From a good piece on time and cost estimation in software engineering, emphasis mine:
All software development effort estimation, even when using formal estimation models, requires expert judgment. But although expert judgment can be very accurate, it’s also easily misled. Perhaps the strongest misleading happens when those responsible for the effort estimates, before or during the estimation work, are made aware of the budget, client expectations, time available, or other values that can act as so-called estimation anchors. Without noticing it, those people will tend to produce effort estimates that are too close to the anchors. Knowing that the client expects a low price or a low number of work - hours, for example, is likely to contribute to an underestimation of effort. Expert judgment can also be misled when an estimation request includes loaded words, such as, “How much will this small and simple project cost?”
In spite of much research on how to recover from being misled and how to neutralize estimation biases, no reliable methods have so far been found. The main consequence is that those in charge of effort estimation should try hard not to be exposed to misleading or irrelevant information - for example, by removing misleading and irrelevant information from requirements documentations.
I'm always shocked when a supplier asks me for a target price on a part I've asked them to bid. Customer-driven price anchors are really dangerous; I avoid them at all costs.