Anything goes before the contract is signed!
If this is the Contractor's offer that they will increase the Prices (target) by X in order to maintain the original Completion Date and that is accepted/signed then that is the Target. There are no rules on how they should have assessed it - although assess it too high and they might just lose the job altogether. At this stage it kind of depends on who needs it most as to who will back down, and also how bothered the Contractor is about relationships as it will not go down well if the Client feels they have been backed into a corner right at the start!
If this is the Contractor's offer that they will increase the Prices (target) by X in order to maintain the original Completion Date and that is accepted/signed then that is the Target. There are no rules on how they should have assessed it - although assess it too high and they might just lose the job altogether. At this stage it kind of depends on who needs it most as to who will back down, and also how bothered the Contractor is about relationships as it will not go down well if the Client feels they have been backed into a corner right at the start!