A large mudslide caused by heavy rains will cost Sabino County $1,000,000 per occurrence in lost property tax revenues. In any given year, there is one chance in 100 that a major mudslide will occur.
A civil engineer has proposed constructing a culvert on a mountain where mudslides are likely. This culvert will reduce the likelihood of a mudslide to near zero. The investment cost would be $50,000, and annual maintenance expenses would be $2,000 in the first year, increasing by 5% per year thereafter. If the life of the culvert is expected to be 20 years and the cost of capital to Sabino County is 7% per year, should the-culvert be built?