uestion # 1: A dam is being considered on a river that periodically overflows. E
ID: 3319069 • Letter: U
Question
uestion # 1: A dam is being considered on a river that periodically overflows. Each time the river overflows, it causes about $600,000 in damages. The project horizon is about 40 years. A 10% interest rate is being used. Three different designs are available, each with different costs and storage capacity (see table 1.1). The U.S. weather service has provided a statistical analysis of annual rainfall in the area draining into the river (See table 1.2) Table 1.1: Design Options Design Alternative Cost () Maximum Storage Capacity (unit 500,000 625,000 900,000 1.5 2.0 Table 1.2: Annual rainfall and probability Units annual rainfa 0 0.1 to 0.!5 0.6 to 1.0O 1.1 to 1.5 1.6 to 2.0 2.0 or more Probabilit 0.10 0.60 0.15 0.10 0.04 0.01 Assume that the dam requires no annual maintenance, has zero salvage value at the end of its 40-yeat life, and it is essentially empty at the start of each annual rainfall season. Which design alternative would you choose?Explanation / Answer
The chosen alternative should have the lowest total annual cost among the three. The total cost will include both the annual cost of the dam and the cost of the damage.
Alternative A: Total cost = 500,000 * (A/P,10%,40) + 600000 (0.10 + 0.04 + 0.01)
= 500000 * 0.1023 + 600000 * 0.15 = $141,129.71
Alternative B: Total cost = 625000 * (A/P,10%,40) + 600000 (0.04 + 0.01)
= 625000 * 0.1023 + 600000 * 0.05 = $93,912.13
Alternative C: Total Cost = 900000 * (A/P,10%,40) + 600000 ( 0.01)
= $98,033.47
Thus, Alternative B must be chosen as it has the lowest cost of the 3.
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