Can Booming Blade be cast with an Improvised Weapon without a cost? [duplicate]

In a bar brawl, the Eldritch Knight picks up a stool and smacks a nearby patron. Can they cast Booming Blade while doing so? The Material Components of the spell state:

Components: S, M (a melee weapon worth at least 1 sp)

Is the improvised weapon eligible for this attack? I’m not sure if the price of a stoll is listed somewhere, if it is then assume some other improvised weapon that has no listed value, like a tree branch or a single arrow.

There are 2 similar questions here and here, however the spell has been changed in errata since these questions were asked, and I am asking about a new part of the spell.