I can't answer your grammatical question, but I agree with Chris that this sentence seems wrong. When I read it it sounds like their act of evaluating the proposal somehow results in the construction of a facility, or they evaluate the proposal in their spare time while they happen to be contructing a facility. I'm pretty sure neither of those is the intended meaning - at least they don't seem to make much sense.

Hmm... good question! I think (and I am willing to be corrected by any other answers) that there is nothing wrong with the grammar of the sentence. Or at least not with the grammatical form. Here is a classic example of this type of sentence (from the British Council website): "The bomb exploded, destroying the building." - To give the result of an action HOWEVER your sentence does seem wrong somehow... I think it's because of the word "evaluate". If you evaluate something you don't actually take action (there is the action of evaluating of course) but it doesn't necessarily follow that any action will result. You then have to make a decision. So your it feels like your sentence has a step missing. Whereas the example sentence above has a very clear direct link between action and result. As I said, that's what I THINK. I'm posting this message partly because I would be interested to see what others have to say. (You live and learn)

As an adjective, "constructing" will modify the nearest noun. If you placed it at the beginning of the sentence, it would modify "they". However, since you placed it at the end, it modifies "proposal". Hence, your sentence says they evaluated a proposal, and that proposal was one for constructing a facility.