Presentation Transcript

1. Cost-Benefit Analysis

   Water Resources Planning and Management Daene C. McKinney
2. 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
3. Benefit – Cost Analysis(Cost – Benefit 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 Def’n: Net Benefits = Benefits - Costs
4. Costs and Benefits Express in similar units (e.g., $’s) Compare for each alternative Viewpoint is important Some groups are concerned with benefits, others with costs Compare differences between alternatives Do not consider effects not attributable to alternatives Opportunity cost Opportunities (net benefits) forgone in the choice of one expenditure over others
5. 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
6. Interest Rate Formulas $100 invested for a year at an “annual” rate of 5% would be worth: What is “APR”? What is “compounding”? F P Time One year t 0
7. Credit Card Interest Rates nominal annual percentage rate (APR) compounded daily not the same as the effective annual rate (EAR) common credit card quoted at 12.99% APR compounded daily, the one-year EAR is
8. Interest Rate Formulas $P invested for Tyears at an annual interest rate of i% is worth $FT in the future: Or $F available T years in the future is worth $P today at an annual interest rate of i% F P Time t years t 0
9. Interest Rate Formulas Uniform payments Ftat the end of every year t for t=1,2,…,T years in the future is worth (in the present) Time t T 0 Ft P at an annual interest rate of i%
10. Interest Rate Formulas P = present value F = Future payment A = annual series A P
11. Interest Rate Formulas P = present value F = Future payment A = annual series A F
12. Home Mortgage Payments Monthly fixed-rate mortgage payments, P where L = total amount of the mortgage i = monthly interest rate-- annual percentage rate divided by 12 n = number of months of the loan Example $250,000 30-year mortgage with 6.5% annual rate (0.065/12= 0.005417 monthly rate)
13. 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”
14. Time (yrs) Time (yrs) 0 0 25 25 50 50 Example: Pumping Plant A $26k (every year) A $525k (one time) B
15. Time (yrs) Time (yrs) 0 0 25 25 50 50 Example: Pumping Plant $50k $50k A B $48k (every year) B $312k $312k
16. Time (yrs) 0 25 50 $26k A $50k $50k $525k $48k B $312k $312k Example: Pumping Plant Annual cost of alternative A
17. Time (yrs) 0 25 50 $26k A $50k $50k $525k $48k B $312k $312k Example: Pumping Plant Annual cost of alternative B
18. Time (yrs) 0 25 50 $26k A $50k $50k $525k $48k B $312k $312k Example: Pumping Plant Annual cost of each alternative
19. Benefits, Bt Benefits Time, t OM&R costs, OMCt Capital cost C0 Costs Cash Flow Diagrams
20. PWB Cash Flow Diagrams Benefits Benefits, Bt Time, t OM&R costs, OMCt Capital cost C0 Costs
21. PWB Annual Benefits, Bt Cash Flow Diagrams Benefits Time, t T Total annual cost, Ct C0 Costs
22. 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” http://www.economics.nrcs.usda.gov/cost/priceindexes/index.html
23. A B C 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
24. A B C Example
25. A B C Example
26. A B C Example e.g., A > B means alternative A is preferred over alt. B
27. Example Project with the highest benefit-cost ratio may not always be the preferred alternative. Consider a project whose benefits equal 3 units and whose costs equal 1 unit and which has an increment of investing an additional 4 units to increate benefits to 10 units.
28. 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.
29. 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.