A power company can develop a hydroelectric project at one of two capacity

levels, $1$ MW or $2$ MW $,$ at the cost of $$1$ billion, or $$1\mathrm{.}75$ billion, respectively.

Construction in either case takes $1$ year's time, with the cost being incurred

immediately. If the smaller capacity is chosen, it is not possible to increase

capacity at a later date. The company can sell the capacity from $1$ MW on

a contractual basis for a net revenue of $$200$ million per year $($in perpetuity$)$

with payments beginning in $2$ years' time $($i$.$e$.,1$ year after the construc$-$

tion period$).$ No customer will currently purchase the second megawatt of

capacity, but a second party $($e$.$g$.,$ another state or country$)$ will contract to

purchase the second megawatt of power for $$300$ million per year in perpe$-$

tuity beginning $10$ years from now $($with the first payment at the end of that

year$).$

$($a$)$ Find the NPV of building for each capacity level if the interest rate is

$5\%.$ Should the power company invest in $0,1,$ or $2$ MW of capacity?