NO, though I'll bet most people do report these fractional shares with $0 basis.
You allocate your original basis in the old "parent" stock between the parent and the new child stock the INCLUDING FRACTIONAL SHARE. Since you now know your basis in the child stock the INCLUDING FRACTIONAL SHARE you simply determine the basis for the fractional share and use that as the basis in the PROCEEDS of the "sale" which is the cash in lieu.
So, got 7.65 shares of new stock at a total basis of $87.69? $87.69/7.65 = $11.463 per share. $11.463 x .65 = $7.45 so that's the basis of the fractional share.
