January 24th Benefit Cost Analysis-BoR Dam 7. Suppose the Bureau of Reclamation
ID: 1147327 • Letter: J
Question
January 24th Benefit Cost Analysis-BoR Dam 7. Suppose the Bureau of Reclamation wants to build a small dam which will flood one acre of land. The costs are as follows: . 1 worker@ $40,000 1 manager$10,000 40 tons concrete delivered @ $5,0001 Permit @$1,000 Buying land@ $20,000 for an acre . The benefits are as follows: Water available in summer, worth $2,000 per year to famers . Cooler water available in the summer for the river, which helps 10 salmon retun and survive in this river. Estimated value is $1,000 per year Assume that costs are incurred immediately and that benefits accrue at the end of the fint year and continue a. Assuming a 3% interest rate to discount the future, what are the net benefits of this project? f forever b. Assuming a 10% interest rate to discount the future, what are the net benefits of this project? why are the net benefits less when the discount rate increases? c. d. Suppose that there is a cheaper method of reducing temperature in the tiver which achieves the same salmon increase, and it actually costs nothing It is a separate technology available without a dam at all. The salmon benefit that is attributable to this dam is now s_ Based on the change in part d, using a 3% interest rate to discount the future, what are the correct net benefits to assign to this project now c.Explanation / Answer
Total (first) cost ($) = 40,000 + 10,000 + 5,000 + 1,000 + 20,000 = 76,000
Total annual benefit ($) = 2,000 + 1,000 = 3,000
Benefits are annual and occur in perpetuity, so Present value (PV) of benefits = $3,000 / Discount rate (r)
(a) r = 3%
Net benefit ($) = (3,000 / 0.03) - 76,000 = 100,000 - 76,000 = 24,000
(b) r = 10%
Net benefit ($) = (3,000 / 0.03) - 76,000 = 30,000 - 76,000 = - 46,000
(c) When discount rate increases, ($3,000 / Discount rate) decreases, therefore Net benefits (= ($3,000 / Discount rate) - First cost) decreases.
(d) In this case, First cost = 0 (Since alternative technology is free), and therefore, Annual benefit = $3,000
(e) New new benefit ($) = 3,000 / 0.03 = 100,000
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