CHAPTER 11 EVALUATING PROJECTS WITH THE BENEFIT / COST RATIO METHOD $$$ $

CHAPTER 11CHAPTER 11

EVALUATING PROJECTS WITH THE BENEFIT / COST RATIO METHOD

EVALUATING PROJECTS WITH THE BENEFIT / COST RATIO METHOD

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PRIVATE VERSUS PUBLIC PROJECTSPRIVATE VERSUS PUBLIC PROJECTS• PURPOSE

Private Project -- Maximize profit, minimize costs

Public Project -- Offer social benefits (i.e., health, employment ) without profit

• CAPITAL SOURCES

Private Project -- Private investors and lenders

Public Project -- Taxation; Private Lenders• FINANCING

Private Project -- Individuals (for sole proprietorships and partnerships); stocks and corporate bonds (for corporations)

Public Projects -- Direct taxes, Low, no-interest or private loans, bonds, subsidies

• PURPOSE

Private Project -- Maximize profit, minimize costs

Public Project -- Offer social benefits (i.e., health, employment ) without profit

• CAPITAL SOURCES

Private Project -- Private investors and lenders

Public Project -- Taxation; Private Lenders• FINANCING

Private Project -- Individuals (for sole proprietorships and partnerships); stocks and corporate bonds (for corporations)

Public Projects -- Direct taxes, Low, no-interest or private loans, bonds, subsidies

PRIVATE VERSUS PUBLIC PROJECTSPRIVATE VERSUS PUBLIC PROJECTS• MULTIPLE PURPOSES

More frequently for public projects ( i.e., reservoir for: flood control, power source, irrigation, recreation)

• PROJECT LIFE

Private Project -- 5 to 20 years;

Public Project -- 20 to 60 years• CAPITAL PROVIDER RELATIONSHIP TO PROJECT

Private Project -- Direct

Public Project -- Indirect or none• NATURE OF BENEFITS

Private Project -- Monetary or near monetary

Public Project -- Non-monetary; difficult to equate to monetary terms

• MULTIPLE PURPOSES

More frequently for public projects ( i.e., reservoir for: flood control, power source, irrigation, recreation)

• PROJECT LIFE

Private Project -- 5 to 20 years;

Public Project -- 20 to 60 years• CAPITAL PROVIDER RELATIONSHIP TO PROJECT

Private Project -- Direct

Public Project -- Indirect or none• NATURE OF BENEFITS

Private Project -- Monetary or near monetary

Public Project -- Non-monetary; difficult to equate to monetary terms

PRIVATE VERSUS PUBLIC PROJECTSPRIVATE VERSUS PUBLIC PROJECTS• PROJECT BENEFICIARIES

Private Project -- Those undertaking project

Public Project -- General public• CONFLICT OF PURPOSES

More common for public projects (i.e., dam for flood control vs environmental preservation)

• CONFLICT OF INTERESTS

More common for public projects (i.e., intra-agency conflicts)• POLITICAL INFLUENCE

More common for public projects ( i.e., changing decision makers, pressure groups, financial and residential restrictions)

• EFFICIENCY MEASUREMENT

Private Project -- Rate of Return on capital

Public Project -- No direct comparison with private projects

• PROJECT BENEFICIARIES

Private Project -- Those undertaking project

Public Project -- General public• CONFLICT OF PURPOSES

More common for public projects (i.e., dam for flood control vs environmental preservation)

• CONFLICT OF INTERESTS

More common for public projects (i.e., intra-agency conflicts)• POLITICAL INFLUENCE

More common for public projects ( i.e., changing decision makers, pressure groups, financial and residential restrictions)

• EFFICIENCY MEASUREMENT

Private Project -- Rate of Return on capital

Public Project -- No direct comparison with private projects

BENEFITS, COSTS, AND BENEFITS, COSTS, AND DISBENEFITSDISBENEFITS

BENEFITS, COSTS, AND BENEFITS, COSTS, AND DISBENEFITSDISBENEFITS

• Benefits - The favorable consequences of the project to the project sponsors (i.e., the public for public projects)

• Costs -- Monetary disbursements required (i.e., of the government for public projects)

• Disbenefits -- The negative consequences of the project to the project sponsors

• Benefits - The favorable consequences of the project to the project sponsors (i.e., the public for public projects)

• Costs -- Monetary disbursements required (i.e., of the government for public projects)

• Disbenefits -- The negative consequences of the project to the project sponsors

SELF-LIQUIDATING PROJECT

SELF-LIQUIDATING PROJECT

Any public project that is expected to earn direct revenue sufficient to repay the project cost(s) in a specified period of time.

Any public project that is expected to earn direct revenue sufficient to repay the project cost(s) in a specified period of time.

