$(50\%)$ UBC Bioenergy Research and Demonstration Facility $($BRDF$)$ is a biomass$-$gasification district heating system, which generates $200,000$ GJ heat $($both steam and hot water$)$ annually to meet $15\%$ of campus heating demand. The facility was built in $2012,$ with a total capital investment of $$19\mathrm{.}2$ million. UBC sources biomass residues with a higher heating value $($HHV$)$ of $18G\frac{J}{?}$ tonne from Gloverdale Fuels at a delivered cost of $$\frac{69}{?}$ tonne. The UBC old boiler house burns natural gas for campus heating. Delivered cost of natural gas is $$\frac{7\mathrm{.}72}{G}J,BC$ carbon tax is currently at $$\frac{50}{?}$ tonne $CO2-$eq$.,$ and a carbon offset fee of $$\frac{1\mathrm{.}25}{G}J$ for fossil fuel use is also imposed to all BC public institutions. Natural gas HHV is $52$ GJ$/$tonne$,$ and GHG emission factor from combustion is $50kgCO2-e\frac{q}{G}J.$

For a $20$ year lifespan of the new BRDF facility and a government subsidy of $50\%$ capital cost, what would have been the net present value of the BRDF facility in $2012?$

The annual interest rate is taken as $5\%,$ compounded annually. Since UBC natural gas boiler house is already in place, the capital cost for natural gas heating is considered as zero. The operating costs and the thermal efficiencies for biomass and natural gas operations are assumed to be the same, with the thermal efficiencies at $85\%.$ The upstream greenhouse gas emissions associated with biomass residues and natural gas processing are out of the system boundary of this current analysis and are excluded.

Additional information which may be needed:

$FV=PV(1+i{)}^n,PV=\frac{O{C}^{**}[(1+i{)}^n-1]}{(i)(1+i{)}^n}$

FV $-$ future value; PV $-$ present value; $OC-$ operating cost; i interest for each compounding period; $n-$ number of compounded periods. no of years $20,$ carbon offset fess not included