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Water Resources Planning and Management Daene C. McKinney Cost-Benefit Analysis

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Water Resources Development Need for water is becoming more acute Governments & investors –Develop water resources –Expenditures are large Choices among alternative should –Be efficient –Meet needs of stakeholders –Spend money wisely O. Eckstein, Water Resources Development, Harvard University Press, 1958

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Benefit – Cost Analysis Goals –Ensure that projects use capital efficiently –Provide a framework for comparing alternative projects –Estimate the impacts of regulatory changes Basic principle –Project benefits must exceed costs

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Comparing Time Streams of Benefits and Costs Alternative plans, p, may involve different benefits and costs over time. Plans need to be compared Define: Net Benefit generated in time t by plan p B p (t) Plan p is characterized by the time stream of net benefits it generates over its planning horizon T p {B p (1), B p (2), B p (3),..., B p (Tp)} If benefits exceed costs, B p (t) > 0

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Benefits and Costs Express in similar units (e.g., $’s) Compare for each alternative Viewpoint is important –Some groups will view some things as benefits, others as costs; other groups may differ. Compare differences between alternatives Do not consider effects not attributable to alternatives Opportunity cost –Net benefits forgone in the choice of one expenditure over others

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Costs of Alternatives Direct costs of each alternative –Capital costs Acquisition of land and materials, construction costs Opportunity costs (what you COULD have made…) –Operation, maintenance, and replacement costs Indirect costs of each alternative –Costs imposed on society or the environment Valuation techniques –Market value Capital costs and O&M costs Benefits from revenues from future deliveries of water –No market value? Then what? Value = cost of cheapest alternative Value can be estimated in other ways

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Imagine you take $100 to the bank and put it into a savings account that has an “annual” rate of 5%. What would it be worth at the end of 1 year.would be worth: Interest Rate Formulas

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$P invested for T years at an annual interest rate of i% is worth $F T in the future: $F available T years in the future is worth $P today at an annual interest rate of i% Interest Rate Formulas

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Uniform payments F t at the end of every year t for t=1,2,…,T years in the future is worth (in the present) Interest Rate Formulas P 0 T Time t at an annual interest rate of i% F1F1 F2F2 FtFt FTFT F T-1

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Interest Rate Formulas P A P = present value F = Future payment A = annual series AAAAA … 0 T Time t

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Home Mortgage Payments Monthly fixed-rate mortgage payments, M where L = total amount of the mortgage (Loan) i = monthly interest rate = annual percentage rate/12 n = number of months of the loan Example $250, year mortgage with 6.5% annual rate

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Cash Flow Diagrams Time, t Benefits OM&R costs, OMC t Capital cost C 0 Benefits, B t Costs

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Benefits OM&R costs, OMC t Time, t Benefits, B t Costs Cash Flow Diagrams PW B Capital cost C 0

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Cash Flow Diagrams Benefits Time, t Costs PW B Annual Benefits, B t Total annual cost, C t T C0C0

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Example: Pumping Plant AlternativeInitial costAnnual O&M cost Salvage value Life (yrs) A$525k$26k050 B$312k$48k$50k Time (yrs) 25 A B $525k (one time) $26k (every year) 050 Time (yrs) 25 A

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050 Time (yrs) 25 A B Example: Pumping Plant AlternativeInitial costAnnual O&M cost Salvage value Life (yrs) A$525k$26k050 B$312k$48k$50k25 $312k $50k $48k (every year) 050 Time (yrs) 25 B

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Example : Pumping Plant $525k $312k $50k $26k $48k 050 Time (yrs) 25 A B Annual cost of alternative A

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Example : Pumping Plant $525k $312k $50k $26k $48k 050 Time (yrs) 25 A B Annual cost of alternative B

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Example : Pumping Plant $525k $312k $50k $26k $48k 050 Time (yrs) 25 A B Annual cost of each alternative

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Discount Rate Time value of capital used when comparing alternatives US federal practice (Water Resources Development Act, 1974) “Average rate of interest on government bonds with terms of 15 years or more”

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Incremental Benefit - Cost Method 1.For each alternative –Define consequences –Estimate value of consequences –Calculate B/C ratios, Discard any with B/C < 1 2.Order alternatives: Lowest to highest cost 3.Select lowest cost alternative as “Current Best” –Next higher cost alternative is “Contender” 4.Compare “Best” to “Contender” –Compute B/ C, If B/ C > 1, Contender becomes Best 5.Repeat Step 4 for all alternatives 6.Final “Current Best” is “Preferred Alternative”

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Example Project with the highest benefit-cost ratio may not always be the preferred alternative. Consider a project with benefits of 3 units and costs of 1 unit Suppose you can invest another 4 units to increase benefits to 10 units.

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Example Project with the highest benefit-cost ratio may not always be the preferred alternative. Consider a project with benefits of 3 units and costs of 1 unit Suppose you can invest another 4 units to increase benefits to 10 units.

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Example Four projects identified for recreational facilities at a Lower Colorado River Authority facility Inspection of the benefit-cost ratios might lead one to select Alternative B because the ratio is a maximum This choice is not correct. Correct alternative selected by incremental benefit-cost method where the additional increment of investment is desirable if the incremental benefit realized exceeds the incremental outlay.

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Example (Cont.) The alternatives must be arranged in order of increasing outlay. Thus, the alternative with the lowest initial cost should be first, the alternative with the next lowest initial cost second, and so forth.

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Example Four projects identified for recreational facilities at a Lower Colorado River Authority facility Inspection of the benefit-cost ratios might lead one to select Alternative B because the ratio is a maximum This choice is not correct. Correct alternative selected by incremental benefit-cost method where the additional increment of investment is desirable if the incremental benefit realized exceeds the incremental outlay.

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Example (Cont.) The alternatives must be arranged in order of increasing outlay. Thus, the alternative with the lowest initial cost should be first, the alternative with the next lowest initial cost second, and so forth.

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Example Flood control alternatives –Dam A, –Dam B, and –Levees C Alternatives –A, B, C, AB, AC, BC, ABC Lives –Dams = 80 years, –Levee = 60 years Discount rate –i = 4 % per year Choose an alternative ABC

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Example ABC ProjectInitial Cost (mln.$) O&M Cost (thous.$) Damage (mln.$) Do nothing A B C AB AC BC ABC

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Example ProjectTotal Investment ($ mln) CRFAnnual Investment Costs ($ mln) Annual Operation and Maintainance ($ mln) Total Annual Cost ($ mln) A B C AB AC BC ABC ABC

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Example CompareProjectBenefit (mln$) Cost (mln $) B/C B (mln $) C (mln $) B/CB/C Decision B B B > B A A A > B A C C C > A C AB AB C > AB C BC BC C > BC C AC AC C > AC C ABC ABC C > ABC ABC e.g., A > B means alternative A is preferred over alt. B

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