Problem $1($Break$-$even Analysis$)$

$25$ pts

A state highway department is planning the construction of a toll road. Construction cost will be $$300M($at period$=$year $0).$ Annual maintenance is estimated to be $$1M$ every year from year $1$ and in perpetuity $($forever$).$ In addition, a major resurfacing will have to be carried out at a cost of $$10M$ every $10$ years in perpetuity $($forever$).$

It is estimated that $5$ M vehicles will use the road in year $1$ and then the traffic will increase with a growth $g=2\%$ per year after year $1$ and in perpetuity $($forever$).$

$[$Geometric gradient: If $i>g$ and $n=,$ then $P=\frac{A_1}{i-g}].$

Each vehicle will pay a constant toll $$t.$

$(a-5pts)$ Show the $($indicative$)$ cash flow diagram for this project.

$($b $-20$ pts $)$ Use PW Analysis to determine what breakeven constant toll $$t$ should be charged to each vehicle to make sure benefits will be economically equivalent to costs. MARR $=10\frac{\%}{?}$ year.

Note: Excel can not be used for an infinite horizon

Problem $2$

$35$ pts

A wastewater treatment plant must be built to improve water quality on a stream. Two options are available: a secondary treatment plant removing $85\%$ of the pollution or a tertiary treatment plant removing $95\%$ of the pollution. Improved water quality is given a dollar value as shown in the table. Assume that, by law, the planning horizon $($analysis period$)$ is $20$ years. The MARR is $8\%.$ Determine the best plant to build using the method listed below.

$\backslash$table$[[,\backslash$table$[[$Secondary$],[($ $ million$)]],\backslash$table$[[$Tertiary$],[($ million$)]]],[$Initial cost$,20\mathrm{.}0,40\mathrm{.}0],[$Annual operating cost,$1\mathrm{.}0,2\mathrm{.}0],[$Annual benefit,$3\mathrm{.}5,7\mathrm{.}0],[$Lifetime $($years$),20,20]]$

$($a$)$ Form the cash flow table for the alternatives showing the correct sign for all entries.

$($b$)$ Solve using present worth analysis.

$($c$)$ Solve using annual cash flow analysis.

$($d$)$ Solve using incremental benefit$-$cost ratio analysis.

Hint: Initial Cost is@yr $0$; Annual transactions begin@yr $1$ and end @yr $20$