QUESTION $1$: $(10$ points$)$ MacPherson C$.,$ the owner of Cailin gold Mining, is evaluating a new gold mine in Quebec. Mohamed Ahmed, the company's geologist, has just finished his analysis of the mine site. He has estimated that the mine would be productive for eight years, after which the gold would be completely mined. Maria has taken an estimate of the gold deposits to Ogunkanmi Faith, the company's financial officer. Ogunkanmi has been asked by MacPherson to perform an analysis of the new mine and present her recommendation on whether the company should open the new mine.

Ogunkanmi has used the estimates provided by Mohamed Ahmed to determine the revenues that could be expected from the mine. She has also projected the expense of opening the mine and the annual operating expenses. If the company opens the mine, it will cost $\backslash (\backslash$$ $1\mathrm{.}2\backslash )$ billion today, and it will have a cash outflow of $\backslash (\backslash$$ $285\backslash )$ million nine years from today in costs associated with closing the mine and reclaiming the area surrounding it$.$ The expected cash flows each year from the mine are shown in the following table. Cailin gold Mining has a $12$ percent required return on all of its gold mines.

$1.$ Calculate the payback period, internal rate of return and net present value of the proposed mine.

$2.$ Based on your analysis, should the company open the mine? Show your work.