An industrial park is being planned for a tract of land near the river. To prevent flood damage to the industrial buildings that will be built on this low-lying land, an earthen embankment can be constructed. The height of the embankment will be determined by an economic analysis of the costs and benefits. The following data has been gathered: Embankment Height Above Roadway (m) 2.0 Initial Cost $100,000
Embankment Height Above Roadway (m) 2.5 Initial Cost $165,000
Embankment Height Above Roadway (m) 3.0 Initial Cost $300,000
Embankment Height Above Roadway (m) 3.5 Initial Cost $400,000
Embankment Height Above Roadway (m) 4.0 Initial Cost $550,000
Flood Level Above Roadway (m) 2.0 Average Frequency that Flood Level Will Exceed Height: Once in 3 years
Flood Level Above Roadway (m) 2.5 Average Frequency that Flood Level Will Exceed Height: Once in 8 years
Flood Level Above Roadway (m) 3.0 Average Frequency that Flood Level Will Exceed Height: Once in 25 years
Flood Level Above Roadway (m) 3.5 Average Frequency that Flood Level Will Exceed Height: Once in 50 years
Flood Level Above Roadway (m) 4.0 Average Frequency that Flood Level Will Exceed Height: Once in 100 years

The embankment can be expected to last 50 years and will require no maintenance. Whenever the flood water flows over the embankment, $300,000 of damage occurs.

a. Should the embankment be built?
b. If so, to which of the five heights above the roadway? A 12% rate of return is required.