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# Cost-Benefit Analysis

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

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

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

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 Bp(t) Plan p is characterized by the time stream of net benefits it generates over its planning horizon Tp {Bp(1), Bp(2), Bp(3), ... , Bp(Tp)} If benefits exceed costs, Bp(t) > 0

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

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

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

Interest Rate Formulas
Uniform payments Ft at the end of every year t for t=1,2,…,T years in the future is worth (in the present) T Time t P F2 FT-1 F1 Ft FT at an annual interest rate of i%

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

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

Cash Flow Diagrams Benefits, Bt OM&R costs, OMCt Capital cost C0
Time, t Benefits OM&R costs, OMCt Capital cost C0 Benefits, Bt Costs

Cash Flow Diagrams Capital cost C0 Benefits Benefits, Bt PWB Time, t
OM&R costs, OMCt Capital cost C0 Costs

Cash Flow Diagrams C0 Benefits PWB Annual Benefits, Bt Time, t T
Total annual cost, Ct T C0 Costs

Example: Pumping Plant
Alternative Initial cost Annual O&M cost Salvage value Life (yrs) A \$525k \$26k 50 B \$312k \$48k \$50k 25 50 Time (yrs) 25 A B \$525k (one time) \$26k (every year)

Example: Pumping Plant
Alternative Initial cost Annual O&M cost Salvage value Life (yrs) A \$525k \$26k 50 B \$312k \$48k \$50k 25 50 Time (yrs) 25 A B 50 Time (yrs) 25 \$50k \$50k B \$48k (every year) \$312k \$312k

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

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

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

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”

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

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.

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.

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.

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.

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.

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.

Example Flood control alternatives Alternatives Lives Discount rate
B C 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

Example Project Initial Cost (mln.\$) O&M Cost (thous.\$) Damage (mln.\$)
B C Project Initial Cost (mln.\$) O&M Cost (thous.\$) Damage (mln.\$) Do nothing 2.00 A 6 90 1.10 B 5 80 1.30 C 100 0.70 AB 11 170 0.90 AC 10 190 0.40 BC 9 180 0.50 ABC 15 270 0.25

Example A B C Project Total Investment (\$ mln) CRF Annual Investment Costs (\$ mln) Annual Operation and Maintainance (\$ mln) Total Annual Cost (\$ mln) A 6 0.251 0.090 0.341 B 5 0.209 0.080 0.289 C 0.265 0.100 0.365 AB 11 0.460 0.170 0.630 AC 10 0.516 0.190 0.706 BC 9 0.474 0.180 0.654 ABC 15 0.725 0.270 0.995

Example e.g., A > B means alternative A is preferred over alt. B
C Compare Project Benefit (mln\$) Cost (mln \$) B/C DB DC DB/DC Decision   B B 0.7 0.289 2.42 2.4 B >  B  A A 0.9 0.341 2.64 0.2 0.052 3.8 A > B A  C C 1.3 0.365 3.56 0.4 0.024 17 C > A C  AB AB 1.1 0.63 1.75 -0.2 0.265 -0.75 C > AB C  BC BC 1.5 0.654 2.29 0.69 C > BC C  AC AC 1.6 0.706 2.27 0.3 0.88 C > AC C  ABC ABC 0.995 1.76 0.45 0.71 C > ABC e.g., A > B means alternative A is preferred over alt. B

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