Per this old report (http://www.stocksontheweb.com/mmgg.pdf), the cost would be around $200-250 million. The exact amount will be determined by the in-process feasibility study.
They plan on using the feasibility study to get bank debt financing for the building of the mine. They're using the same team that conducted the feasibility study for the Skorpion mine in Africa, the lowest cost zinc producer in the industry. That team produced a bankable feasibility study to finance that mine and also executed it to get Skorpion into production.
I also created a MMGG valuation spreadsheet by taking the stock valuation methodology from that old stocksontheweb report (linked at top) and updating the numbers to current figures. I also added an alternative valuation model which takes the present value of the assumed after-tax cash flow from the zinc mine. They point to a current fair value of $7-15/share (for the zinc portion only) given the assumptions. PM me if you'd like me to email that to you.
The stock took a big hit in recent months as investors from the previous private placement sold and the company had to lower the price for its new placement to complete the feasibility study down to .80. Now that the second placement is closing, the selling pressure is abating and the stock is starting to rebound, joining other zinc stocks which have been rallying on the new 16-year high price of zinc: http://www.kitcometals.com/charts/ZINC_historical.html
The price of zinc has doubled in the past year and a half and looks headed much higher given the supply/demand situation. MMGG trading at less than 1/3 what it was when zinc was half the current price (and before the feasibility study had started and the metallurgy was proven) is a steal, particularly if they can get listed (most likely in Canada). MMGG should at least return to above the $3 it traded at in 2004 once the feasibility study is completed.