Environmental Economics

Vijaya Raj Sharma, Ph.D.



LECTURE NOTES ON PART II: BENEFIT-COST ANALYSIS



These notes are not edited. They also do not necessarily cover everything that would be discussed in the class. Students are responsible for any additional materials discussed in the class.

These notes frequently refer to exhibits and tables in the textbook - Environmental Economics, An Introduction by Barry C. Field, Second Edition, Irwin/McGraw Hill, 1997.



IV. BENEFIT-COST ANALYSIS

(Chapter 6)





Objective of B-C Analysis

Estimate and Compare Benefits and Costs of a Project or Policy to decide whether the project or policy should be implemented.





Decision Criterion

Implement the Project if

Benefits exceed Costs

or, Net Benefits exceed 0

or, Benefits / Costs exceeds 1





Steps for B-C Analysis - 1

Decide: Analysis From Whose Perspective?

Always Take "Social" Perspective

Which Society? Local/Regional/National

Specify the Project Fully

Location

Size

Timing, Linkages with other projects, etc.





Steps for B-C Analysis - 2

Estimate Benefits and Costs over the entire life period of the Project

Calculate Total Net Benefits and the Benefit-Cost Ratio

Total net benefits = Benefits - Costs

Benefit-Cost Ratio = Benefits / Costs





Estimation of Benefits and Costs - 1

Specify the life period of the Project

Example: 50 years

Identify each output or benefit of the Project. Example: Benefits of a Dam

Energy, Irrigation, Recreation, etc.

Identify each cost item of the Project

Construction: materials, labor, others

Operation, Repair and Maintenance

Environmental Costs





Estimation of Benefits and Costs - 2

Quantify in Physical Units Each Benefit and Cost Heading for Each Year of the Life Period of the Project

Year 0 1 2 50
Energy (kWh) 0 20 50 100

Convert Physical Units into $ Values

Energy, $ 0 2 5 10




You may use current prices (to allow inflation) or constant prices (to eliminate inflation) to convert physical units to $ values. Whether you use current or constant prices would later require you to choose nominal or real discount rate.





Estimation of Benefits & Costs - 3

Example: Dam

Year 0 1 2 3 50

Benefits, $

Energy 0 2 5 10 10
Irrigation 0 1 2 5 5
Recreation 0 0.1 0.2 0.5 0.5
Benefits, $ 0 3.1 7.2 15.5 15.5

Estimation of Benefits & Costs - 4

Example: Dam

Year 0 1 2 3 50

Costs, $

Construction 400 100 0 0 0
Operation 2 2 4 5 5
Rep & Maint. 0 0.1 0.2 0.5 0.5
Env Costs 100 1 1 2 2
Costs, $ 502 103.1 4.2 7.5 7.5

Estimation of Benefits & Costs - 5

Example: Dam

Year 0 1 2 3 50
Benefits, $ 0 3.1 7.2 15.5 15.5
Costs, $ 502 103.1 4.2 7.5 7.5
Net Benefits, $ -502 -100 3.0 8.0 8.0


Calculation of Total Net Benefits

& B-C Ratio - 1

Convert Each Year's Benefits & Costs into Present Values

Add Present Values of Benefits and Costs

Calculate Total Net Benefits

Calculate B-C Ratio



Present Value Formula

FV = future value, n years from now

r = discount rate, % per year

PV = present value of FV

PV = FV [1/ (1+r)n]

[1/ (1+r)n] is called the discount factor.

Example: PV Calculation

Year (n) 0 1 2 3
FV, $ 100 100 100 100
[1/ (1+r)n],

r = 5%

1 0.95 0.91 0.86
[1/ (1+r)n],

r=10%

1 0.91 0.83 0.75
PV, $,

when r=5%

100 95 91 86
PV, $,

when r=10%

100 91 83 75

The farther the future, the lower the PV.

The higher the r, the lower the PV.

Sensitivity to Choice of Discount Rate

Year 0 1 2
FV of Benefits. $ 0 50 100
PV of benefits, r=2%, $ 0 49.0 96.1
PV of benefits, r=5%, $ 0 47.6 90.7
FV of Costs, $ 100 20 25
PV of costs, r=2%, $ 100 19.6 24.0
PV of costs, r=5%, $ 100 19.1 22.7
FV of Net Benefits, $ -100 30 75
PV of net benefits, r=2%, $ -100 29.4 72.1
PV of net benefits, r=5%, $ -100 28.5 68.0

PV(Total Net Benefits) = $1.5 at 2%, -$3.5 at 5%

Choice of Discount Rate:

Conservationists' Dilemma - 1

Zero (the Lowest Possible) Discount Rate?

