As he demonstrated decades ago, the automated colonization of a galaxy is doable in a few million years, at a profit. That is, if you're capable as a species of planning on a horizon of a few centuries.

Capital markets have proven capable of pricing certain securities that do not pay back for a century. So we may prove capable of it. If that fails, and we last, some generation we just may have the hubris to do it anyways. Eventually sending machines to the next star will get cheap enough for a single wealthy individual to finance it.

Cheers,
Ben