BenefitCost Analysis and Public Sector Economics

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Benefit/Cost Analysis and Public Sector
Economics

• Chapter 9

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Learning Objectives
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Benefit/Cost Ratio

• The benefit/cost ratio (B/C) is an economic
  analysis technique used commonly, especially by
  governmental agencies. In its purest form, the
  numerator B consists of economic consequences to
  the people (benefits and disbenefits), while the
  denominator C consists of consequences to the
  government (costs and savings).
• The units in the calculation can be present
  worth, annual worth or future worth dollars they
  have to be the same in the numerator and
  denominator.
• A B/C ratio gt 1 indicates that the project is
  economically attractive. If disbenefits are
  involved, they are substracted from the benefits
  if government savings are involved, they are
  subtracted from the costs.

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• The benefit/cost (B/C) ratio was developed, in
  part, to introduce objectivity into the economic
  analysis of public sector evaluation in an effort
  to reduce the effects of politics and special
  interests.
• However, there is always predictable disagreement
  among individuals and groups about how the
  benefits of an alternative are defined and
  economically valued.
• The different formats of B/C analysis and
  associated disbenefits of an alternative, are
  discussed in Chapter 9.
• The B/C analysis can use equivalency computations
  based on PW, AW or FW values.
• Performed correctly, the benefit/cost method will
  always select the same alternative as PW, AW, and
  ROR analyses.

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Public Sector Examples

• Hospitals and clinics
• Transportation highways, bridges, waterways,
  airports
• Parks and recreation
• Utilities water, electricity, gas, sewer,
  sanitation
• Police and fire protection
• Courts and prisons
• Sports arenas
• Emergency relief

• Schools primary, secondary, Community colleges,
  universities
• Food stamp and rent relief programs
• Job training
• Economic development
• Public housing
• Convention centers
• Codes and standards

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Characteristics
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Public Sector Projects

• To perform an economic analysis of public
  alternatives, the costs (initial and annual), the
  benefits, and the disbenefits must be estimated
  as accurately as possible in monetary units.
• Costs - estimated expenditures to the government
  entity for construction, operation, and
  maintenance of the project, less any expected
  salvage value.
• Benefits - advantages experienced by the owners
  (the public).
• Disbenefits - expected undesirable or negative
  consequences to the owners if the alternative is
  implemented. Disbenefits may be indirect economic
  disadvantages of the alternative.
• The following is important to realize It is
  difficult to estimate and agree upon the economic
  impact of benefits and disbenefits for a public
  sector alternative.

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Viewpoints

• There are often public meetings and debates
  associated with public sector projects to
  accommodate the various interests of citizens
  (owners). Elected officials commonly assist with
  the selection, especially when pressured by
  voters, developers and environmentalists.
• The selection process is not as clean as in
  private sector evaluation.
• The viewpoint of the public sector analysis must
  be determined before cost, benefit and disbenefit
  estimates are made and before the evaluation is
  formulated and performed.
• There are several viewpoints for any situation,
  and the different perspectives may alter how a
  cash flow estimate is classified.

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• The Capital Improvement Projects (CIP) Committee
  has recommended a 5 million bond issue for the
  purchase of greenbelt/floodplain land to preserve
  low-lying green areas and wildlife habitat in a
  rapidly expanding city of 62,000. The proposal is
  referred to as the Greenway Acquisition
  Initiative.
• Developers immediately opposed the proposal due
  to the reduction of available land for commercial
  development. The city engineer and economic
  development director have made the following
  preliminary estimates for some obvious areas,
  considering the Initiatives consequences in
  maintenance, parks, commercial development, and
  flooding over a projected 15-year planning
  horizon.
• The inaccuracy of these estimates is made very
  clear in the report to the City Council. The
  estimates are not yet classified as costs,
  benefits or disbenefits.
• If the Greenway Acquisition Initiative is
  implemented, the estimates are as follows.

