So, the question is: "Is profit known for Fixed Price Contracts?"

I believe that the answer is "NO" since it is a fixed price contract and the seller has put the profit inside the fixed price and buyer usually does not have any idea what is the cost and profit expected by the seller.

However, when answering some PMP preparation questions, I often see "Fixed Price Incentive fee" contracts with buyer/seller share ratio for cost overruns. And the author of the question usually provides the target cost, target profit and asks to calculate what is the actual contract price based on the cost overrun share ration

For me this does not make sense for two reasons:

1. As I wrote above, the target cost and target profit are usually not known to the buyer. So, he cannot deal with the buyer on share ratios in case of cost overruns. Moreover, the buyer has selected the Fixed Price because probably he didn't want to verify and manage cost invoices from the seller and take any cost risk. 

2. Moreover, the buyer should not even care what is the cost overrun for the seller and they should not agree on any sharing ration because this is a fixed price contract at the end. I understand there is an incentive for meeting buyer's needs regarding schedule, customer satisfaction or quality and this incentive may change the Actual Contract Price. However, the Actual Price should not be changed due to Cost Overruns. One of the reasons for selecting Fixed Price contract is to avoid a cost risk. Therefore, I believe that the Actual Price can either be the agreed Fixed Price itself (in case Incentive Objectives are not met) or "Fixed price plus incentive fee" which is the "Ceiling Price" for me. 

However, I see questions regarding Cost Overrun Share Ration in FPIF contracts a lot.

Is there something wrong in my understanding? :)