies should=20 have a plan for periodic, results-oriented evaluation of program = effectiveness. They should also discuss the results of relevant=20 evaluation studies when proposing reauthorizations or increased = program=20 funding.


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6. = Identifying and Measuring Benefits and Costs. Analyses = should=20 include comprehensive estimates of the expected benefits and costs = to=20 society based on established definitions and practices for = program=20 and policy evaluation. Social net benefits, and not the benefits = and costs=20 to the Federal Government, should be the basis for evaluating = government=20 programs or policies that have effects on private citizens or = other levels=20 of government. Social benefits and costs can differ from private = benefits=20 and costs as measured in the marketplace because of imperfections = arising=20 from: (i) external economies or diseconomies where actions = by one=20 party impose benefits or costs on other groups that are not = compensated in=20 the market place; (ii) monopoly power that distorts the = relationship=20 between marginal costs and market prices; and (iii) taxes or = subsidies.=20

a. = Identifying=20 Benefits and Costs. Both intangible and tangible benefits and = costs=20 should be recognized. The relevant cost concept is broader than=20 private-sector production and compliance costs or government cash=20 expenditures. Costs should reflect the opportunity cost of any = resources=20 used, measured by the return to those resources in their most = productive=20 application elsewhere. Below are some guidelines to consider when=20 identifying benefits and costs.

  • Incremental=20 Benefits and Costs. Calculation of net present value should = be based=20 on incremental benefits and costs. Sunk costs and realized = benefits=20 should be ignored. Past experience is relevant only in helping = to=20 estimate what the value of future benefits and costs might be. = Analyses=20 should take particular care to identify the extent to which a = policy=20 such as a subsidy program promotes substitutes for activities of = a=20 similar nature that would occur without the policy. Either = displaced=20 activities should be explicitly recorded as costs or only = incremental=20 gains should be recorded as benefits of the policy.

  • Interactive=20 Effects. Possible interactions between the benefits and = costs being=20 analyzed and other government activities should be considered. = For=20 example, policies affecting agricultural output should reflect = real=20 economic values, as opposed to subsidized prices.

  • International=20 Effects. Analyses should focus on benefits and costs = accruing to the=20 citizens of the United States in determining net present value. = Where=20 programs or projects have effects outside the United States, = these=20 effects should be reported separately.

  • Transfers.=20 There are no economic gains from a pure transfer payment = because=20 the benefits to those who receive such a transfer are matched by = the=20 costs borne by those who pay for it. Therefore, transfers should = be=20 excluded from the calculation of net present value. Transfers = that arise=20 as a result of the program or project being analyzed should be=20 identified as such, however, and their distributional effects = discussed.=20 It should also be recognized that a transfer program may have = benefits=20 that are less than the program's real economic costs due to=20 inefficiencies that can arise in the program's delivery of = benefits and=20 financing.

b. = Measuring=20 Benefits and Costs. The principle of willingness-to-pay = provides an aggregate measure of what individuals are willing to = forego to=20 obtain a given benefit. Market prices provide an invaluable = starting point=20 for measuring willingness-to-pay, but prices sometimes do not = adequately=20 reflect the true value of a good to society. Externalities, = monopoly=20 power, and taxes or subsidies can distort market prices. =

Taxes, = for example,=20 usually create an excess burden that represents a net loss = to=20 society. (The appropriate method for recognizing this excess = burden in=20 public investment analyses is discussed in Section 11.) In other = cases,=20 market prices do not exist for a relevant benefit or cost. When = market=20 prices are distorted or unavailable, other methods of valuing = benefits may=20 have to be employed. Measures derived from actual market behavior = are=20 preferred when they are available.

  1. Inframarginal=20 Benefits and Costs. Consumers would generally be willing to = pay more=20 than the market price rather than go entirely without a good = they=20 consume. The economist's concept of consumer surplus = measures the=20 extra value consumers derive from their consumption compared = with the=20 value measured at market prices. When it can be determined, = consumer=20 surplus provides the best measure of the total benefit to = society from a=20 government program or project. Consumer surplus can sometimes be = calculated by using econometric methods to estimate consumer = demand.=20

  2. Indirect=20 Measures of Benefits and Costs. Willingness-to-pay can = sometimes be=20 estimated indirectly through changes in land values, variations = in wage=20 rates, or other methods. Such methods are most reliable when = they are=20 based on actual market transactions. Measures should be = consistent with=20 basic economic principles and should be replicable.

  3. Multiplier=20 Effects. Generally, analyses should treat resources as if = they were=20 likely to be fully employed. Employment or output multipliers = that=20 purport to measure the secondary effects of government = expenditures on=20 employment and output should not be included in measured social = benefits=20 or costs.

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7. = Treatment=20 of Inflation. Future inflation is highly uncertain. Analysts = should=20 avoid having to make an assumption about the general rate of = inflation=20 whenever possible.

a. = Real or Nominal=20 Values. Economic analyses are often most readily accomplished = using=20 real or constant-dollar values, i.e., by measuring = benefits=20 and costs in units of stable purchasing power. (Such estimates may = reflect=20 expected future changes in relative prices, however, where there = is a=20 reasonable basis for estimating such changes.) Where future = benefits and=20 costs are given in nominal terms, i.e., in terms of the = future=20 purchasing power of the dollar, the analysis should use these = values=20 rather than convert them to constant dollars as, for example, in = the case=20 of lease-purchase analysis.

