Let $B$ be a monoidal category with multiplication $\Box$. Let $P$ be a category and let $T \colon P^\mathrm{op} \to B$ and $S \colon P \to B$ be functors. MacLane [CWM, p226] says that these two functors have a "tensor product"
$ T \Box_P S = \int^{p\colon P} (Tp) \Box (Sp) .$
Is that coend guaranteed to exist? Do we need more assumptions on the structure of $B?$