$[8$ points$]$ In $2016,$ the City of Los Angeles was considering installing a large solar array on the roof of the Los Angeles

Convention Center as part of Mayor Garcetti's "Sustainable City pLAn." As initially proposed, construction would

take place in $2016$ and impose costs of $$3,200,000$ for the solar array hardware and $$650,000$ for installation. Given an

expected functional lifespan of $25$ years, the array would then operate from $2017$ through $2041,$ during which time it

would require routine maintenance at an annual cost of $$4,000.$ The solar array's inverter, a critical component, must

also be replaced every ten years $($in $2026$ and $2036)$ at a cost of $$18,000.$

Once operational, the solar array is expected to produce $1\mathrm{.}5$ million $kWh($kilowatt$-$hours$)$ of energy per year. Two sorts

of benefits result from this production: one is the cost saving from reduced production via alternative methods, and the

other is the reduction in greenhouse gas emissions. Any energy produced by the solar array will avoid the production

and purchase of the same amount from an alternative source, which would otherwise cost $$0\mathrm{.}21$ per $kWh.($In order to

calculate the total annual benefit of reduced alternative production, we simply multiply the annual number of kWh

produced by the avoided cost per $kWh.)$ Additionally, switching to solar panels will reduce carbon dioxide emission by

$0\mathrm{.}000311$ tons per $kWh$ relative to the alternative sources that would otherwise be used to generate this electricity. Each

ton of avoided carbon dioxide emissions, in turn, is valued at the social cost of $$46$ specified in Environmental Protection

Agency guidelines. ${?}^2($In order to calculate the total annual benefit of reduced emissions, we first multiply the annual

number of $kWh$ produced by the tons of $C{O}_2$ per $kw{H}_L,$ and then multiply the result by the social cost of one ton of $C{O}_2.)$

All dollar amounts have been expressed in real $2016$ dollars, so there is no need to adjust them for inflation.

Using a discount rate of $3\%,$ calculate the net present value of this solar array project.