Nominal = and real=20 values must not be combined in the same analysis. Logical = consistency=20 requires that analysis be conducted either in constant dollars or = in terms=20 of nominal values. This may require converting some nominal values = to real=20 values, or vice versa.

b. = Recommended=20 Inflation Assumption. When a general inflation assumption is = needed,=20 the rate of increase in the Gross Domestic Product deflator from = the=20 Administration's economic assumptions for the period of the = analysis is=20 recommended. For projects or programs that extend beyond the = six-year=20 budget horizon, the inflation assumption can be extended by using = the=20 inflation rate for the sixth year of the budget forecast. The=20 Administration's economic forecast is updated twice annually, at = the time=20 the budget is published in January or February and at the time of = the=20 Mid-Session Review of the Budget in July. Alternative inflation = estimates,=20 based on credible private sector forecasts, may be used for = sensitivity=20 analysis.


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8. = Discount=20 Rate Policy. In order to compute net present value, it is = necessary to=20 discount future benefits and costs. This discounting reflects the = time=20 value of money. Benefits and costs are worth more if they are = experienced=20 sooner. All future benefits and costs, including nonmonetized = benefits and=20 costs, should be discounted. The higher the discount rate, the = lower is=20 the present value of future cash flows. For typical investments, = with=20 costs concentrated in early periods and benefits following in = later=20 periods, raising the discount rate tends to reduce the net present = value.=20 (Technical guidance on discounting and a table of discount = factors=20 are provided in Appendix B.)

a. = Real versus=20 Nominal Discount Rates. The proper discount rate to use = depends on=20 whether the benefits and costs are measured in real or nominal = terms.=20

  1. A real = discount=20 rate that has been adjusted to eliminate the effect of expected=20 inflation should be used to discount constant-dollar or real = benefits=20 and costs. A real discount rate can be approximated by = subtracting=20 expected inflation from a nominal interest rate.

  2. A = nominal discount=20 rate that reflects expected inflation should be used to discount = nominal=20 benefits and costs. Market interest rates are nominal interest = rates in=20 this sense.

b. = Public=20 Investment and Regulatory Analyses. The guidance in this = section=20 applies to benefit-cost analyses of public investments and = regulatory=20 programs that provide benefits and costs to the general public. = Guidance=20 related to cost-effectiveness analysis of internal planning = decisions of=20 the Federal Government is provided in Section 8.c.

In = general, public=20 investments and regulations displace both private investment and=20 consumption. To account for this displacement and to promote = efficient=20 investment and regulatory policies, the following guidance should = be=20 observed.

  1. Base-Case=20 Analysis. Constant-dollar benefit-cost analyses of proposed=20 investments and regulations should report net present value and = other=20 outcomes determined using a real discount rate of 7 percent. = This rate=20 approximates the marginal pretax rate of return on an average = investment=20 in the private sector in recent years. Significant changes in = this rate=20 will be reflected in future updates of this Circular.

  2. Other Discount=20 Rates. Analyses should show the sensitivity of the = discounted net=20 present value and other outcomes to variations in the discount = rate. The=20 importance of these alternative calculations will depend on the = specific=20 economic characteristics of the program under analysis. For = example, in=20 analyzing a regulatory proposal whose main cost is to reduce = business=20 investment, net present value should also be calculated using a = higher=20 discount rate than 7 percent.

    Analyses may=20 include among the reported outcomes the internal rate of = return=20 implied by the stream of benefits and costs. The internal rate = of return=20 is the discount rate that sets the net present value of the = program or=20 project to zero. While the internal rate of return does not = generally=20 provide an acceptable decision criterion, it does provide useful = information, particularly when budgets are constrained or there = is=20 uncertainty about the appropriate discount rate.

  3. Using = the=20 shadow price of capital to value benefits and costs is = the=20 analytically preferred means of capturing the effects of = government=20 projects on resource allocation in the private sector. To use = this=20 method accurately, the analyst must be able to compute how the = benefits=20 and costs of a program or project affect the allocation of = private=20 consumption and investment. OMB concurrence is required if this = method=20 is used in place of the base case discount rate. =

c.=20 Cost-Effectiveness, Lease-Purchase, Internal Government = Investment, and=20 Asset Sales Analyses. The Treasury's borrowing rates should be = used as=20 discount rates in the following cases:

  1. Cost-Effectiveness Analysis. Analyses that = involve=20 constant-dollar costs should use the real Treasury borrowing = rate on=20 marketable securities of comparable maturity to the period of = analysis.=20 This rate is computed using the Administration's economic = assumptions=20 for the budget, which are published in January of each year. A = table of=20 discount rates based on the expected interest rates for the = first year=20 of the budget forecast is presented in Appendix C of this = Circular.=20 Appendix C is updated annually and is available upon request = from OMB.=20 Real Treasury rates are obtained by removing expected inflation = over the=20 period of analysis from nominal Treasury interest rates. = (Analyses that=20 involve nominal costs should use nominal Treasury rates for = discounting,=20 as described in the following paragraph.)

