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# week10 - XV A Role of Cost Benefit Analysis COST BENEFIT...

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1 XV. COST BENEFIT ANALYSIS A. Role of Cost Benefit Analysis 1. Decide if a project is worth pursuing (admissibility). 2. Compare and rank alternative projects. 3. Helps policy makers choose program with highest net benefit. B. Comparing costs and benefits that occur over time. 1. Most costs and benefits are not incurred at once, but are spread out over many years. a. U.S. Navy submarines: takes 12 years from design start to commissioning to build a submarine (actual construction is about 5 years). The ship remains in service for 30 years. b. Upgrade educational attainment of disadvantaged minorities: takes 12 to 18 years to complete school, and its benefits – both private and public – occur over lifetime. c. Safe Drinking Water Act regulations: big capital costs upfront for many water systems; provides public health benefits for 30 years (or more). 2. Time value of money. a. A dollar earned in future is worth less than a dollar earned today. b. If invest \$100 for 1 year at 5 percent, receive (\$100)*1.05=\$105 in 1 year. c. If you are promised to be paid \$100 in one year, would be willing to pay \$95.24 today (\$100/1.05). d. The present value of \$1 next year = \$1/(1+r), where r is the discount rate.

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2 e. The present value of \$1in two years = \$1/(1+r)2. (Interest is compounded for 2 years.) f. In general, present value of \$1 in t years = \$1/(1+r)t. g. Present value of stream of payments of p that occur over n years is: ( 29 p r t t n 1 0 + = C. Compare two projects. Assume discount rate (r) is equal to 5 percent. Year Cost Project 1 Project 2 Benefit Net Benefit Discount factor Net Present Value Benefit Net Benefit Discount factor Net Present Value 0 100 100 0 1.000 0 0 -100 1.00 -100 1 0 100 100 0.952 95 0 0 0.95 0 2 0 100 100 0.907 91 0 0 0.91 0 3 0 100 100 0.864 86 0 0 0.86 0 4 0 100 100 0.823 82 500 500 0.82 411 Total
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week10 - XV A Role of Cost Benefit Analysis COST BENEFIT...

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