1
Chapter 11 – Cost-Benefit
Analysis
Public Economics
2
Introduction
? Cost-benefit analysis is a set of
practical procedures for guiding public
expenditure decisions.
3
Present Value
? Project evaluation usually requires
comparing costs and benefits from
different time periods
? Dollars across time periods are not
immediately comparable,because of
inflation and returns in the market.
4
Present Value:
Present Dollars into the Future
? Suppose you invest $100 today in the
bank
– At the end of year 1,it is worth (1+.05)x$100,
or $105
– At the end of year 2,it is worth (1+.05)x$105,
or $110.25
– The interest compounds over time,that is the
interest is also earning interest
5
Present Value:
Present Dollars into the Future
? Define
– R=initial investment amount
– r=rate of return on investment
– T=years of investment
? The future value (FV) of the investment is:
? ?FV R r T? ?1
6
Present Value:
Future Dollars into the Present
? Suppose someone promises to pay you
$100 one year from now.
? What is the maximum amount you should
be willing to pay today for such a promise?
? You are forgoing the interest that you
could earn on the money that is being
loaned.
7
Present Value:
Future Dollars into the Present
? The present value of a future amount of
money is the maximum amount you
would be willing to pay today for the right
to receive the money in the future.
8
Present Value:
Present Dollars into the Future
? Define
– R=amount to be received in future
– r=rate of return on investment
– T=years of investment
? The present value (PV) of the investment is:
? ?
PV
R
r
T?
?1
9
Present Value:
Future Dollars into the Present
? In previous equation,r is often referred to as the
discount rate,and (1+r)-T is the discount factor.
? Finally consider a promise to pay a stream of
money,$R0 today,$R1 one year from now,and
so on,for T years?
? ? ? ? ? ?PV R
R
r
R
r
R
r
T
T? ? ? ? ? ? ? ?0
1 2
21 1 1.,,
10
Present Value:
Future Dollars into the Present
? Present value is an enormously important
concept
? A $1,000,000 payment 20 years from
now is only worth today:
– $376,889 if r=.05
– $148,644 if r=.10
11
Present Value:
Inflation
? Nominal amounts are valued according
to the level of prices in the year the return
occurs.
? Real amounts are valued according to
the level of prices in one particular year.
? Inflation affects both the payout stream,
and the discount factor,and these two
cancel each other out.
12
Private Sector Project Evaluation
? Suppose there are two projects,X and Y
? Each entails certain benefits and costs,
denoted as BX,CX,BY,and CY.
? Need to ask:
– Is the project admissible?
– Is the project preferable?
13
Private Sector Project Evaluation
? Admissible,Are the benefits greater than
the costs?
? Preferable,Are the net benefits the
highest?
? Most projects involve a stream of benefits
and costs over time.
14
Private Sector Project Evaluation
? Define:
Bti ?
Cti ?
Benefits from project i at time t
Costs from project i at time t
? Then the present value of project i is:
? ? ? ?? ? ? ?
? ?
PV B C
B C
r
B C
r
i i i
i i
T
i
T
i
T? ? ?
?
?
? ?
?
?
0 0
1 1
1 1
.,,
15
Private Sector Project Evaluation
? The present value criteria for project
evaluation are that:
– A project is admissible only if its present
value is positive
– When two projects are mutually exclusive,
the preferred project is the one with the
highest present value.
16
Private Sector Project Evaluation
? Table 11.2 shows two different projects
(R&D or Advertising).
? The discount rate plays a key role in
deciding what project to choose,because
the cash inflows occur at different times.
? The lower the discount rate,the more
valuable the back-loaded project.
Table 11.2
18
Private Sector Project Evaluation
? Several other criteria are often used for
project evaluation,but can give
misleading answers
– Internal rate of return
– Benefit-cost ratio
19
Private Sector Project Evaluation
? The internal rate of return,ρ,is defined as the ρ
that solves the equation:
? ? ? ?? ? ? ?? ?0 1 10 0 1 1? ? ? ?? ? ? ??B C B C B CT TT? ?.,,
? The IRR is the discount rate that would make the
present value of the project equal to zero.
– Admissible if ρ>r
– The flawed analysis would choose an admissible project
with the higher internal rate of return,ignoring scale
20
Private Sector Project Evaluation
? The benefit-cost ratio divides the discounted
stream of benefits by the discounted stream of
costs,In this case
? B=stream of benefits and C=stream of costs:
? ? ? ?B B
B
r
B
r
T
T? ? ? ? ? ?0
1
1 1.,,
? ? ? ?C C
C
r
C
r
T
T? ? ? ? ? ?0
1
1 1.,,
21
Private Sector Project Evaluation
? Admissibility using the benefit-cost ratio requires:
B
C ?1
? This ratio is virtually useless for comparing
across admissible projects however.
