Your example is really complex—because the true value of the old house (defined as the value of the best and highest use) is probably the value of the land minus the demolition cost of the house.
:-)
That’s another good point, and yet all of that might be further confounded by historical preservation laws that might prevent demolition. It’s not unknown in San Francisco for developers to dig up and physically move some old dump to another location because they can’t get clearance for the new project without preserving the old dump in one way or another.