Year 0 1 2 50
Benefits, $ 0 21 21 21
Costs, $ 1,000 0 0 0
NB, $ -1000 21 21 21

Total Net Benefits = -$1,000 + ($21x50 years) =$50

In spite of large initial environmental cost, a project can pass with small benefits spread over many years.

Choice of Discount Rate:

Conservationists' Dilemma - 2

Large Discount Rate?

Generation Present Future
Benefits, $ 900 10
Costs, $ 10 1,000

A large discount rate will drastically reduce the present value of the large future cost.

Projects that generate immediate short-run benefits but very large future environmental costs can pass with a large discount rate.



Choice of Discount Rate - 3

Choose an appropriate discount rate.

In the U.S., the Office of Management and Budget specifies the discount rate for federal projects.

Time Preference Approach of Selecting r

Average interest rate paid by banks to savings account depositors - a reflection of people's rate of time preference

Marginal Productivity Approach of Selecting r

Average interest rate charged by banks to business borrowers - a reflection of the marginal productivity of (return on) capital



Choice of Discount Rate - 4

Nominal or Real Interest Rate as Discount Rate?

Real rate if benefit and cost estimates in constant $

Nominal rate if benefit and cost estimates include inflation

Real Interest Rate = Nominal Interest Rate - Inflation rate

Redo the PV calculations with different discount rates: Sensitivity Analysis



Comparison of Scopes of a Project

You may do B-C analyses for a little larger or little smaller scope or size of the Project, to find the optimal scope (the one with the maximum total net benefits).

For comparison of Scopes of a Project, compare only total net benefits. Do not compare B-C ratios.

Show graphically why B-C ratio may be misleading in the comparison of scope.



Comparison of Scopes: Example

Description Scope A Scope B
PV(Total Benefits) $1,000 $1,350
PV(Total Costs) $700 $1,000
PV(Net Benefits) $300 $350
B-C Ratio 1.43 1.35

Although B-C ratio is lower, Scope B has higher net benefits.



Equity

Equity - Fairness of distribution of net benefits

Horizontal Equity: Distribution among similarly-situated people

Vertical Equity: Distribution among different groups of people, e.g. rich and poor

Proportional: distribution in equal proportion of income. Ex: net benefits to both poor and rich equal to 10% of their income

Progressive: more distribution to poor as a proportion of income. Ex: net benefits to poor 15% of income and to rich 10% of income

Regressive: less distribution to poor as a proportion of income. Ex: 15% of income to rich, but 10% to poor.



Example on Equity

Description Scope A Scope B
Total Net Benefits $300 $350
NBs to 10 rich families $ 80 $110
NBs to 100 poor families $220 $240
Average family income of rich $ 80 $ 80
Average family income of poor $ 20 $ 20
NB as % of income to rich 10% 13.8%
NB as % of income to poor 11% 12%
Vertical Equity Progressive Regressive

Benefit-cost analysis of risky projects

Example:

Insecticide spraying

Dumping of hazardous wastes

Preparedness against oil-spill disasters

May have to make a choice among uncertain or risky outcomes

Number of oil spills in any year is uncertain. For how many events of oil spills should we plan preparedness?

Different insecticides have different levels of risks to health, but also different levels of effectiveness against insects. Which insecticide to spray?



Expected Value

Risky events have certain probabilities of their occurrence.

Example: Probability of number of oil spills in a year

One oil spill: 0.70

Two oil spills: 0.20

Three oil spills: 0.07

Four oil spills: 0.03

More than 4 oil spills: 0.00

Expected Value of number of oil spills in a year = 1x0.70 + 2x0.20 + 3x0.07 + 4x0.03 = 1.43.

Expected Value =probability-weighted average outcome of a risky event.



Types of Risk Preferences

How does a person choose among risky outcomes?