  2. Lease-Purchase=20 Analysis. Analyses of nominal lease payments should use the = nominal=20 Treasury borrowing rate on marketable securities of comparable = maturity=20 to the period of analysis. Nominal Treasury borrowing rates = should be=20 taken from the economic assumptions for the budget. A table of = discount=20 rates based on these assumptions is presented in Appendix C of = this=20 Circular, which is updated annually. (Constant dollar = lease-purchase=20 analyses should use the real Treasury borrowing rate, described = in the=20 preceding paragraph.)

  3. Internal=20 Government Investments. Some Federal investments provide = "internal"=20 benefits which take the form of increased Federal revenues or = decreased=20 Federal costs. An example would be an investment in an = energy-efficient=20 building system that reduces Federal operating costs. Unlike the = case of=20 a Federally funded highway (which provides "external" benefits = to=20 society as a whole), it is appropriate to calculate such a = project's net=20 present value using a comparable-maturity Treasury rate as a = discount=20 rate. The rate used may be either nominal or real, depending on = how=20 benefits and costs are measured.

    Some = Federal=20 activities provide a mix of both Federal cost savings and = external=20 social benefits. For example, Federal investments in information = technology can produce Federal savings in the form of lower=20 administrative costs and external social benefits in the form of = faster=20 claims processing. The net present value of such investments = should be=20 evaluated with the 7 percent real discount rate discussed in = Section=20 8.b. unless the analysis is able to allocate the investment's = costs=20 between provision of Federal cost savings and external social = benefits.=20 Where such an allocation is possible, Federal cost savings and = their=20 associated investment costs may be discounted at the Treasury = rate,=20 while the external social benefits and their associated = investment costs=20 should be discounted at the 7 percent real rate.

  4. Asset Sale=20 Analysis. Analysis of possible asset sales should reflect = the=20 following:

    (a) = The net=20 present value to the Federal Government of holding an asset is = best=20 measured by discounting its future earnings stream using a = Treasury=20 rate. The rate used may be either nominal or real, depending on = how=20 earnings are measured.

    (b) = Analyses of=20 government asset values should explicitly deduct the cost of = expected=20 defaults or delays in payment from projected cash flows, along = with=20 government administrative costs. Such analyses should also = consider=20 explicitly the probabilities of events that would cause the = asset to=20 become nonfunctional, impaired or obsolete, as well as = probabilities of=20 events that would increase asset value.

    (c) = Analyses of=20 possible asset sales should assess the gain in social efficiency = that=20 can result when a government asset is subject to market = discipline and=20 private incentives. Even though a government asset may be used = more=20 efficiently in the private sector, potential private-sector = purchasers=20 will generally discount such an asset's earnings at a rate in = excess of=20 the Treasury rate, in part, due to the cost of bearing risk. = When there=20 is evidence that government assets can be used more efficiently = in the=20 private sector, valuation analyses for these assets should = include=20 sensitivity comparisons that discount the returns from such = assets with=20 the rate of interest earned by assets of similar riskiness in = the=20 private sector.


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9. = Treatment=20 of Uncertainty. Estimates of benefits and costs are typically=20 uncertain because of imprecision in both underlying data and = modeling=20 assumptions. Because such uncertainty is basic to many analyses, = its=20 effects should be analyzed and reported. Useful information in = such a=20 report would include the key sources of uncertainty; expected = value=20 estimates of outcomes; the sensitivity of results to important = sources of=20 uncertainty; and where possible, the probability distributions of=20 benefits, costs, and net benefits.

a. = Characterizing=20 Uncertainty. Analyses should attempt to characterize the = sources and=20 nature of uncertainty. Ideally, probability distributions of = potential=20 benefits, costs, and net benefits should be presented. It should = be=20 recognized that many phenomena that are treated as deterministic = or=20 certain are, in fact, uncertain. In analyzing uncertain data, = objective=20 estimates of probabilities should be used whenever possible. = Market data,=20 such as private insurance payments or interest rate differentials, = may be=20 useful in identifying and estimating relevant risks. Stochastic = simulation=20 methods can be useful for analyzing such phenomena and developing = insights=20 into the relevant probability distributions. In any case, the = basis for=20 the probability distribution assumptions should be reported. Any=20 limitations of the analysis because of uncertainty or biases = surrounding=20 data or assumptions should be discussed.

b. = Expected=20 Values. The expected values of the distributions of benefits, = costs=20 and net benefits can be obtained by weighting each outcome by its=20 probability of occurrence, and then summing across all potential = outcomes.=20 If estimated benefits, costs and net benefits are characterized by = point=20 estimates rather than as probability distributions, the expected = value (an=20 unbiased estimate) is the appropriate estimate for use. =

