No, you can't just select an arbitrary date the corresponding price. You have to have some reasonable basis for selecting a date and the corresponding price for the stock. For example, if you know the stock was purchased in 2010, you could use the lowest price that the stock traded at during 2010. If you can't determine a date or a period, you could use the historical low price for the stock. If you can't come up with some reasonable basis to determine a cost, you will have to use $0.00 as your cost basis.