And thus we get to the root of the problem. As as business executive, why not simply track how long your big projects tend to take, rather than try and dictate how long they should take?
You make projections instead of estimates. You split the work that needs to be done into many tasks and project from past experiences.
You cannot rely 100% on any estimates either, and all you are doing by demanding estimates is creating stress and making people less productive. The meta work imposed by that in itself will make a project take more time, as everyone will be padding their estimates.