PROBLEMS ASSOCIATED WITH MULTIPURPOSE PROJECTS

PROBLEMS ASSOCIATED WITH MULTIPURPOSE PROJECTS

• Difficult to evaluate and compare all benefits and all disbenefits associated with the project.

• Difficult to allocate costs appropriately to each of the various purposes.

• Difficult to prioritize importance of purposes where conflict of interest occurs between purposes.

• Difficult to deal with the various political sensitivities of Multipurpose public projects.

• Difficult to evaluate and compare all benefits and all disbenefits associated with the project.

• Difficult to allocate costs appropriately to each of the various purposes.

• Difficult to prioritize importance of purposes where conflict of interest occurs between purposes.

• Difficult to deal with the various political sensitivities of Multipurpose public projects.

DIFFICULTIES IN EVALUATING PUBLIC SECTOR PROJECTS

DIFFICULTIES IN EVALUATING PUBLIC SECTOR PROJECTS

1. No profit standard as a measure of effectiveness

2. Difficult to quantify monetary impact of benefits

3. Little or no connection between project and public

4. Short-term rather than long-term benefits are emphasized for political reasons

5. Profit motive as a stimulus for effectiveness is absent

6. More legal restrictions with public projects

7. Greater difficulty in obtaining capital for public projects

8. Selection of interest rates controversial and politically sensitive

1. No profit standard as a measure of effectiveness

2. Difficult to quantify monetary impact of benefits

3. Little or no connection between project and public

4. Short-term rather than long-term benefits are emphasized for political reasons

5. Profit motive as a stimulus for effectiveness is absent

6. More legal restrictions with public projects

7. Greater difficulty in obtaining capital for public projects

8. Selection of interest rates controversial and politically sensitive

CHOOSING AN INTEREST RATE FOR A PUBLIC PROJECT

CHOOSING AN INTEREST RATE FOR A PUBLIC PROJECT

The choice of an interest rate in the public sector is intended to determine how available funds should best be allocated among competing projects to achieve social goals --

maximization of social benefits.

The choice of an interest rate in the public sector is intended to determine how available funds should best be allocated among competing projects to achieve social goals --

maximization of social benefits.

INTEREST RATE CONSIDERATIONSINTEREST RATE CONSIDERATIONS1. Interest rate on borrowed capital

Generally, this is the interest selected for any project targeted for these borrowed funds

2. Opportunity cost of capital to governmental agency

If projects are selected based on estimated return (in terms of benefits) -- return on all accepted projects is higher than on any rejected project -- the interest rate used is that of the best opportunity foregone.

3. Opportunity cost of capital to taxpayers

The interest on the best taxpayer opportunity foregone -- usually the highest of the three, and the most recommended

1. Interest rate on borrowed capital

Generally, this is the interest selected for any project targeted for these borrowed funds

2. Opportunity cost of capital to governmental agency

If projects are selected based on estimated return (in terms of benefits) -- return on all accepted projects is higher than on any rejected project -- the interest rate used is that of the best opportunity foregone.

3. Opportunity cost of capital to taxpayers

The interest on the best taxpayer opportunity foregone -- usually the highest of the three, and the most recommended

SOCIAL DISCOUNT RATESOCIAL DISCOUNT RATE

An additional theory on establishing interest rates for federal projects advocates which suggests the interest rate be the market-determined risk-free rate for private investments -- 3 to 4%

An additional theory on establishing interest rates for federal projects advocates which suggests the interest rate be the market-determined risk-free rate for private investments -- 3 to 4%

BENEFIT / COST RATIO METHODBENEFIT / COST RATIO METHOD

• The time-value of money must be considered to account for the timing of cash flows (benefits) occurring after inception of project

• A ratio of discounted benefits to discounted costs

• The ratio of equivalent worth (i.e., AW, PW or FW) of benefits to the equivalent worth of costs

• Also known as savings-investment ratio by some governmental agencies

• The time-value of money must be considered to account for the timing of cash flows (benefits) occurring after inception of project

• A ratio of discounted benefits to discounted costs

• The ratio of equivalent worth (i.e., AW, PW or FW) of benefits to the equivalent worth of costs

• Also known as savings-investment ratio by some governmental agencies

CONVENTIONAL BENEFIT / COST (B/C) RATIO WITH PRESENT WORTH (PW)


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PW (benefits of the proposed project)

B/C = ---------------------------------------- PW(total costs of the proposed project)

PW (benefits of the proposed project)

B/C = ---------------------------------------- PW(total costs of the proposed project)

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PW (benefits of the proposed project) PW(B)

B/C = ---------------------------------------- = ------------- PW(total costs of the proposed project) I +PW(O&M)



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where: PW(•) = present worth of (•)

B = benefits of the proposed project

I = initial investment of the proposed project

O&M = operating and maintenance costs of the proposed project






O&M = operating and maintenance costs of the proposed project$$$$$$$$$$ $$$$$$$$$$

