Cost Benefit Analysis

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Cost Benefit Analysis and Discounting
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Cost Benefit Analysis What is it? Good
overviews of CBA Paul Portney Matthew
Kotchen. Portney it is an attempt to
identify and express in dollar terms all of the
effects of proposed government policies or
projects It is a useful tool to assess the
social welfare impacts of a project or
policy. Many economists favor using it when
assessing a project though it still raises
concerns in many quarters and can be difficult to
get right.

• See Paul R. Portney, "Benefit-Cost
  Analysis." The Concise Encyclopedia of
  Economics. 2008. Library of Economics and
  Liberty. 4 September 2013. lthttp//www.econlib.org
  /library/Enc/BenefitCostAnalysis.htmlgt.
• Kotchen, Matthew J., Cost Benefit Analysis,
  Encyclopedia of Climate and Weather 2nd Edition,
  Stephen Schneider
• (ed.), New York Oxford University Press, 2010.
  lthttp//environment.yale.edu/kotchen/pubs/CBAchap.
  pdfgt.

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Cost Benefit Analysis How do we do it? Add up
costs and add up benefits if net benefits are
positive do the project! Simple, right? Not
quite! Issue of measurement of costs and
benefits. Often times, costs simpler tend to
be one-off and are market transactions e.g. one
time cost of constructing a dam Benefits can be
trickier e.g. what is the value of cleaner air
after an emissions standard policy is
implemented?
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Cost Benefit Analysis How do we do
it? Methodological points Need to turn to
non-market valuation techniques (travel cost
method, contingent valuation). Need to be
cognizant of timing of costs and benefits costs
and benefits can be out in the future.
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Cost Benefit Analysis Debatable Issues 1.
Discount rate the value of future events 2.
Distribution of income wealth may affect
willingness to pay for a benefit 3. Compensation
(Kaldor-Hicks criterion) always winners and
losers but will losers be compensated?
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Discounting What is it? Many times we want to
assess value of events in the future e.g. costs
and benefits that occur in the future. Projects
span time activities occur over many
months/years. How do we think about activities
that have value but occur at times other than the
present? Idea reduce all future values to a
common present value.
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Discounting What is it? We need to convert
future values into a present value. To do this
we discount the future back to the present. Why?
Because money today is worth more than money
tomorrow. The discount rate is a product of
societys time value of money (composed of the
pure rate of time preference and the goods
discount rate).
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Discounting How do we do it? Use this formula
to convert all future values to present
values PV FVt/(1 r)t Where PV is present
value, FV is future value, r is the discount rate
and t is time.
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• Discounting How do we do it?
• Lets use that formula.
• What is the value of a 100 tomorrow (one period
  in the future)?
• Assume discount rate, r, is set to 0.05
• Then,
• PV FVt/(1 r)t
• PV 100/(1 0.05)1
• PV 95.2381