? Ratio can be manipulated by counting benefits
as,negative costs” and vice-versa.
22
Discount rate for government
projects
? Government decision making involves
present value calculations
? Costs,benefits and discount rates are
somewhat different from private sector
23
Discount rate for government
projects
? Less consensus on appropriate discount rate in
public sector,One possibility are rates based
on returns in private sector.
– Assumes all of the money that is raised would have
been invested in a private sector project
– In reality,funding comes from a variety of sources –
investment and consumption
– Funding that come from consumption should be
discounted at the after-tax discount rate
– Hard in reality to determine what proportions of
funding come from consumption or investment
24
Discount rate for government
projects
? Another possibility is the social rate of
discount – which measures the valuation
society place on consumption that is sacrificed
in the present.
? Differs from market returns because it:
– Accounts for concern about future generations
– Involves paternalism
– May solve some market inefficiency such as positive
externalities
25
Discount rate for government
projects
? In reality,federal agencies are required to
use a real rate of return of 7%,on the
assumption that this measures the
before-tax rate of return in the private
sector.
? Some use 2% real return instead,thought
to measure the after-tax rate of return.
26
Discount rate for government
projects
? When a new tax or expenditure is
introduced,its effects over a 5-year or 10-
year period are analyzed to see whether
it will put the budget out of balance
– Ignores discounting
– Costs (or benefits) outside of the window are
not counted toward deficit (or surplus)
27
Valuing Public Benefits and Costs
? Recall that the discount rate,benefits,
and costs are needed to compute the
present value of a project
? For private company:
– Benefits = revenues received
– Costs = firm’s payments for inputs
28
Valuing Public Benefits and Costs
? For public sector,market prices may not reflect
social benefits and costs.
– Externalities,for example
? Several ways of measuring benefits and costs
– Market prices
– Adjusted market prices
– Consumer surplus
– Inferences from economic behavior
– Valuing intangibles
29
Valuing Public Benefits and Costs
? Market prices
– In a properly functioning competitive
economy,the price of a good simultaneously
reflects its marginal social cost of production
and its marginal value to consumers.
– Ignores market imperfections
– Easy to gather
30
Valuing Public Benefits and Costs
? Adjusted market prices
– If markets are imperfect,prices generally do
not reflect true marginal social cost
– Shadow price of a commodity is its true,
underlying marginal social cost,which can
sometimes be estimated
– Examples where insights can be gleaned
include monopoly price,taxes,and
unemployment
31
Valuing Public Benefits and Costs
? Consumer surplus
– Public sector projects can be large,and
change market prices
– Figure 11.1 measures the change in
consumer surplus from a government
irrigation project that lowers the cost of
agricultural production
Figure 11.1
33
Valuing Public Benefits and Costs
? In this figure,the change in consumer
surplus is area bcgd.
? Provided the government planner can
accurately measure the demand curve,
the project’s benefit can be measured
with this change.
34
Valuing Public Benefits and Costs
? Inferences from Economic Behavior
? Many times a good in question is not
explicitly traded,so no market price exists.
? Examples:
– Value of time
– Value of life
35
Valuing Public Benefits and Costs
? Value of time
? In cost-benefit analysis,need to estimate
the value of time to take advantage of
theory of leisure-income choice.
– After-tax wage is often used
– But hours of work not always a,choice,” and
not all uses of time away from job equivalent.
36
Valuing Public Benefits and Costs
? Researchers have examined value of
time by travel commuting choices.
– Trains are more expensive,but less time-
consuming,than buses,The same is true
about non-stop airline flights versus those
with a layover.
– Estimates are that value of time
approximately half of the before-tax wage.
37
Valuing Public Benefits and Costs
? Value of life
? The mindset that,life is priceless”
presents obvious difficulties for cost-
benefit analysis.
? If the benefits of a saved life are infinite,
any project that leads to even a single life
saved has an infinitely high present value.
38
Valuing Public Benefits and Costs
? Economists use two methods to assign finite
values to human life:
– Lost earnings,Net present value of individual’s
after-tax earnings over lifetime.
? Taken literally,no loss for aged,infirm,or severely
handicapped
– Probability of death,Most projects affect probability
of death (e.g,cancer research),People are willing to
accept increases in the probability of death for a finite
amount of money.