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Identify three different viewpoints for the
economic analysis of the proposal, and classify
the estimates.
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Solution

• There are many perspectives. The viewpoints and
  goals are identified and each estimate is
  classified as a cost, benefit or disbenefit. (How
  the classification is made will vary depending
  upon who does the analysis. This solution offers
  only one answer.)
• Viewpoint 1 Citizens
• Goal Maximize the quality and wellness of
  citizens with family and neighborhood as prime
  concerns.
• Costs 1, 2, 3 - Benefits 6, 7, 8 -
  Disbenefits 4, 5
• Viewpoint 2 City budget.
• Goal Ensure the budget is balanced and
  sufficient to fund rapidly growing city services.
• Costs 1, 2, 3, 5 - Benefits 6, 7, 8 -
  Disbenefits 4
• Viewpoint 3 Economic development.
• Goal Promote new commercial and industrial
  economic development for creation and retention
  of jobs.
• Costs 1, 2, 3, 4, 5 - Benefits 6, 7, 8 -
  Disbenefits none

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B/C Analysis of a Single Project

• All cost and benefit estimates must be converted
  to a common equivalent monetary unit (PW, AW or
  FW) at the discount rate (interest rate). The B/C
  ratio is then calculated using one of these
  relations

If B/C gt1.0, accept the project as economically
acceptable for the estimates and discount rate
applied. If B/C lt 1.0, the project is not
economically acceptable.
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B/C ratio
Conventional most commonly used

• The modified B/C ratio includes maintenance and
  operation (MO) costs in the numerator and treats
  them in a manner similar to disbenefits. The
  denominator includes only the initial investment.
  Once all amounts are expressed in PW, AW or FW
  terms, the modified B/C ratio is calculated as

It makes no difference which approach is used
the ratio values will differ. But, the same
absolute (accept/reject) decision will be the same
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Sign Conventions

• Revenues are assigned () signs
• Costs are assigned () signs
• Salvage values are subtracted from costs
• Disbenefit values are subtracted from benefits
  or
• Disbenefit values are added to costs
• Either approach will result in a consistent
  analysis but be consistent through out an
  analysis

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• The Ford Foundation expects to award 15 million
  in grants to public high schools to develop new
  ways to teach the fundamentals of engineering
  that prepare students for university-level
  material. The grants will extend over a 10-year
  period and will create an estimated savings of
  1.5 million per year in faculty salaries and
  student-related expenses. The Foundation uses a
  rate of return of 6 per year on all grant
  awards. This grant program will share Foundation
  funding with ongoing activities, so an estimated
  200,000 per year will be removed from other
  program funding. To make this program successful,
  a 500,000 per year operating cost will be
  incurred from the regular MO budget.
• Use the B/C method to determine if the grant
  program is economically justified.

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The project is also not justified by the modified
B/C method, as expected. For the (B - C) model, B
is the net benefit, and the annual MO cost is
included with costs. B -C (1,500,000 - 200,000)
- (2,038,050 500,000) - 1.24 million Since
(B - C) lt 0, the program is not justified.
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Benefit and Cost difference measure of worth

• The benefit and cost difference measure of worth
  does not involve a ratio, and is based on the
  difference between the PW, AW or FW of benefits
  and costs (B C).
• If (B - C) gt 0, the project is acceptable. This
  method has the advantage of eliminating the
  discrepancies noted when disbenefits are regarded
  as costs, because B represents net benefits. For
  the numbers 10, 8 and 8 the same result is
  obtained regardless of how disbenefits are
  treated.
• Subtracting disbenefits from benefits B - C
  (10 - 8) - 8 -6
• Adding disbenefits to costs B - C 10 - (8
  8) -6
• If the numbers 10, 8 and 8 are used to represent
  the PW of benefits, disbenefits and costs,
  respectively, the correct procedure results in
  B/C (10 - 8)/8 0.25.
• The incorrect placement of disbenefits in the
  denominator results in B/C 10/(8 8) 0.625,
  more than twice the correct B/C value of 0.25.
• Clearly, then, the method affects the magnitude
  of the B/C ratio.