Estimates = that differ=20 from expected values (such as worst-case estimates) may be = provided in=20 addition to expected values, but the rationale for such estimates = must be=20 clearly presented. For any such estimate, the analysis should = identify the=20 nature and magnitude of any bias. For example, studies of past = activities=20 have documented tendencies for cost growth beyond initial = expectations;=20 analyses should consider whether past experience suggests that = initial=20 estimates of benefits or costs are optimistic.

c. = Sensitivity=20 Analysis. Major assumptions should be varied and net present = value and=20 other outcomes recomputed to determine how sensitive outcomes are = to=20 changes in the assumptions. The assumptions that deserve the most=20 attention will depend on the dominant benefit and cost elements = and the=20 areas of greatest uncertainty of the program being analyzed. For = example,=20 in analyzing a retirement program, one would consider changes in = the=20 number of beneficiaries, future wage growth, inflation, and the = discount=20 rate. In general, sensitivity analysis should be considered for = estimates=20 of: (i) benefits and costs; (ii) the discount rate; (iii) the = general=20 inflation rate; and (iv) distributional assumptions. Models used = in the=20 analysis should be well documented and, where possible, available = to=20 facilitate independent review.

d. = Other=20 Adjustments for Uncertainty. The absolute variability of a = risky=20 outcome can be much less significant than its correlation with = other=20 significant determinants of social welfare, such as real national = income.=20 In general, variations in the discount rate are not the = appropriate method=20 of adjusting net present value for the special risks of particular = projects. In some cases, it may be possible to estimate=20 certainty-equivalents which involve adjusting uncertain = expected=20 values to account for risk.


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10.=20 Incidence and Distributional Effects. The principle of = maximizing=20 net present value of benefits is based on the premise that gainers = could=20 fully compensate the losers and still be better off. The presence = or=20 absence of such compensation should be indicated in the analysis. = When=20 benefits and costs have significant distributional effects, these = effects=20 should be analyzed and discussed, along with the analysis of net = present=20 value. (This will not usually be the case for cost-effectiveness = analysis=20 where the scope of government activity is not changing.)

a. = Alternative=20 Classification. Distributional effects may be analyzed by = grouping=20 individuals or households according to income class (e.g., income=20 quintiles), geographical region, or demographic group (e.g., age). = Other=20 classifications, such as by industry or occupation, may be = appropriate in=20 some circumstances.

Analysis = should aim=20 at identifying the relevant gainers and losers from policy = decisions.=20 Effects on the preexisting assignment of property rights by the = program=20 under analysis should be reported. Where a policy is intended to = benefit a=20 specified subgroup of the population, such as the poor, the = analysis=20 should consider how effective the policy is in reaching its = targeted=20 group.

b. = Economic=20 Incidence. Individuals or households are the ultimate = recipients of=20 income; business enterprises are merely intermediaries. Analyses = of=20 distribution should identify economic incidence, or how costs and = benefits=20 are ultimately borne by households or individuals.

Determining economic=20 incidence can be difficult because benefits and costs are often=20 redistributed in unintended and unexpected ways. For example, a = subsidy=20 for the production of a commodity will usually raise the incomes = of the=20 commodity's suppliers, but it can also benefit consumers of the = commodity=20 through lower prices and reduce the incomes for suppliers of = competing=20 products. A subsidy also raises the value of specialized resources = used in=20 the production of the subsidized commodity. As the subsidy is = incorporated=20 in asset values, its distributional effects can change. =


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11. Special=20 Guidance for Public Investment. This guidance applies only to = public=20 investments with social benefits apart from decreased Federal = costs. It is=20 not required for cost-effectiveness or lease-purchase analyses. = Because=20 taxes generally distort relative prices, they impose a burden in = excess of=20 the revenues they raise. Recent studies of the U.S. tax system = suggest a=20 range of values for the marginal excess burden, of which a = reasonable=20 estimate is 25 cents per dollar of revenue.

a. = Analysis of=20 Excess Burdens. The presentation of results for public = investments=20 that are not justified on cost-saving grounds should include a=20 supplementary analysis with a 25 percent excess burden. Thus, in = such=20 analyses, costs in the form of public expenditures should be = multiplied by=20 a factor of 1.25 and net present value recomputed.

b. = Exceptions.=20 Where specific information clearly suggests that the excess burden = is=20 lower (or higher) than 25 percent, analyses may use a different = figure.=20 When a different figure is used, an explanation should be provided = for it.=20 An example of such an exception is an investment funded by user = charges=20 that function like market prices; in this case, the excess burden = would be=20 zero. Another example would be a project that provides both cost = savings=20 to the Federal Government and external social benefits. If it is = possible=20 to make a quantitative determination of the portion of this = project's=20 costs that give rise to Federal savings, that portion of the costs = may be=20 exempted from multiplication by the factor of 1.25. =


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12. Special=20 Guidance for Regulatory Impact Analysis. Additional guidance = for=20 analysis of regulatory policies is provided in Regulatory = Program of=20 the United States Government which is published annually by = OMB. (See=20 "Regulatory Impact Analysis Guidance," Appendix V of Regulatory = Program=20 of the United States Government for April 1, 1991 to March 31, = 1992.)=20
Top of=20 Page

