How do I determine the value of the shares of a publicly traded stock I received in a merger?

The initial cost basis would be the stock's price at the time you obtained the shares. So if you had ten shares at $10 per share, your cost basis is $100. If you sell the 10 shares at $11 per share, your capital gain is $10. The average cost basis is the average of the cost of the shares. Most brokerage firms will figure the cost basis for you so you don't have to dig up the details. When selling stock shares, you also typically have the option of "First In, First Out" (FIFO) or Specific Identification "SpecID," the latter allows you to choose which shares you want to sell (for some, selling the shares that rose the least will incur the least tax consequence).