$($a$)$ You are considering constructing a new plant in a remote wilderness area to process the ore from a planned mining operation. You anticipate that the plant will take a year to build and cost $$102$ million upfront. Once built, it will generate cash flows of $$18$ million per year starting from the end of Year $2.$ At the end of Year $21,$ i$.$e$.,$ after its $20$th year of operation, the mine will run out of ore and you expect to pay $$258$ million to shut the plant down and restore the area to its pristine state. The required rate of return is $11\%.$

i$.(6$ points$)$ What is the NPV of the project?

ii$.(6$ points$)$ Is using the IRR rule reliable for this project? Explain.