13. Special=20 Guidance for Lease-Purchase Analysis. The special guidance in = this=20 section does not apply to the decision to acquire the use of an = asset. In=20 deciding that, the agency should conduct a benefit-cost analysis, = if=20 possible. Only after the decision to acquire the services of an = asset has=20 been made is there a need to analyze the decision whether to lease = or=20 purchase.

a. = Coverage.=20 The Circular applies only when both of the following tests of=20 applicability are satisfied:

  1. The = lease-purchase=20 analysis concerns a capital asset, (including durable goods, = equipment,=20 buildings, facilities, installations, or land) which:

    (a) = Is leased=20 to the Federal Government for a term of three or more years; or, =

    (b) Is = new, with an=20 economic life of less than three years, and leased to the = Federal=20 Government for a term of 75 percent or more of the economic life = of the=20 asset; or,

    (c) Is = built for=20 the express purpose of being leased to the Federal Government; = or,=20

    (d) Is = leased to=20 the Federal Government and clearly has no alternative commercial = use=20 (e.g., a special-purpose government installation).

  2. The = lease-purchase=20 analysis concerns a capital asset or a group of related assets = whose=20 total fair market value exceeds $1 million.

b. = Required=20 Justification for Leases. All leases of capital assets must be = justified as preferable to direct government purchase and = ownership. This=20 can be done in one of three ways:

  1. By = conducting a=20 separate lease-purchase analysis. This is the only acceptable = method for=20 major acquisitions. A lease represents a major acquisition if: =

    (a) = The=20 acquisition represents a separate line-item in the agency's = budget;=20

    (b) The = agency or=20 OMB determines the acquisition is a major one; or

    (c) The = total=20 purchase price of the asset or group of assets to be leased = would exceed=20 $500 million.

  2. By = conducting=20 periodic lease-purchase analyses of recurrent decisions to lease = similar=20 assets used for the same general purpose. Such analyses would = apply to=20 the entire class of assets. OMB approval should be sought in = determining=20 the scope of any such generic analysis.

  3. By = adopting a=20 formal policy for smaller leases and submitting that policy to = the OMB=20 for approval. Following such a policy should generally result in = the=20 same lease-purchase decisions as would conducting separate=20 lease-purchase analyses. Before adopting the policy, it should = be=20 demonstrated that:

    (a) = The leases=20 in question would generally result in substantial savings to the = Government that could not be realized on a purchase;

    (b) The = leases are=20 so small or so short-term as to make separate lease-purchase = analysis=20 impractical; and

    (c) = Leases of=20 different types are scored consistently with the instructions in = Appendices B and C of OMB Circular No. A-11. =

c. = Analytical=20 Requirements and Definitions. Whenever a Federal agency needs = to=20 acquire the use of a capital asset, it should do so in the way = that is=20 least expensive for the Government as a whole.

  1. Life-Cycle=20 Cost. Lease-purchase analyses should compare the net = discounted=20 present value of the life-cycle cost of leasing with the full = costs of=20 buying or constructing an identical asset. The full costs of = buying=20 include the asset's purchase price plus the net discounted = present value=20 of any relevant ancillary services connected with the purchase.=20 (Guidance on the discount rate to use for lease-purchase = analysis is in=20 Section 8.c.)

  2. Economic=20 Life. For purposes of lease-purchase analysis, the economic = life of=20 an asset is its remaining or productive lifetime. It begins when = the=20 asset is acquired and ends when the asset is retired from = service. The=20 economic life is frequently not the same as the useful life for = tax=20 purposes.

  3. Purchase=20 Price. The purchase price of the asset for purposes of=20 lease-purchase analysis is its fair market value, defined as the = price a=20 willing buyer could reasonably expect to pay a willing seller in = a=20 competitive market to acquire the asset.

    (a) = In the case=20 of property that is already owned by the Federal Government or = that has=20 been donated or acquired by condemnation, an imputed purchase = price=20 should be estimated. (Guidance on making imputations is provided = in=20 Section 13.c.(6).)

    (b) If = public land=20 is used for the site of the asset, the imputed market value of = the land=20 should be added to the purchase price.

    (c) The = asset's=20 estimated residual value, as of the end of the period of = analysis,=20 should be subtracted from its purchase price. (Guidance on = estimating=20 residual value is provided in Section 13.c.(7).)

  4. Taxes. In=20 analyzing the cost of a lease, the normal payment of taxes on = the=20 lessor's income from the lease should not be subtracted from the = lease=20 costs since the normal payment of taxes will also be reflected = in the=20 purchase cost. The cost to the Treasury of special tax benefits, = if any,=20 associated with the lease should be added to the cost of the = lease.=20 Examples of such tax benefits might include highly accelerated=20 depreciation allowances or tax-free financing.

