The original post says an exchange for $$$$. If exchanged for cash, it's a sale. If exchanged for the new stock, nothing is reported except cash received for partial share (when the exchange equals something like xxx.33 shares, cash will be paid for the .33). Okay to report that with no basis, since it will usually be minimal and allows for the new shares to retain the original basis of the old. This client has to find out the original basis, because it will become the basis of the total number of new shares. Catherine's link should help determine what the new per share basis is, but the starting point is the old basis. If dividends were reinvested, those get added to the old basis. Have fun!
Actually, I've been handing these messes to the broker and asking him/her to calculate it for the client. They have the fancy software to look up CUSIPs. It's hard to find historical prices for stocks that no longer exist without the data they can access.