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COST-BENEFIT ANALYSIS
Chapter 8
Projecting Present Dollars into the Future
R=$ T=years r=interest rate
How much will $1000 earn in 2 years at an interest rate of 10%
R0 = $1000
R1 = $1000*(1+.01) = $1010
R2 = $1010*(1+.01) = $1020.10
R2 = $1000*(1+.01)2 = $1020.10
RT = R0*(1+r)T
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Projecting Future Dollars into the Present
How much will $1000 earned in 2 years at an interest rate of 10% be worth today
Since RT = R0*(1+r)T
R0 = RT/(1+r)T
Present Value
discount rate
discount factor
Low r – more future-oriented and benefits projects in which returns are concentrated further into the future
High r – more present-oriented and benefits projects in which returns are concentrated closer into the future
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Present Value of a Stream of Money
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Inflation
How to incorporate inflation – price level increases – into the procedure
Given: ∏ = inflation rate
However, (1+∏) terms cancel out, leaving the PV equation from previous slide!
CAUTION: $ values and r values must be measured consistently – if real values are used for R, the r must be measured in real terms
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Private Sector Project Evaluation
Present Value Criterion
Annual Net Return PV of R&D vs. Advertising
Year R&D Advertising r = R&D Advertising
0 $1,000 -$1,000 0 $150 $200
1 600 0 0.01 128 165
2 0 0 0.05 46 37
3 550 1,200 0.07 10 -21
Note choice of r is critical:
Low r benefits Advertising; High r benefits R&D.
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Private Sector Project Evaluation Internal Rate of Return
Project Year 0 Year 1 ρ Profit PV
X -$100 $110 10% $4 3.77
Y -$1,000 $1,080 8% $20 18.87
IRR: Discount rate that would make a project’s NPV zero
This criterion is flawed when comparing projects of much differing sizes. Although X has the higher IRR, Y yields the higher profit.
Note that the PV criteria, using r=6%, would prefer Y.
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Private Sector Project Evaluation Benefit-Cost Ratio
Benefit-cost ratio = B/C
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Problems with the Benefit-Cost Ratio
“Costs or Negative Benefits ”
Project B C B/C
I $250 $100 2.5
II $200 $100 2.0
Suppose that $40 of costs need to be added to project I
I: Subtract $40 from B $210 $100 2.1
OR
I: Add $40 to C $250 $140 1.79
Benefit-Cost criterion can lead to incorrect inferences
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Private Sector Project Evaluation
The Present-Value Criterion is the most reliable evaluation guide
Both IRR and Benefit-Cost Ratio Criteria can lead to incorrect inferences
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What is the Appropriate Discount Rate for Government Projects
Based on Returns in Private Sector: the market rate
Social Discount Rate: the rate at which society is willing to trade off present consumption for future consumption
Arguments for SDR:
Paternalism
Market Inefficiency
Example: Discounting and the Economics of Climate Change
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Government Discounting in Practice
U.S. Office of Management and Budget (OMB) requires federal agencies to use a variety of discount rates, depending on the agency and the type of project
One using real discount rate of 7%
One using real discount rate of 3%
Evidence shows that government’s incorrect use of discounting has favored policies that increase revenue in the short run, but reduce it in the long run
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Valuing Public Benefits and Costs
Use Market Prices
Use Adjusted Market Prices in imperfect markets
= Shadow price
= underlying social MC of a good
Monopoly
Taxes
Unemployment
Use Consumer Surplus
Pounds of avocados per year
Price per pound of avocados
Da
Sa
d
A0
Sa’
$1.35
$2.89
b
c
g
A1
e
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Valuing Public Benefits and Costs
Inferences from Economic Behavior
How to place a value on the time saved by a proposed project like a new highway
Earnings
Other methods
How to place a value on a life saved by a proposed project such as a 4-lane divided highway
Lost earnings
Probability of death
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Valuing Public Benefits and Costs
Intangibles
Intangibles can subvert cost-benefit exercises
C/B tools can reveal limits on valuing intangibles
Cost-effectiveness analysis might be best in the presence of intangible benefits
Comparing the costs of various alternatives that attain similar benefits to determine which one is the cheapest
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Games Cost-Benefit Analysts Play
Common Errors
The Chain-Reaction Game
Including secondary profits (but not costs)
The Labor Game
Including project workers’ wages as a benefit (rather than what it is, which is a cost)
The Double-Counting Game
Including benefits from all possible projects, when only one project can be undertaken
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Distributional Considerations
Should who gains and who loses be taken into account Should benefits and costs be weighted
NO: Hicks-Kaldor Criterion – a project should be undertaken if it has positive net present value, regardless of distributional consequences
NO: Let the government costlessly correct any undesirable distributional aspects
NO: Relies too much on value judgments and politics
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Uncertainty
Project Benefit Probability CE*
X $1,000 1.00 $1,000
Y 0 0.50
$1,000
$2,000 0.50
*Certainty Equivalents (Expected Value)
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An Application:
Are Reductions in Class Size Worth It
Discount rate
Costs
Benefits
The Bottom Line and Evaluation
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Use (and Nonuse) by Government
Using Cost-Benefit Analysis
Not Using Cost-Benefit Analysis
Clean Air Act
Endangered Species Act
Food, Drug, and Cosmetic Act
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Chapter 8 Summary
Cost-Benefit analysis is used to evaluate potential public sector projects
Present value of future expected costs and benefits must be calculated in order to allow correct comparisons
Although the IRR and B-C Ratio are used to evaluate projects, the NPV criterion has fewer biases and problems
Choice of the discount rate is critical
The costs and benefits of public projects can be measured using market prices in the absence of market failures. Otherwise, shadow prices or consumer surplus can be used
CONT
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Chapter 8 Summary (cont)
Quantifying the value of time and life, is necessary in measuring benefits, but using earnings as a proxy has limitations
Whether the distribution of future costs and benefits on various groups of people should be included in C-B analysis is under debate
Uncertainty of future costs and benefits can be included through the use of certainty equivalents
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Appendix: Calculating the Certainty Equivalent Value
Income per year
Utility
C
E
E + y
U(E)
U*
U(E + y)
U
Expected income
Certainty Equivalent
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O

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