39
Valuing Public Benefits and Costs
? Examples:
– Purchasing a more expensive,safer car with
a lower probability of death versus a less
expensive,less safe car.
– Occupational choice,Riskier jobs have
higher wages,all else equal
– Willingness to pay for safety devises like
smoke alarms.
40
Valuing Public Benefits and Costs
? Estimates suggest value of a life between
$4,000,000-$9,000,000
? Can contrast this versus the cost per life
saved:
– Emergency floor lights on airplanes cost
about $900,000 per life saved
– Asbestos removal rules cost $100,000,000
per life saved
41
Valuing Public Benefits and Costs
? Valuing intangibles
– National prestige,others
? Can be used to subvert entire cost-benefit
analysis
? Could use difference between costs and
benefits to make an argument on how large
intangibles would have to be to make the
project admissible
42
Cost-Benefit,Games”
? Chain-Reaction game
– Include secondary benefits to make a proposal
appear more favorable,without also including the
secondary costs
? Labor game
– Wages are viewed as benefits rather than costs of
the project
? Double counting game
– Benefits are erroneously counted twice
43
Distributional considerations
? The Hicks-Kaldor criterion bases project
selection on whether there is a potential Pareto
improvement
– May imposes costs on some if benefits on others are
larger
? Others view some groups in population as
“more deserving” and argue this should be
taken into account in project selection
44
Uncertainty
? The results of many projects are
uncertain (e.g.,AIDS vaccine research or
defense research).
? In risky projects,benefits or costs must
be converted into certainty equivalents
– the amount of certain income the
individual would trade for a set of
uncertain outcomes generated by project.
45
Uncertainty
? Requires information on distribution of
returns,and risk aversion.
? Figure 11.2 shows a risky project (E,E+y)
and a certain project (C) that given the
same expected utility.
Figure 11.2
47
Uncertainty
? Requires information on distribution of
returns,and risk aversion.
? Figure 11.2 shows a risky project (E,E+y)
and a certain project (C) that given the
same expected utility.
48
Recap of Cost-Benefit Analysis
? Present value
? Private Sector Project Evaluation
? Discount rate for government projects
? Valuing Public Benefits and Costs
? Cost-Benefit,Games”
? Distributional considerations
? Uncertainty
Chapter 11 – Cost-Benefit
Analysis
Public Economics
2
Introduction
? Cost-benefit analysis is a set of
practical procedures for guiding public
expenditure decisions.
3
Present Value
? Project evaluation usually requires
comparing costs and benefits from
different time periods
? Dollars across time periods are not
immediately comparable,because of
inflation and returns in the market.
4
Present Value:
Present Dollars into the Future
? Suppose you invest $100 today in the
bank
– At the end of year 1,it is worth (1+.05)x$100,
or $105
– At the end of year 2,it is worth (1+.05)x$105,
or $110.25
– The interest compounds over time,that is the
interest is also earning interest
5
Present Value:
Present Dollars into the Future
? Define
– R=initial investment amount
– r=rate of return on investment
– T=years of investment
? The future value (FV) of the investment is:
? ?FV R r T? ?1
6
Present Value:
Future Dollars into the Present
? Suppose someone promises to pay you
$100 one year from now.
? What is the maximum amount you should
be willing to pay today for such a promise?
? You are forgoing the interest that you
could earn on the money that is being
loaned.
7
Present Value:
Future Dollars into the Present
? The present value of a future amount of
money is the maximum amount you
would be willing to pay today for the right
to receive the money in the future.
8
Present Value:
Present Dollars into the Future
? Define
– R=amount to be received in future
– r=rate of return on investment
– T=years of investment
? The present value (PV) of the investment is:
? ?
PV
R
r
T?
?1
9
Present Value:
Future Dollars into the Present
? In previous equation,r is often referred to as the
discount rate,and (1+r)-T is the discount factor.
? Finally consider a promise to pay a stream of
money,$R0 today,$R1 one year from now,and
so on,for T years?
? ? ? ? ? ?PV R
R
r
R
r
R
r
T
T? ? ? ? ? ? ? ?0
1 2
21 1 1.,,
10
Present Value:
Future Dollars into the Present
? Present value is an enormously important
concept
? A $1,000,000 payment 20 years from
now is only worth today:
– $376,889 if r=.05
– $148,644 if r=.10
11
Present Value:
Inflation
? Nominal amounts are valued according
to the level of prices in the year the return
occurs.
? Real amounts are valued according to
the level of prices in one particular year.
