Dr$.$ Ron Patterson, the owner of Chadron Gold Mining, is evaluating a new gold mine in Colorado. Dr$.$ Tawny Tibbits, the company's geologist, has just finished

her analysis of the mine site. She has estimated that the mine would be productive for eight years, after which the gold would be completely mined. Tawny has

taken an estimate of the gold deposits to Dr$.$ Pil Joon Kim, the company's financial officer. Pil Joon has been asked by Ron to perform an analysis of the new

mine and present his recommendation on whether the company should open the new mine.

Pil Joon has used the estimates provided by Tawny to determine the revenues that could be expected from the mine. He has also projected the expense of

opening the mine and the annual operating expenses. If the company opens the mine, it will cost $$650$ million today, and it will have a cash outflow $$72$ 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 table above. Chadron Gold Mining has a $12$ percent required return on all of its gold mines.

Questions:

Show the detailed calculation process and results for the payback method, internal rate of return, modified internal rate of return and net present value of

the proposed mine.

Based on your analysis, should the company open the mine? Please explain in detail.