  5. Ancillary=20 Services. If the terms of the lease include ancillary = services=20 provided by the lessor, the present value of the cost of = obtaining these=20 services separately should be added to the purchase price. Such = costs=20 may be excluded if they are estimated to be the same for both = lease and=20 purchase alternatives or too small to affect the comparison. = Examples of=20 ancillary services include:

    (a) = All costs=20 associated with acquiring the property and preparing it for use, = including construction, installation, site, design, and = management=20 costs.

    (b) = Repair and=20 improvement costs (if included in lease payments).

    (c) = Operation and=20 maintenance costs (if included in lease payments).

    (d) = Imputed=20 property taxes (excluding foreign property taxes on overseas=20 acquisitions except where actually paid). The imputed taxes = approximate=20 the costs of providing municipal services such as water, sewage, = and=20 police and fire protection. (See Section (6) below.)

    (e) = Imputed=20 insurance premiums. (See Section (6) below.)

  6. Estimating=20 Imputed Costs. Certain costs associated with the Federal = purchase of=20 an asset may not involve a direct monetary payment. Some of = these=20 imputed costs may be estimated as follows.

    (a) = Purchase=20 Price. An imputed purchase price for an asset that is = already owned=20 by the Federal Government or which has been acquired by donation = or=20 condemnation should be based on the fair market value of similar = properties that have been traded on commercial markets in the = same or=20 similar localities. The same method should be followed in = estimating the=20 imputed value of any Federal land used as a site for the asset. =

    (b) = Property=20 Taxes. Imputed property taxes may be estimated in two ways.=20

    (i) = Determine the=20 property tax rate and assessed (taxable) value for comparable = property=20 in the intended locality. If there is no basis on which to = estimate=20 future changes in tax rates or assessed values, the first- year = tax rate=20 and assessed value (inflation adjusted for each subsequent year) = can be=20 applied to all years. Multiply the assessed value by the tax = rate to=20 determine the annual imputation for property taxes.

    (ii) As = an=20 alternative to step (i) above, obtain an estimate of the current = local=20 effective property tax rate from the Building Owners and = Managers=20 Association's Regional Exchange Reports. Multiply the fair = market value=20 of the government-owned property (inflation adjusted for each = year) by=20 the effective tax rate.

    (c) = Insurance=20 Premiums. Determine local estimates of standard commercial = coverage=20 for similar property from the Building Owners and Managers = Association's=20 Regional Exchange Reports.

  7. Residual=20 Value. A property's residual value is an estimate of the = price that=20 the property could be sold for at the end of the period of the=20 lease-purchase analysis, measured in discounted present value = terms.=20

    (a) = The=20 recommended way to estimate residual value is to determine what = similar,=20 comparably aged property is currently selling for in commercial = markets.=20

    (b) = Alternatively,=20 book estimates of the resale value of used property may be = available=20 from industry or government sources.

    (c) = Assessed values=20 of similar, comparably aged properties determined for property = tax=20 purposes may also be used.

  8. Renewal=20 Options. In determining the term of a lease, all renewal = options=20 shall be added to the initial lease period. =

Top of=20 Page

14. Related=20 Guidance.
  1. OMB = Circular No.=20 A-11,"Preparation and Submission of Annual Budget = Estimates."=20
  2. OMB = Circular No.=20 A-19,"Legislative Coordination and Clearance."=20
  3. OMB = Circular No.=20 A-70,"Federal Credit Policy."=20
  4. OMB = Circular No.=20 A-76,"Performance of Commercial Activities."=20
  5. OMB = Circular No.=20 A-109,"Policies to Be Followed in the Acquisition of Major=20 Systems."=20
  6. OMB = Circular No.=20 A-130,"Management of Federal Information Resources."=20
  7. "Joint = OMB and=20 Treasury Guidelines to the Department of Defense Covering Lease = or=20 Charter Arrangements for Aircraft and Naval Vessels."=20
  8. Executive Order=20 12291, "Federal Regulation."=20
  9. "Regulatory Impact=20 Analysis Guidance," in Regulatory Program of the United = States=20 Government.=20
  10. "Federal Energy=20 Management and Planning Programs; Life Cycle Cost Methodology = and=20 Procedures,"
  11. Federal Register,=20 Vol. 55, No. 17, January 25, 1990, and Vol. 55, No. 224, = November 20,=20 1990.=20
  12. Presidential=20 Memorandum of April 29, 1992, "Benefits and Costs of Legislative = Proposals."

Top of=20 Page

15.=20 Implementation. Economic analyses submitted to OMB will be = reviewed=20 for conformity with Items 5 to 13 in this Circular, through the = Circular=20 No. A-11 budget justification and submission process, and Circular = No.=20 A-19,legislative review process.

Top of=20 Page

16.=20 Effective Date. This Circular is effective = immediately.
Top of=20 Page

17.=20 Interpretation. Questions concerning interpretation of this = Circular should be addressed to the Office of Economic Policy, = Office of=20 Management and Budget (202-395-5873) or, in the case of regulatory = issues=20 and analysis, to the Office of Information and Regulatory Affairs=20 (202-395-4852).


