Renovation is not always cheaper. There is a point where keeping the old building adds cost and uncertainty instead.
Renovation is often chosen because it is assumed to be cheaper. In many cases it is. But there are situations where keeping the old building makes costs harder to predict.
The first consideration is structure. If the columns, beams and foundations are still sound and the layout still makes sense, renovation is almost always more efficient. If the structure needs reinforcing throughout, however, the cost of demolition and strengthening can approach that of building new, with a more limited result.
The second is how much you want to change. Replacing finishes, updating bathrooms and reorganising interiors are reasonable renovation works. But once main walls are to be moved and openings enlarged, little of the original building remains. At that point, keeping it becomes a burden.
The third is uncertainty. Renovation always holds the possibility of mid-project discoveries: undocumented old services, damp that only appears once a wall is opened, or structure that turns out to differ from what was assumed. For that reason a renovation budget should carry a larger contingency than a new build.
Weighing it up is straightforward. Survey the condition of the building before setting the budget, not after. If the survey shows most of the structure is still usable, renovation is usually the right call. If not, building new offers better certainty, even if the opening figure looks higher.