Corporate restructuring sometimes involves exchanging shares of stock in one corporation for shares of stock in another corporation. Reorganizations are frequently nontaxable events for the shareholders of both corporations involved. However, sometimes the exchange formula results in shareholders receiving fractional shares of stock.
Since most companies don’t want the administrative burden of maintaining fractional shares, they will immediately sell the fractional share and send you a check. This cash is usually referred to as "cash paid in lieu of" on the Form 1099-B that you receive from your broker. The basis of the fractional share is the amount you paid for the original shares.
Example: You have 301 shares of stock in Company ABC. Now, Company XYZ buys Company ABC using its own stock in a 3-for-1 exchange. This means that you exchange the 301 shares of Company ABC for 100 shares of Company XYZ stock, and have 1 share of Company ABC stock remaining. This 1 share is equal to 1/3 of a share of Company XYZ stock. Instead of issuing a fractional share, Company XYZ sends you a check with the notation "cash paid in lieu of."
The basis of the fractional share is the basis in the share(s) you exchanged for the fractional share. Continuing the example, the basis of the fractional share is the basis you had in one share of Company ABC stock.
The sale of fractional share(s) is reported on Schedule D of Form 1040.