General Instructions:

Write your first and last name on every page on the space provided.

Show all your solutions clearly.

Each problem contains $15$ points.

A major roadway project is proposed by a transport agency. Two alternatives are considered. Alternative $1$ has an initial cost of $$60$ million, the average annual maintenance cost of $$0\mathrm{.}30$ million, and the salvage value will be $$8$ million. Besides, alternative $1$ requires a major rehabilitation that requires $$0\mathrm{.}5$ million at the end of year $5.$ Alternative $2$ has an initial cost of $$45$ million, the average annual maintenance cost is $$0\mathrm{.}65$ million, and the salvage value will be $$7\mathrm{.}5$ million. For alternative $2,$ a major rehabilitation cost of $$0\mathrm{.}4$ million should be invested at the end of year $5.$ Both alternatives have a useful life of $10$ years. Which alternative should be selected? Use the Present Worth of Costs method. Assume a $5\%$ interest rate.

For problem $2,$ determine the equivalent uniform annual cost of each alternative.

A transportation agency is considering implementing one of the following safety improvement projects. Project A has an initial cost of $$160,000,$ an estimated life of $8$ years, an annual maintenance cost of $$10,000$ at the end of years $1,2,$ and $3,$ and an annual maintenance cost of $$8,000$ at years $6,7$ and $8.$ Also, project A requires a maintenance cost of $$15,000$ at the end of year $4$ and has a salvage value of $$25,000.$ Project B has an initial cost of $$170,000,$ an estimated life of $6$ years, an annual maintenance cost of $$15,000$ at the end years $1,2,$ and $3,$ and an annual maintenance cost of $$10,000$ at years $4,5$ and $6.$ Project $B$ has a salvage value of $$20,000.$ Find the equivalent uniform annual cost of each alternative and decide which safety improvement project should be selected. Assume a $6\%$ interest rate.