The current pool facility loses $$40,000$ per year. A Feasibility Study has indicated the cost to be $$6\mathrm{.}6$ million with a $30-$year useful life. Operating & Maintenance costs are expected to be $$212,000,$ rising at $3\mathrm{.}2\%$ annually. Usage is expected to be between $80,000($pessimistic$)$ to $250,000($optimistic$)$ residents per year, with half of any estimate being children. The admission price is recommended to be $$6$ for an adult and $$4\mathrm{.}50$ for a child, increasing by $25\%$ every ten years. The $30-$year general obligation bond to be extended would have an interest rate of $3\mathrm{.}5\%.$

a$.$ Calculate both the pessimistic and the optimistic

$($a$)$ PBP$,($b$)$ DPBP$,($c$)$ NPV$,$ & $($d$)$ IRR.