MODIFIED BENEFIT / COST (B/C) RATIO WITH PRESENT WORTH (PW)

MODIFIED BENEFIT / COST (B/C) RATIO WITH PRESENT WORTH (PW)

PW(B) - PW(O&M)

B/C = --------------------------

I

PW(B) - PW(O&M)

B/C = --------------------------

I

CONVENTIONAL BENEFIT / COST (B/C) RATIO WITH ANNUAL WORTH (AW)

CONVENTIONAL BENEFIT / COST (B/C) RATIO WITH ANNUAL WORTH (AW)

AW (benefits of the proposed project) AW(B)

B/C = ---------------------------------------- = ------------- AW(total costs of the proposed project) CR +AW(O&M)

where: AW(•) = annual worth of (•)


CR = capital recovery amount (i.e., the equivalent annual cost of the initial investment, I, including an allowance

for salvage value, if any)


AW (benefits of the proposed project) AW(B)

B/C = ---------------------------------------- = ------------- AW(total costs of the proposed project) CR +AW(O&M)

where: AW(•) = annual worth of (•)


CR = capital recovery amount (i.e., the equivalent annual cost of the initial investment, I, including an allowance

for salvage value, if any)


MODIFIED BENEFIT / COST (B/C) RATIO WITH ANNUAL WORTH (AW)

MODIFIED BENEFIT / COST (B/C) RATIO WITH ANNUAL WORTH (AW)

AW(B) - AW(O&M)

B/C = --------------------------

CR

AW(B) - AW(O&M)

B/C = --------------------------

CR


SALVAGE VALUE INCLUDED


SALVAGE VALUE INCLUDED


B/C = ----------------------------------- = ----------------- PW(total costs of the proposed project) I - PW(S)

+PW(O&M)




S= salvage value of investment O&M = operating and maintenance costs of the

proposed project


B/C = ----------------------------------- = ----------------- PW(total costs of the proposed project) I - PW(S)

+PW(O&M)




S= salvage value of investment O&M = operating and maintenance costs of the

proposed project

MODIFIED BENEFIT / COST (B/C) RATIO WITH PRESENT WORTH (PW), WITH SALVAGE

VALUE INCLUDED

MODIFIED BENEFIT / COST (B/C) RATIO WITH PRESENT WORTH (PW), WITH SALVAGE

VALUE INCLUDED

PW(B) - PW(O&M)

B/C = --------------------------

I - PW(S)

PW(B) - PW(O&M)

B/C = --------------------------

I - PW(S)

BENEFIT / COST ANALYSIS IN DETERMINING ACCEPTABILITY OF A PROJECT

BENEFIT / COST ANALYSIS IN DETERMINING ACCEPTABILITY OF A PROJECT

All of the preceding formulations for benefit / cost analysis result in consistent acceptance or rejection:

• B / C > 1.0 --- Project accepted• B / C = 1.0 --- Project accepted• B / C < 1.0 --- Project Rejected

Conventional B / C ratios for PW and AW formulations result in the same numerical values

Modified B / C ratios for PW and AW formulations result in the same numerical values (but not the same as the conventional B / C ratios)

All of the preceding formulations for benefit / cost analysis result in consistent acceptance or rejection:

• B / C > 1.0 --- Project accepted• B / C = 1.0 --- Project accepted• B / C < 1.0 --- Project Rejected

Conventional B / C ratios for PW and AW formulations result in the same numerical values

Modified B / C ratios for PW and AW formulations result in the same numerical values (but not the same as the conventional B / C ratios)

DISBENEFITS IN THE BENEFITS / COST (B / C) RATIO

DISBENEFITS IN THE BENEFITS / COST (B / C) RATIO

• The traditional approach to incorporating disbenefits into a benefit / cost analysis to reduce the benefits by the amount of disbenefits (i.e., to subtract disbenefits from benefits in the numerator of the B/C ratio).

• Alternatively, the disbenefits could be treated as costs (i.e., add disbenefits to costs in the denominator).

• The traditional approach to incorporating disbenefits into a benefit / cost analysis to reduce the benefits by the amount of disbenefits (i.e., to subtract disbenefits from benefits in the numerator of the B/C ratio).

• Alternatively, the disbenefits could be treated as costs (i.e., add disbenefits to costs in the denominator).