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Discounting How do we do it? By the way
opposite of discounting is compounding If we
have a present value and wish to see what the
future value is, we use compounding FVt PV(1
r)t
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Discounting The Debate! Choice of discount
rate is at the heart of CBA controversies It is
a key issue as it determines whether a project is
beneficial or not, whether a project should be
implemented or not Two major schools of
thought Descriptive We observe the rate of
return in the market (e.g. Nordhaus) Prescriptive
We derive the discount rate based on
philosophical/ethical basis (e.g. Stern)
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Discounting The Debate! Regardless of how it is
derived, the important thing is how high it is
set. High discount rate we dont value the
future as much as the present Low discount rate
we value the future almost as much as the
present
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Case Study Irrigation as an Adaptation to
Climate Change Climate change affects
temperature and precipitation among other climate
phenomena Changes in the hydrological cycle will
be some of the most obvious changes that will
affect agriculture Irrigation systems are a way
to adapt to changes in the hydrologic cycle
(especially changes in the quantity and timing of
precipitation)
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The prices of staple foods are at near historic
lows, and stockpiles are adequate. This is a
situation that would be inconceivable without the
last half-century's investments in
irrigation. Irrigation is the largest
recipient of public agricultural investment in
the developing world. (World Bank (1995))
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Senegal Irrigation Project Nianga Irrigation
Pilot Project (NIPP). Life-span of about 30
years. One of the analyses of this project
provided a very clear schedule of costs and
benefits. Measured in thousands of 1975 CFA
Francs (Senegalese currency) Weiler, Edward
M. and Wallace E. Tyner (1981). Social
Cost-Benefit Analysis of the Nianga Irrigation
Pilot Project, Senegal. The Journal of Developing
Areas , Vol. 15, No. 4 (Jul., 1981), pp. 655-670.
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Note were only considering agricultural output
as a benefit and no others. However a whole slew
of other benefits (unmeasured in this project) do
exist.(1) agricultural production (2)
production of rice seed (3) increased knowledge
of the agronomy of irrigated agriculture in the
Fleuve Region (4) improved technical skills of
both the farmers who participate in the Pilot
Project and those who receive training from the
B.I.T. Center and (5) shelter provided by the 17
houses at Cite SAED
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Should we go ahead with this project? We need to
determine if the total benefits exceed the total
costs If benefits gt costs then the project is
worth doing As discussed, we will discount all
future costs and benefits to their present
value
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Results
Year Period Total Agricultural Benefits Total Cost Benefits without Project Net Benefits Discount Rate PV(TB) 5 PV(TC) 5 BC Ratio
1973 0 0.0 31,320.7 7,248.0 -38,568.7 0.05 0.0 31320.7 .
1974 1 0.0 354,174.0 7,248.0 -361,422.0 0.05 0.0 337308.571 .
1975 2 43,781.3 512,089.9 7,248.0 -475,556.6 0.05 39710.9 464480.635 .
1976 3 157,552.7 124,573.8 7,248.0 25,730.9 0.05 136099.9 107611.532 .
1977 4 164,809.6 144,853.9 7,248.0 12,707.7 0.05 135589.3 119171.662 .
. .
1998 25 215,364.2 113,642.0 7,248.0 94,474.2 0.05 63597.6 33558.7976 .
1999 26 215,364.2 113,642.0 7,248.0 94,474.2 0.05 60569.2 31960.7596 .
2000 27 215,364.2 113,642.0 7,248.0 94,474.2 0.05 57684.9 30438.8187 .
2001 28 215,364.2 113,642.0 7,248.0 94,474.2 0.05 54938.0 28989.3511 .
2002 29 215,364.2 113,642.0 7,248.0 94,474.2 0.05 52321.9 27608.9058 .
Sum 2,746,329.56 2,490,685.93 1.10
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Graph over Time No Discounting and Discounting
B/C 1.10
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Agricultural Productivity and Climate
Change Benefits in NIPP are those of
agricultural output (rice and tomatoes) What if
future climate change reduces the possible
output? This will require careful study
farmers may adapt their crop and input choice to
a changed climate. For the moment, lets make
some simple assumptions 50 chance that climate
change induces a 25 decline in agricultural
revenues per year. 50 chance that climate
change induces a 25 increase in agricultural
revenues per year. This change comes about in
the 15th year of the project.
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Graph over Time High, Low and Expected Benefits
with Climate Damages
Climate Change Kicks In
Result E(B)/C 1.10264 But, BH/C 1.226883
BL/C 0.978396
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Scenario High Benefits with Climate Damages
Climate Change Kicks In
Result BH/C 1.35
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• Hands-on Exercise
• Let us conduct the above cost benefit analysis
• We have already seen the results but we can do a
  couple of new things
• Check the impact that the choice of discount rate
  has on our decision
• Check the impact of climate change based on when
  it begins to impact our project

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Hands-on Exercise Open Excel file titled CBA
and Discounting Exercise Base Case Discount
Rate Climate Damage (20 yrs) Climate Damage (15
yrs)