i$.$ A consulting engineering firm is preparing a preliminary cost estimate for a $50-$MW advanced combined cycle natural gas$-$fired power plant. The firm, which completed a similar project in $2015$ with a total cost $($construction and equipment$)$ of $$810$ million, wants to use a construction cost index to update the construction cost. If the construction cost was assumed to be $25\%$ of the total cost and the index value in $2012$ was $8750,$ estimate the cost of construction for a similar$-$size plant in $2024$ when the index is $9234.(4$ marks$)$

ii$.$ If the powerplant stated is a government asset with annual benefits of $12$ million, is it economically justifiable over a $15$ year period? Discount rate is $8\%$ per year