CONVENTIONAL BENEFIT / COST RATIO WITH ANNUAL WORTH, BENEFITS REDUCED

BY AMOUNT OF DISBENEFITS


BY AMOUNT OF DISBENEFITS AW(benefits) - AW(disbenefits)

B / C = -----------------------------------------

AW(costs)

AW(benefits) - AW(disbenefits)

B / C = -----------------------------------------

AW(costs)




BY AMOUNT OF DISBENEFITS AW(benefits) - AW(disbenefits) AW(B) -

AW(D)

B / C = ----------------------------------------- = --------------------

AW(costs) CR + AW(O&M)

AW(benefits) - AW(disbenefits) AW(B) - AW(D)

B / C = ----------------------------------------- = --------------------





BY AMOUNT OF DISBENEFITS AW(benefits) - AW(disbenefits) AW(B) -

AW(D)

B / C = ----------------------------------------- = --------------------


where AW(•) =annual worth of (•)

B =benefits of proposed project

D =disbenefits of proposed project

CR =capital recovery amount (i.e., the equivalent annual cost of the initial investment, I, including an allowance for salvage value, if any)

O&M =operating and maintenance costs of the proposed project

AW(benefits) - AW(disbenefits) AW(B) - AW(D)

B / C = ----------------------------------------- = --------------------







CONVENTIONAL BENEFIT / COST RATIO WITH ANNUAL WORTH, COSTS INCREASED


CONVENTIONAL BENEFIT / COST RATIO WITH ANNUAL WORTH, COSTS INCREASED

BY AMOUNT OF DISBENEFITS AW(benefits) AW(B)

B / C = ------------------------------ = ---------------------------

AW(costs) + AW(disbenefits) CR + AW(O&M) + AW(D)






AW(benefits) AW(B)

B / C = ------------------------------ = ---------------------------

AW(costs) + AW(disbenefits) CR + AW(O&M) + AW(D)






IS ANALYSIS AFFECTED BY IDENTIFYING A POSITIVE CHANGE IN BENEFIT AS AN INCREASED BENEFIT OR

REDUCED COST ?

IS ANALYSIS AFFECTED BY IDENTIFYING A POSITIVE CHANGE IN BENEFIT AS AN INCREASED BENEFIT OR

REDUCED COST ? • Arbitrarily classifying a cost or benefit has no

impact on project acceptability:Let B = equivalent annual worth of project benefits

C = equivalent annual worth of project costs

X = equivalent annual worth of cash flow (added benefit or reduced cost) not included in B or C

If you classify X as added benefit: B / C = (B+X) / C

If you classify X as reduced cost: B / C = B / (C - X)

Given project is acceptable:

[ (B+X) / C ] > 1 : ( B + X ) must be greater than C

[ B / (C - X) ] > 1 : B must be greater than C -X (or transposing X, ( B + X ) must be greater than C)

• Arbitrarily classifying a cost or benefit has no impact on project acceptability:

Let B = equivalent annual worth of project benefits

C = equivalent annual worth of project costs

X = equivalent annual worth of cash flow (added benefit or reduced cost) not included in B or C

If you classify X as added benefit: B / C = (B+X) / C

If you classify X as reduced cost: B / C = B / (C - X)

Given project is acceptable:

[ (B+X) / C ] > 1 : ( B + X ) must be greater than C

[ B / (C - X) ] > 1 : B must be greater than C -X (or transposing X, ( B + X ) must be greater than C)

COMPARISON OF MUTUALLY-EXCLUSIVE PROJECTS BY B / C RATIOS

COMPARISON OF MUTUALLY-EXCLUSIVE PROJECTS BY B / C RATIOS

• When using equivalent worth methods to select among mutually-exclusive alternatives (MEAs), the best alternative selected by maximizing PW, AW, or FW.

• When using B / C method, no direct measure of each project’s profit potential is provided.– Only a ratio of benefits to costs is provided for each project– Selecting the project that maximizes the B / C ratio does not

guarantee the best project is selected.• Ranking of projects changes when using conventional

versus modified B / C ratio.• Approach of classifying cash flow items as added

benefits rather than reduced costs could also change preference for one MEA over another.

• When using equivalent worth methods to select among mutually-exclusive alternatives (MEAs), the best alternative selected by maximizing PW, AW, or FW.

• When using B / C method, no direct measure of each project’s profit potential is provided.– Only a ratio of benefits to costs is provided for each project– Selecting the project that maximizes the B / C ratio does not

guarantee the best project is selected.• Ranking of projects changes when using conventional

versus modified B / C ratio.• Approach of classifying cash flow items as added

benefits rather than reduced costs could also change preference for one MEA over another.

CRITICISMS AND SHORTCOMINGS OF THE BENEFIT / COST RATIO METHODCRITICISMS AND SHORTCOMINGS OF THE BENEFIT / COST RATIO METHOD

1. It is often used for after-the-fact justifications

2. Distributional inequities (i.e., one group benefits while another group incurs costs) are typically not accounted for by the B / C analysis

3. Qualitative information is often ignored in a B / C analysis

1. It is often used for after-the-fact justifications

2. Distributional inequities (i.e., one group benefits while another group incurs costs) are typically not accounted for by the B / C analysis

3. Qualitative information is often ignored in a B / C analysis

CHAPTER 11 EVALUATING PROJECTS WITH THE BENEFIT / COST RATIO METHOD $$$ $

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