Answer: The Shulchan Aruch (OC 296:2) writes that
one cannot say havdala over bread. One may use beer, however, providing
that it is chamar medina, a national beverage. This is different to
Friday night kiddush where the Shulchan Aruch (OC 272:9) writes that one
should use bread for kiddush rather than other drinks, though similar to
the daytime kiddush when beer would be second best.
The Rema (OC 296:2) writes that the minhag is to use
beer for havdala on motzaei Pesach as one appreciates beer more
then. The Taz (296:3) and Shulchan Aruch Harav (OC 296:10) note that this is
subjective, and if one prefers wine then one should use wine for havdala.
R’ Chaim Volozhin (Maaseh
Rav 185) notes that the Vilna Gaon was particular to eat chametz on motzaei
Pesach. The Taamei Haminhagim (Kuntres Acharon 593) explains that he wanted
to demonstrate that the reason that he avoided chametz for the past
week was only because it was a mitzva to do so. For this reason, there
were various acharonim who were particular to use beer for havdala
(See Nitei Gavriel, Pesach 3:21:2). The Torah Temima (Shemos 12:168) even
relates that the Vilna Gaon himself used to use beer for havdala on motzaei
Pesach.
The Kaf Hachaim (OC 296:26), however, disagrees, writing that even if
one prefers beer, one should use wine for kabbalistic reasons. Nonetheless, other poskim
aren’t particular about this. Thus, the Aruch Hashulchan (OC 551:26) writes
that it is ideal to use beer for havdala during the nine days
when it is best not to have wine.
The Aruch Hashulchan (OC 448:28) stresses that the
Rav should buy back the chametz that’s been sold as soon as possible as
one can’t take it until then.
In conclusion, some have the minhag to use beer for havdala
on motzaei Pesach. They should only do so if they like beer, and must
either buy it then or wait until the chametz that they sold has been
bought back.