Here is a brief article in the Boston Globe regarding making and responding to offers. Many litigators consider this approach to be a sound negotiating strategy. Now there is some science to support it.
“NEXT TIME YOU find yourself in a negotiation, don’t just throw out a round number. In a series of experiments, researchers from Columbia University found that offering a precise number—e.g., $4,925 compared to $5,000—resulted in a significantly more deferential counteroffer, due to the perception that a precise opening offer was more reasoned and informed.”
Mason, M. et al., “Precise Offers Are Potent Anchors: Conciliatory Counteroffers and Attributions of Knowledge in Negotiations,” Journal of Experimental Social Psychology (forthcoming).
The question that i would ask, is what is the best time to do such an offer. I would suggest that making a final offer or close to final offer with such precision is much more effective in the litigation context than the early offers. However, in much of the real world negotiations outside of litigation, having such an offer from the outset might give more credibility to the other side really thinking about why you made the offer so specific.