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Page 7 of 7 Problem7: A small dam is being planned for a river tributary...

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Page 7 of 7 Problem7: A small dam is being planned for a river tributary that is subject to frequent flooding. From past experience, the probabilities that water flow will exceed the design capacity of the dam during a year, plus relevant cost information, are as follows: Estimated Annual Dam DesignFlow During a Year Damages if Water (Independent forDesign Capacity Probability of Greater Flow During a Year i Dam Design( Flows Exceed Capital Investment (S) different years) 0.055 0.045 0.035 0.04 0.02 2,300,000 2,000,000 1.800,000 1300,000 1,750,000 1,650,000 2,200,000 2,500,000 2,800,000 950,000 The life of the dam is expected to be 48 years, with negligible salvage value. The capital will cost 8% per year compounded semi-annually. Determine which design should be implemented. (Hint: Calculate the expected total annual costs throughout the 50-year period, including the annual worth of the capital investment)

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