Benefit-Cost Analysis

The city of Fargo lies in a floodplain along the Red River of the North. Fargo is considering an expensive project to divert the river around the city in the event of high water, similar to what the city of Grand Forks did after most of the town flooded in 1997. The expected benefits of the program depend on how likely it is that a flood would occur without the diversion, which in turn depends on precipitation (rain and snow) and the speed with which spring temperatures rise causing the snow to melt. Precipitation can be Low, Medium, High, Very High, or Extreme with respective probabilities pL=.3,pM=.36,pH=.3,pVH=.03,pE=.01. Temperature rise can be Slow, Medium or Fast with probabilities pS=.3,pM=.5,pF=.2. (1-15) What are the 15 possible outcomes, and what are the odds of each occurring? 2. Now, a 500-year flood will occur only if Extreme rainfall and Fast temperature change occur in the same year. (16) Why is this outcome called a 500-year flood, given your calculations? Damages are estimated by the North Dakota State Water Commission in that case at $6 billion. A 100-year flood results if Extreme rain meets Medium melt, or if VH rain meets Fast melt rate, resulting in an estimated $2 billion loss. A more typical flood, costing \$64 million each year, happens when Extreme rain meets slow melt, VH Rain meets medium melt, or High rain meets Fast melt. Local flooding occurs when VH and low melt happens, or H rain and Medium melt, or Medium rain but high melt occurs, resulting in a mere $1 million in damages. In all other cases, no flooding occurs. (17) What is the EV of flooding each year if the city does nothing? The city is considering building a diversion system, costing $909 million today; benefits will begin next year and last for at least 50 years. If it is built, no floods will occur. (18) If we ignore discounting and the DWL of taxation, should this diversion system be built? (19) That is, is the NPV of building the dam positive? (20) Would it be positive if we discounted the project at 3% ? The city of Fargo lies in a floodplain along the Red River of the North. Fargo is considering an expensive project to divert the river around the city in the event of high water, similar to what the city of Grand Forks did after most of the town flooded in 1997. The expected benefits of the program depend on how likely it is that a flood would occur without the diversion, which in turn depends on precipitation (rain and snow) and the speed with which spring temperatures rise causing the snow to melt. Precipitation can be Low, Medium, High, Very High, or Extreme with respective probabilities pL=.3,pM=.36,pH=.3,pVH=.03,pE=.01. Temperature rise can be Slow, Medium or Fast with probabilities pS=.3,pM=.5,pF=.2. (1-15) What are the 15 possible outcomes, and what are the odds of each occurring? 2. Now, a 500-year flood will occur only if Extreme rainfall and Fast temperature change occur in the same year. (16) Why is this outcome called a 500-year flood, given your calculations? Damages are estimated by the North Dakota State Water Commission in that case at $6 billion. A 100-year flood results if Extreme rain meets Medium melt, or if VH rain meets Fast melt rate, resulting in an estimated $2 billion loss. A more typical flood, costing \$64 million each year, happens when Extreme rain meets slow melt, VH Rain meets medium melt, or High rain meets Fast melt. Local flooding occurs when VH and low melt happens, or H rain and Medium melt, or Medium rain but high melt occurs, resulting in a mere $1 million in damages. In all other cases, no flooding occurs. (17) What is the EV of flooding each year if the city does nothing? The city is considering building a diversion system, costing $909 million today; benefits will begin next year and last for at least 50 years. If it is built, no floods will occur. (18) If we ignore discounting and the DWL of taxation, should this diversion system be built? (19) That is, is the NPV of building the dam positive? (20) Would it be positive if we discounted the project at 3%