Highway 51 west of Stillwater is to undergo a major renovation due to growth patterns of the city and increased traffic due to university sporting events. The road used to be two lanes and has a 40-year-old two-lane steel bridge on the south side. When the highway was expanded to four lanes 30 years ago, a two-lane concrete bridge was used on the newer two lanes. It is still very functional and will be kept. Now the city must decide whether or not to replace the steel bridge with a modern concrete bridge. A new concrete bridge will cost \(\$ 300,000\), installed. It will require \(\$ 2,500\) maintenance per year, with \(\$ 30,000\) resurfacing every 15 years. The concrete bridge will last 60 years with salvage value decreasing linearly to \(\$ 0\) at that time. The existing steel bridge cost \(\$ 150,000\) when it was new, installed. If kept, it is good for another 20 years provided that some beams are replaced immediately due to rust at a cost of \(\$ 115,000\). Maintenance will cost \(\$ 12,000\) per year. It will require resurfacing now, and again in 10 years, at a cost of \(\$ 30,000\) each time. It has no salvage value now, nor will it in 20 years. The city has successfully set aside sufficient money, and even though the money came from the state, \(i=7\) percent. The benefits perceived by the public will be the same, regardless of which bridge is selected. Planning horizons used by the city are usually 20 years for roads. A concerned citizen presented the following analysis at a recent city council meeting:

Retain steel bridge:

Yearly cost of bridge \(\$ 150,000 / 40=\$ 2,500\)

Maintenance \(\$ 12,000+\$ 30,000 / 10+2(\$ 30,000) / 20=\$ 18,000\)

Total cost \(=\$ 20,500 /\) year Replace with concrete bridge:

Yearly cost of bridge \(\$ 300,000 / 60=\$ 5,000\)

Maintenance \(\$ 2,500+3(\$ 30,000) / 45=\$ 4,500\)

Total cost \(=\$ 9,500 /\) year

a. Critique the citizen's analysis listing any deficiencies you notice.

b. Prepare your own analysis using an annual cost comparison.