? Inflation affects both the payout stream,
and the discount factor,and these two
cancel each other out.
12
Private Sector Project Evaluation
? Suppose there are two projects,X and Y
? Each entails certain benefits and costs,
denoted as BX,CX,BY,and CY.
? Need to ask:
– Is the project admissible?
– Is the project preferable?
13
Private Sector Project Evaluation
? Admissible,Are the benefits greater than
the costs?
? Preferable,Are the net benefits the
highest?
? Most projects involve a stream of benefits
and costs over time.
14
Private Sector Project Evaluation
? Define:
Bti ?
Cti ?
Benefits from project i at time t
Costs from project i at time t
? Then the present value of project i is:
? ? ? ?? ? ? ?
? ?
PV B C
B C
r
B C
r
i i i
i i
T
i
T
i
T? ? ?
?
?
? ?
?
?
0 0
1 1
1 1
.,,
15
Private Sector Project Evaluation
? The present value criteria for project
evaluation are that:
– A project is admissible only if its present
value is positive
– When two projects are mutually exclusive,
the preferred project is the one with the
highest present value.
16
Private Sector Project Evaluation
? Table 11.2 shows two different projects
(R&D or Advertising).
? The discount rate plays a key role in
deciding what project to choose,because
the cash inflows occur at different times.
? The lower the discount rate,the more
valuable the back-loaded project.
Table 11.2
18
Private Sector Project Evaluation
? Several other criteria are often used for
project evaluation,but can give
misleading answers
– Internal rate of return
– Benefit-cost ratio
19
Private Sector Project Evaluation
? The internal rate of return,ρ,is defined as the ρ
that solves the equation:
? ? ? ?? ? ? ?? ?0 1 10 0 1 1? ? ? ?? ? ? ??B C B C B CT TT? ?.,,
? The IRR is the discount rate that would make the
present value of the project equal to zero.
– Admissible if ρ>r
– The flawed analysis would choose an admissible project
with the higher internal rate of return,ignoring scale
20
Private Sector Project Evaluation
? The benefit-cost ratio divides the discounted
stream of benefits by the discounted stream of
costs,In this case
? B=stream of benefits and C=stream of costs:
? ? ? ?B B
B
r
B
r
T
T? ? ? ? ? ?0
1
1 1.,,
? ? ? ?C C
C
r
C
r
T
T? ? ? ? ? ?0
1
1 1.,,
21
Private Sector Project Evaluation
? Admissibility using the benefit-cost ratio requires:
B
C ?1
? This ratio is virtually useless for comparing
across admissible projects however.
? Ratio can be manipulated by counting benefits
as,negative costs” and vice-versa.
22
Discount rate for government
projects
? Government decision making involves
present value calculations
? Costs,benefits and discount rates are
somewhat different from private sector
23
Discount rate for government
projects
? Less consensus on appropriate discount rate in
public sector,One possibility are rates based
on returns in private sector.
– Assumes all of the money that is raised would have
been invested in a private sector project
– In reality,funding comes from a variety of sources –
investment and consumption
– Funding that come from consumption should be
discounted at the after-tax discount rate
– Hard in reality to determine what proportions of
funding come from consumption or investment
24
Discount rate for government
projects
? Another possibility is the social rate of
discount – which measures the valuation
society place on consumption that is sacrificed
in the present.
? Differs from market returns because it:
– Accounts for concern about future generations
– Involves paternalism
– May solve some market inefficiency such as positive
externalities
25
Discount rate for government
projects
? In reality,federal agencies are required to
use a real rate of return of 7%,on the
assumption that this measures the
before-tax rate of return in the private
sector.
? Some use 2% real return instead,thought
to measure the after-tax rate of return.
26
Discount rate for government
projects
? When a new tax or expenditure is
introduced,its effects over a 5-year or 10-
year period are analyzed to see whether
it will put the budget out of balance
– Ignores discounting
– Costs (or benefits) outside of the window are
not counted toward deficit (or surplus)
27
Valuing Public Benefits and Costs
? Recall that the discount rate,benefits,
and costs are needed to compute the
present value of a project
? For private company:
– Benefits = revenues received
– Costs = firm’s payments for inputs
28
Valuing Public Benefits and Costs
? For public sector,market prices may not reflect
social benefits and costs.
– Externalities,for example
? Several ways of measuring benefits and costs
– Market prices
– Adjusted market prices
– Consumer surplus
– Inferences from economic behavior
– Valuing intangibles
29
Valuing Public Benefits and Costs
? Market prices
– In a properly functioning competitive
economy,the price of a good simultaneously
reflects its marginal social cost of production
and its marginal value to consumers.
