Vision company is a startup which specialize in hi$-$tech visual technology. It is considering to go for an IPO. While the company has no revenues or profits yet on its only products, it has a $20$ year patent to the product that will enable contact lens users to integrate the virtual world with the real world using AR$.$ While the product is technically viable, it is exorbitantly expensive to manufacture and the potential market for it will be relatively small initially. $($A cash flow analysis of the project suggests that the present value of the cash inflows on the project, if adopted now, would be $$250$ million, while the cost of the project will be $$800$ million.$)$ The technology is rapidly evolving and a simulation of alternative scenarios yields a wide range of present values, with an annualized standard deviation of $50\%.$ The $20-$year T$-$bond rate is $5\%.$ Estimate the value of this company.