I'm in the component side, private sector; Your query contains 2 very mixed questions.
How does a mining company value a potential project <- Exploration, Grades, Processing.
Say a company was planning to do an IPO and sell down a percentage of their asset <- Sell down of? A site = Exploration, Grades/(1/3 life expectancy generally but reports are required for remaining and grades of section), equipment = depreciation values and demands eg I see new machines worth over 500k get sold for as little as 1k after use and out of code (5yrs after new) Grays online is perfect example to see this.
rough estimate of how much money the new company (IPO) <- You would need to know what can't be accessed till after release of exploration, grades, processing, whats in the ground is it just 1 element or more did they just get a mother load or they get the raw end of the stick.
But an easy calculation if pure mine of 1 thing is current v2o5 value is 15.55EUR(http://www.vanadiumprice.com/) = Site says Grade = 0.28% and there is 13.1 billion pounds = 36,680,000 marketable = $570,374,000 EUR remove its qty(% selling) and you have your net site value for both directions but remember you need to consider processing, consumables, equipment are they mining the other resources and processing? etc to get its figures more accurate and another bit that doesn't come to public light till report time including the how reliable is the equipment in use.
This is a subject that has to be said as do your research make sure you feel right about your choices don't act on another persons view or input or there is times your best just give your bank details to them saying you don't need it.