– Ignores market imperfections
– Easy to gather
30
Valuing Public Benefits and Costs
? Adjusted market prices
– If markets are imperfect,prices generally do
not reflect true marginal social cost
– Shadow price of a commodity is its true,
underlying marginal social cost,which can
sometimes be estimated
– Examples where insights can be gleaned
include monopoly price,taxes,and
unemployment
31
Valuing Public Benefits and Costs
? Consumer surplus
– Public sector projects can be large,and
change market prices
– Figure 11.1 measures the change in
consumer surplus from a government
irrigation project that lowers the cost of
agricultural production
Figure 11.1
33
Valuing Public Benefits and Costs
? In this figure,the change in consumer
surplus is area bcgd.
? Provided the government planner can
accurately measure the demand curve,
the project’s benefit can be measured
with this change.
34
Valuing Public Benefits and Costs
? Inferences from Economic Behavior
? Many times a good in question is not
explicitly traded,so no market price exists.
? Examples:
– Value of time
– Value of life
35
Valuing Public Benefits and Costs
? Value of time
? In cost-benefit analysis,need to estimate
the value of time to take advantage of
theory of leisure-income choice.
– After-tax wage is often used
– But hours of work not always a,choice,” and
not all uses of time away from job equivalent.
36
Valuing Public Benefits and Costs
? Researchers have examined value of
time by travel commuting choices.
– Trains are more expensive,but less time-
consuming,than buses,The same is true
about non-stop airline flights versus those
with a layover.
– Estimates are that value of time
approximately half of the before-tax wage.
37
Valuing Public Benefits and Costs
? Value of life
? The mindset that,life is priceless”
presents obvious difficulties for cost-
benefit analysis.
? If the benefits of a saved life are infinite,
any project that leads to even a single life
saved has an infinitely high present value.
38
Valuing Public Benefits and Costs
? Economists use two methods to assign finite
values to human life:
– Lost earnings,Net present value of individual’s
after-tax earnings over lifetime.
? Taken literally,no loss for aged,infirm,or severely
handicapped
– Probability of death,Most projects affect probability
of death (e.g,cancer research),People are willing to
accept increases in the probability of death for a finite
amount of money.
39
Valuing Public Benefits and Costs
? Examples:
– Purchasing a more expensive,safer car with
a lower probability of death versus a less
expensive,less safe car.
– Occupational choice,Riskier jobs have
higher wages,all else equal
– Willingness to pay for safety devises like
smoke alarms.
40
Valuing Public Benefits and Costs
? Estimates suggest value of a life between
$4,000,000-$9,000,000
? Can contrast this versus the cost per life
saved:
– Emergency floor lights on airplanes cost
about $900,000 per life saved
– Asbestos removal rules cost $100,000,000
per life saved
41
Valuing Public Benefits and Costs
? Valuing intangibles
– National prestige,others
? Can be used to subvert entire cost-benefit
analysis
? Could use difference between costs and
benefits to make an argument on how large
intangibles would have to be to make the
project admissible
42
Cost-Benefit,Games”
? Chain-Reaction game
– Include secondary benefits to make a proposal
appear more favorable,without also including the
secondary costs
? Labor game
– Wages are viewed as benefits rather than costs of
the project
? Double counting game
– Benefits are erroneously counted twice
43
Distributional considerations
? The Hicks-Kaldor criterion bases project
selection on whether there is a potential Pareto
improvement
– May imposes costs on some if benefits on others are
larger
? Others view some groups in population as
“more deserving” and argue this should be
taken into account in project selection
44
Uncertainty
? The results of many projects are
uncertain (e.g.,AIDS vaccine research or
defense research).
? In risky projects,benefits or costs must
be converted into certainty equivalents
– the amount of certain income the
individual would trade for a set of
uncertain outcomes generated by project.
45
Uncertainty
? Requires information on distribution of
returns,and risk aversion.
? Figure 11.2 shows a risky project (E,E+y)
and a certain project (C) that given the
same expected utility.
Figure 11.2
47
Uncertainty
? Requires information on distribution of
returns,and risk aversion.
? Figure 11.2 shows a risky project (E,E+y)
and a certain project (C) that given the
same expected utility.
48
Recap of Cost-Benefit Analysis
? Present value
? Private Sector Project Evaluation
? Discount rate for government projects
? Valuing Public Benefits and Costs
? Cost-Benefit,Games”
? Distributional considerations
? Uncertainty