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Alternative Selection Using Incremental B/C
Analysis

• Follow these steps to correctly perform a
  conventional B/C ratio analysis of two
  alternatives. Equivalent values can be expressed
  in PW, AW or FW terms.
• 1. Determine the total equivalent costs for both
  alternatives.
• 2. Order the alternatives by total equivalent
  cost smaller first, then larger. Calculate the
  incremental cost (?C) for the larger-cost
  alternative. This is the denominator in B/C.
• 3. Calculate the total equivalent benefits and
  any disbenefits estimated for both alternatives.
  Calculate the incremental benefits (? B) for the
  larger cost alternative. (This is ?(B - D) if
  disbenefits are considered.)
• 4. Calculate the incremental B/C ratio using
  Equation 9.2, (B - D)/C.
• 5. Use the selection guideline to select the
  higher-cost alternative if B/C gt1.0.

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• A city in Florida has received designs for a new
  patient room wing to the municipal hospital from
  two architectural consultants. One of the two
  designs must be accepted to announce it for
  construction bids. The costs and benefits are the
  same in most categories, but the city financial
  manager decided that the three estimates should
  be considered to determine which design to
  recommend at the city council meeting next week
  and to present to the public in preparation for
  an upcoming bond referendum next month.
• The patient usage cost is an estimate of the
  amount paid by patients over the insurance, the
  building is estimated at 30 years.

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• When the two designs were publicized, another
  hospital lodged a complaint that design A will
  reduce its income by an estimated 500,000 per
  year some of the day-surgery features of design
  A duplicate its services.
• Subsequently, the merchants association argued
  that design B could reduce its annual revenue by
  an estimated 400,000 it will eliminate an
  entire parking lot used by their patrons for
  short-term parking.
• The city financial manager stated that these
  concerns would be entered into the evaluation as
  disbenefits of the respective designs.

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• Use B/C ratio analysis to select design A or B.
  Most of the cash flows are already annualized, so
  the incremental B/C ratio uses AW values. No
  disbenefit estimates are considered.

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Redo the B/C analysis to determine if the
economic decision is still the same as when
disbenefits were not considered.
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Incremental B/C Analysis of Multiple Alternatives

• Choose the largest-cost alternative that is
  justified with an incremental B/C gt 1.0 when this
  selected alternative has been compared with
  another justified alternative.

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• The Economic Development Corporation (EDC) for
  the city of Bahia, California, and Moderna County
  is operated as a not-for-profit corporation. It
  is seeking a developer that will place a major
  water park in the city or county area. Financial
  incentives will be awarded. In response to a
  request for proposal (RFP) to the major water
  park developers in the country, four proposals
  have been received. Larger and more intricate
  water rides and increased size of the park will
  attract more customers, therefore, different
  levels of initial incentives are requested in the
  proposals. One of these proposals will be
  accepted by the EDC and recommended to the Bahia
  City Council and Moderna County Board of Trustees
  for approval.
• Approved and in-place economic incentive
  guidelines allow entertainment industry prospects
  to receive up to 500,000 cash as a first-year
  incentive award and 10 of this amount each year
  for 8 years in property tax reduction. All the
  proposals meet the requirements for these two
  incentives. Each proposal includes a provision
  that residents of the city or county will benefit
  from reduced entrance (usage) fees when using the
  park. This fee reduction will be in effect as
  long as the property tax reduction incentive
  continues. The EDC has estimated the annual total
  entrance fees with the reduction included for
  local residents. Also, EDC estimated the extra
  sales tax revenue expected for the four park
  designs. These estimates and the costs for the
  initial incentive and annual 10 tax reduction
  are summarized in Table 91.

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Perform an incremental B/C study to determine
which park proposal is the best economically.
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Solution

• The discount rate used by the EDC is 7 per year.
  
