You are the program manager for a large city water and sewer infrastructure system.

You manage over $3200$ miles of water and sewer lines as well as $6$ water and wastewater treatment facilities. You have over $1000$ valves that need to be replaced in the next year and an average of $200$ valves to replace every year after that for the next $12$ years.

$$ Material costs for valves have risen $28\%$ in the past $12$ months due to steel prices, manufacturing costs, and tariffs.

$$ Over the previous decade $($not counting the last $12$ months$),$ material costs have risen at an average of $1\mathrm{.}75\%$ per year.

$$ Labor increases at an average rate of $3\%$ per year.

$2\%$ of all valves that exceed their replacement interval fail and create an emergency repair that costs $20$ times as much as a typical replacement.

$1.$ If a valve costs $$2,450$ today, and the current replacement cost of labor is $$4,355$ each, how much is the labor and material budget for the coming year?

$2.$ If a valve costs $$2,450$ today, and the current replacement cost of labor is $$4,355$ each, then assuming the average material and labor escalation $(1\mathrm{.}75\%$ and $3\%$ respectively$)$ remains consistent, what is the budgeted cost for the $200$ valve replacements in $4$ years?

$3.$ Let's say a valve costs $$2,450$ today, and the current replacement cost of labor is $$4,355$ each. If in year $4,$ no valves are replaced, what is the expected cost in emergency repairs?