Top of=20 Page

APPENDIX = A

DEFINITION OF=20 TERMS

Benefit-Cost Analysis -- A systematic quantitative = method of=20 assessing the desirability of government projects or policies when = it is=20 important to take a long view of future effects and a broad view = of=20 possible side-effects.

Capital Asset=20 -- Tangible property, including durable goods, equipment, = buildings,=20 installations, and land.

Certainty-Equivalent -- A certain (i.e., = nonrandom) outcome=20 that an individual values equally to an uncertain outcome. For a=20 risk-averse individual, the certainty-equivalent for an uncertain = set of=20 benefits may be less than the mathematical expectation of the = outcome; for=20 example, an individual may value a 50-50 chance of winning $100 or = $0 as=20 only $45. Analogously, a risk-averse individual may have a=20 certainty-equivalent for an uncertain set of costs that is larger = in=20 magnitude than the mathematical expectation of costs.

Cost-Effectiveness -- A systematic quantitative = method for=20 comparing the costs of alternative means of achieving the same = stream of=20 benefits or a given objective.

Consumer=20 Surplus -- The maximum sum of money a consumer would be = willing to pay=20 to consume a given amount of a good, less the amount actually = paid. It is=20 represented graphically by the area between the demand curve and = the price=20 line in a diagram representing the consumer's demand for the good = as a=20 function of its price.

Discount Rate=20 -- The interest rate used in calculating the present value of = expected=20 yearly benefits and costs.

Discount=20 Factor -- The factor that translates expected benefits or = costs in any=20 given future year into present value terms. The discount factor is = equal=20 to 1/(1 + i)t where i is the interest rate = and=20 t is the number of years from the date of initiation for = the=20 program or policy until the given future year.

Excess = Burden=20 -- Unless a tax is imposed in the form of a lump sum unrelated to = economic=20 activity, such as a head tax, it will affect economic decisions on = the=20 margin. Departures from economic efficiency resulting from the = distorting=20 effect of taxes are called excess burdens because they = disadvantage=20 society without adding to Treasury receipts. This concept is also=20 sometimes referred to as deadweight loss.

External Economy=20 or Diseconomy -- A direct effect, either positive or negative, = on=20 someone's profit or welfare arising as a byproduct of some other = person's=20 or firm's activity. Also referred to as neighborhood or spillover = effects,=20 or externalities for short.

Incidence --=20 The ultimate distributional effect of a tax, expenditure, or = regulatory=20 program.

Inflation --=20 The proportionate rate of change in the general price level, as = opposed to=20 the proportionate increase in a specific price. Inflation is = usually=20 measured by a broad-based price index, such as the implicit = deflator for=20 Gross Domestic Product or the Consumer Price Index.

Internal Rate of=20 Return -- The discount rate that sets the net present value of = the=20 stream of net benefits equal to zero. The internal rate of return = may have=20 multiple values when the stream of net benefits alternates from = negative=20 to positive more than once.

Life = Cycle=20 Cost -- The overall estimated cost for a particular program=20 alternative over the time period corresponding to the life of the = program,=20 including direct and indirect initial costs plus any periodic or=20 continuing costs of operation and maintenance.

Multiplier --=20 The ratio between the direct effect on output or employment and = the full=20 effect, including the effects of second order rounds or spending.=20 Multiplier effects greater than 1.0 require the existence of = involuntary=20 unemployment.

Net = Present=20 Value -- The difference between the discounted present value = of=20 benefits and the discounted present value of costs.

Nominal Values=20 -- Economic units measured in terms of purchasing power of the = date in=20 question. A nominal value reflects the effects of general price = inflation.=20

Nominal Interest=20 Rate -- An interest rate that is not adjusted to remove the = effects of=20 actual or expected inflation. Market interest rates are generally = nominal=20 interest rates.

Opportunity=20 Cost -- The maximum worth of a good or input among possible=20 alternative uses.

Real = or Constant=20 Dollar Values -- Economic units measured in terms of constant=20 purchasing power. A real value is not affected by general price = inflation.=20 Real values can be estimated by deflating nominal values with a = general=20 price index, such as the implicit deflator for Gross Domestic = Product or=20 the Consumer Price Index.

Real = Interest=20 Rate -- An interest rate that has been adjusted to remove the = effect=20 of expected or actual inflation. Real interest rates can be = approximated=20 by subtracting the expected or actual inflation rate from a = nominal=20 interest rate. (A precise estimate can be obtained by dividing one = plus=20 the nominal interest rate by one plus the expected or actual = inflation=20 rate, and subtracting one from the resulting quotient.) =

Relative Price=20 -- A price ratio between two goods as, for example, the ratio of = the price=20 of energy to the price of equipment.

Shadow = Price=20 -- An estimate of what the price of a good or input would be in = the=20 absence of market distortions, such as externalities or taxes. For = example, the shadow price of capital is the present value of the = social=20 returns to capital (before corporate income taxes) measured in = units of=20 consumption.

Sunk = Cost -- A=20 cost incurred in the past that will not be affected by any present = or=20 future decision. Sunk costs should be ignored in determining = whether a new=20 investment is worthwhile.