• Can the current incentive guidelines be used to
  accept the winning proposal?
• The viewpoint taken for the economic analysis is
  that of a county resident.
• The first-year cash incentives and annual tax
  reduction incentives are real costs to the
  residents.
• Benefits are derived from two components the
  decreased entrance fee estimates and the
  increased sales tax receipts. These will benefit
  each citizen indirectly through the increase in
  money available to those who use the park and
  through the city and county budgets where sales
  tax receipts are deposited. Since these benefits
  must be calculated indirectly from these two
  components, the initial proposal B/C values
  cannot be calculated to initially eliminate any
  proposals. A B/C analysis incrementally comparing
  two alternatives at a time must be conducted.
• Equivalent AW values are used for benefit and
  cost amounts per year. Since the benefits must be
  derived indirectly from the entrance fee
  estimates and sales tax receipts, step 4 is not
  used.
• 1. For each alternative, the capital recovery
  amount over 8 years is determined and added to
  the annual property tax incentive cost.
• For proposal 1,
• AW of total costs initial incentive (A/P, 7,
  8) tax cost 250,000 (A/P, 7, 8) 25,000
  66,867

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• 2. The alternatives are ordered by the AW of
  total costs in Table 91.
• 3. The annual benefit of an alternative is the
  incremental benefit of the entrance fees and
  sales tax amounts. These are calculated in step
  5.
• 4. This step is not used.
• 5. Table 91 shows incremental costs calculated
  by Equation 9.4. For the 2-to-1 comparison,
• ?C 93,614 - 66,867 26,747
• Incremental benefits for an alternative are the
  sum of the resident entrance fees compared to
  those of the next-lower-cost alternative, plus
  the increase in sales tax receipts over those of
  the next-lower-cost alternative. The benefits are
  determined incrementally for each pair of
  alternatives. For example, when proposal 2 is
  compared to proposal 1, the resident entrance
  fees decrease by 50,000 per year and the sales
  tax receipts increase by 10,000. Then the total
  benefit is the sum of these, that is,
• B 60,000 per year.
• 6. For the 2-to-1 comparison, Equation 9.7
  results in B/C 60,000 / 26,747 2.24
• Alternative 2 is incrementally justified.
  Alternative 1 is eliminated, and alternative 3
  is now compared to 2.
• 7. This process is repeated for the 3-to-2
  comparison that has an incremental B/C of 0.62
  because the incremental benefits are
  substantially less than the increase in costs.
• Therefore, proposal 3 is eliminated, and the
  4-to-2 comparison results in
• B/C 220,000 / 120,360 1.83
• Since B/C gt 1.0, proposal 4 is retained and
  selected.
• The recommendation for proposal 4 requires an
  initial incentive of 800,000 that exceeds the
  500,000 limit of the approved incentive limits.
  The EDC will have to request the City Council and
  County Trustees to grant an exception to the
  guidelines. If the exception is not approved,
  proposal 2 is accepted.

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Summary

• The benefit/cost method is used primarily to
  evaluate projects and to select from alternatives
  in the public sector. When comparing mutually
  exclusive alternatives, the incremental B/C ratio
  must be greater than or equal to 1.0 for the
  incremental equivalent total cost to be
  economically justified.
• The PW, AW or FW of the initial costs and
  estimated benefits can be used to perform an
  incremental B/C analysis.
• If alternative lives are unequal, the AW values
  should be used, provided the assumption of
  project repetition is not unreasonable.
• For independent projects, no incremental B/C
  analysis is necessary. All projects with B/C gt
  1.0 are selected provided there is no budget
  limitation.
• Public sector economics are substantially
  different from those of the private sector. For
  public sector projects, the initial costs are
  usually large, the expected life is long (25, 35
  or more years), and the sources for capital are
  usually a combination of taxes levied on the
  public, user fees, bond issues and private
  lenders. It is very difficult to make accurate
  estimates of benefits for a public sector
  project. The interest rates, called the discount
  rates in the public sector, are lower than those
  for corporate capital financing.