Transfer of title for trade-in to buy new

Let me see if I understand.

The government provided the contractor with equipment or some other item of government-furnished property (GFP). The GFP is currently in used but serviceable condition.

The contractor would like the government to abandon the GFP "in place" so that the contractor can then take title, then use the (now former) GFP for a trade-in credit to reduce the cost of acquiring new equipment, which it would then own.

Is that right?

If so, your question "should the government allow this?" is hard to answer without knowing the circumstances. For example, can the current contract or future contracts be performed without the need for new equipment? Are there cost savings associated with using new (versus used) equipment, and will the government see those cost savings (if any) reflected in current and/or future contract prices? 

I would also like to know why the government felt the need to provide the original items of GFP to the contractor. Was the contractor unable to perform without the GFP? What happens if the GFP is taken away by the government? What does the contractor do then?

Also, is the GFP capable of being used on any other contract or just on this contract (or series of contracts) for just this one particular government customer? In other words, if the government gives the contractor title, does that lead to the contractor using the GFP on commercial contracts?

Lots of questions over here, with no way to give you a good answer until some clarity is provided.