Depends on risk preference of the person - 3 types of risk preferences

Risk averseness

Risk seeking

Risk neutral

Example on Risk Preference



Program A Program B
Net benefits Probability Net benefits, Probability
$500,000 0.475 $500,000 0.99
$300,000 0.525 - $10,000 0.01
Expected value = $500,000x0.475 + $300,000x0.525 = $395,000 Expected value = $500,000x0.99 +

(-) $10,000x0.01 = $395,000



Definition of Risk Preferences

Risk neutral person compares expected values and should be indifferent between the two programs in the above example.

Risk averse person avoids large risks and is likely to choose Program A in the above example.

Risk seeking person likes to take large beneficial risks and is likely to choose Program B in the above example.

Therefore, willingness to pay of an individual for reducing risks depends on the individual's risk preference.

If a policy is associated with risks of disastrous or irreversible damage to environment or to human health, a risk-averse policy may have to be considered for the sake of sustainability.



V. TECHNIQUES OF BENEFIT ESTIMATION

(Chapter 7)



Techniques of Estimating Benefits of Improvement in Environmental Quality



Estimation of Direct Damages

Estimation of Willingness to Pay

Indirect Method

Direct Method of Determining Willingness to Pay (Contingent Valuation Method)

Use Values and Nonuse Values of Environmental Resources

Willingness to Accept (WTA)

VI. TECHNIQUES OF COST ESTIMATION

(Chapter 8)



Besides having monetary costs, a project may impose environmental costs. The National Environmental Policy act of 1970 requires all federal projects to conduct environmental impact analysis (EIA). EIA is the determination of all direct physical effects of a project on the environment, including the after-effects of the project when people adapt to the project. EIA is mostly done by natural scientists.

FEW PRINCIPLES OF COST ESTIMATION



With/Without as opposed to Before/After



Ex: Cost of a Regulation to Control Emissions of Power Plants



Cost Headings Year 1998, before the regulation Year 1999, after or with the regulation Year 1999, without the regulation Cost difference
Before/

After

With/ without



Wages


$10,000


$12,500


$11,000


$2,500


$1,500


Materials


$40,000


$45,000


$42,000


$5,000


$3,000


Social Opportunity Costs as opposed to Accounting or Monetary Costs



Cost Headings Year 1999, with the project Year 1999, without the project Cost difference Social Opportunity cost
Materials

Sales tax

$45,000

$2,250

$42,000

$2,100

$3,000

$150

$3,000

exclude tax

Wages, skilled

Wages, unskilled

(competitive wages)

$4,500

$10,625

($8,500)

$3,500

$10,000

($8,000)

$1,000

$625

($500)

$1,000

$500 (use competitive wage)

Interest on Purchase of Scrubbers ($50,000 @5%) Interest free

( $2,500)

$0



$0

$2,500 (cost of capital - a social cost)


An executive order of 1981 calls for federal agencies to conduct regulatory impact analysis (RIA) for all major federal regulations. RIA is evaluation of benefits and costs of a regulation.



SOME EXAMPLES OF COST ESTIMATES



A SINGLE FACILITY PROJECT:

SMALL WASTEWATER TREATMENT PLANT

See Table 8-1 of the textbook.



A LOCAL ENVIRONMENTAL REGULATION:

TO REDUCE CHEMICAL USE IN AN APPLE ORCHARD

Cost of Regulation = Decrease in net income of the orchard

Net Income = Revenue - Cost

Assume market price of apple is fixed in the locality.



If the regulation forces closure of the Orchard, the entire net income is wiped out, which is the cost of regulation.

* Do not include costs of labor laid off, unless they remain unemployed. But, add any adjustment costs to obtain alternative employment.



COST OF AN INDUSTRY-WIDE REGULATION:

TO REDUCE EMISSIONS IN METAL FINISHING INDUSTRY

Cost of Regulation = Sum of increase in costs of each firm

Representative Firm Approach (when many firms):

Group firms into few categories by size or technology.

Choose one representative firm in each category.

Estimate increase in costs of each representative firm and weigh by the number of firms in each category.

Sum the weighted-increase in costs of all categories.



Example: Table 8-2.



COST OF NATIONWIDE REGULATION

Basic Approach:

Do as in III for each industry.

Find the sum of the costs of regulation of all industries.

Regulation may change outputs in certain industries, which may have impacts on outputs of other industries.

Regulation may expand the pollution-control-technology industry and its outputs.

Need to include all changes in calculating the cost of regulation in an industry.



Problems in Cost Estimation