Transfer=20 Payment -- A payment of money or goods. A pure transfer is = unrelated=20 to the provision of any goods or services in exchange. Such = payments alter=20 the distribution of income, but do not directly affect the = allocation of=20 resources on the margin.

Treasury Rates=20 -- Rates of interest on marketable Treasury debt. Such debt is = issued in=20 maturities ranging from 91 days to 30 years.

Willingness to=20 Pay -- The maximum amount an individual would be willing to = give up in=20 order to secure a change in the provision of a good or service.=20

APPENDIX = B

ADDITIONAL GUIDANCE=20 FOR DISCOUNTING

1. Sample = Format for=20 Discounting Deferred Costs and Benefits

Assume a = 10-year=20 program which will commit the Government to the stream of real (or = constant-dollar) expenditures appearing in column (2) of the table = below=20 and which will result in a series of real benefits appearing in = column=20 (3). The discount factor for a 7 percent discount rate is shown in = column=20 (4). The present value cost for each of the 10 years is calculated = by=20 multiplying column (2) by column (4); the present value benefit = for each=20 of the 10 years is calculated by multiplying column (3) by column = (4). The=20 present values of costs and benefits are presented in columns (5) = and (6)=20 respectively.

Year since initiation renewal or expansion =
(1)		 Expected yearly cost
(2)		 Expected yearly benefit
(3)		 Discount factors for 7%
(4)		 Present value of costs Col. 2 x Col. 4 =
(5)		 Present value of benefits Col. 3 x Col. 4=20
(6)
1
$10.00
$=20 0.00
0.9346
$=20 9.35
$0.00
2
20.00
0.00
0.8734
17.47
0.00
3
30.00
5.00
0.8163
24.49
4.08
4
30.00
10.00
0.7629
22.89
7.63
5
20.00
30.00
0.7130
14.26
21.39
6
10.00
40.00
0.6663
6.66
26.65
7
5.00
40.00
0.6227
3.11
24.91
8
5.00
40.00
0.5820
2.91
23.28
9
5.00
40.00
0.5439
2.72
21.76
10
5.00
25.00
0.5083
2.54
12.71
Total
  
 
 
$106.40
$142.41


NOTE: The=20 discount factor is calculated as 1/(1 + = i)t=20 where i is the interest rate (.07) and t is the = year.=20

The sum = of column (5)=20 is the total present value of costs and the sum of column (6) is = the total=20 present value of benefits. Net present value is $36.01, the = difference=20 between the sum of discounted benefits and the sum of discounted = costs.=20

2. = End-of-Year and=20 Mid-Year Discount Factors

The = discount factors=20 presented in the table above are calculated on the implicit = assumption=20 that costs and benefits occur as lump sums at year-end. When costs = and=20 benefits occur in a steady stream, applying mid-year discount = factors is=20 more appropriate. For instance, the first cost in the table may be = estimated to occur after six months, rather than at the end of one = year to=20 approximate better a steady stream of costs and benefits occurring = over=20 the first year. Similarly, it may be assumed that all other costs = and=20 benefits are advanced six months to approximate better a = continuing steady=20 flow.

The = present values of=20 costs and benefits computed from the table above can be converted = to a=20 mid-year discounting basis by multiplying them by 1.0344 (the = square root=20 of 1.07). Thus, if the above example were converted to a mid-year = basis,=20 the present value of costs would be $110.06, the present value of = benefits=20 would be $147.31, and the net present value would be $37.25. =

3. = Illustrative=20 Discount Factors for Discount Rate of 7 percent

Year since Initiation, Renewal or=20 Expansion
Year-end Discount Factors
Mid-year Discount Factors
Beginning-of-year Discount = Factors
1
0.9346
0.9667
1.0000
2
0.8734
0.9035
0.9346
3
0.8163
0.8444
0.8734
4
0.7629
0.7891
0.8163
5
0.7130
0.7375
0.7629
6
0.6663
0.6893
0.7130
7
0.6227
0.6442
0.6663
8
0.5820
0.6020
0.6227
9
0.5439
0.5626
0.5820
10
0.5083
0.5258
0.5439
11
0.4751
0.4914
0.5083
12
0.4440
0.4593
0.4751
13
0.4150
0.4292
0.4440
14
0.3878
0.4012
0.4150
15
0.3624
0.3749
0.3878
16
0.3387
0.3504
0.3624
17
0.3166
0.3275
0.3387
18
0.2959
0.3060
0.3166
19
0.2765
0.2860
0.2959
20
0.2584
0.2673
0.2765
21
0.2415
0.2498
0.2584
22
0.2257
0.2335
0.2415
23
0.2109
0.2182
0.2257
24
0.1971
0.2039
0.2109
25
0.1842
0.1906
0.1971
26
0.1722
0.1781
0.1842
27
0.1609
0.1665
0.1722
28
0.1504
0.1556
0.1609
29
0.1406
0.1454
0.1504
30
0.1314
0.1359
0.1406

Appendix=20 C: Discount Rates for Cost-Effectiveness, Lease-Purchase, and = Related=20 Analyses for OMB Circular No. A-94

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