Can you use the Fair Market Value of Property to determine your basis?

It would be helpful if you could give a bit more detail - what kind of property are you asking about, and how did you come to own it? The reason I ask is that the answer can be "yes" and it could be "no," depending on the circumstances.

It's "no" because for most capital gains calculations for tax purposes you must use your actual purchase cost (plus the cost of any capital improvements made to real estate, minus any depreciation you've taken in previous years). The problem with using FMV is that you may not have actually paid FMV when you bought your house from your Aunt Sally.

It's "yes" because for inherited property you do indeed use FMV as of the date of death of the decedant. And for cost basis of gifts it's possible that FMV on the date you receive the gift may be used under certain circumstances (although in most cases you have to use the same cost basis as the person who gave you the gift).

From a practical perspective - if you are trying to determne cost basis for an investment (stocks or bonds, for example) then the market price on the date you bought the stock or bond is a good substitute. The IRS is unlikely to complain if you use the average of the high and low price for the stock for the day you bought it. If this is about a stock purchase and sale be sure to account for any splits or spin-offs that may have occurred while you owned the stock.