A client approached us with a project, we gave an estimate based on the fairly loose spec with the expectation that before work began we'd have the chance to discuss a full spec and sign off on the total budget.
However time went on and due to their workload we didn't get all the details necessary for a final price and we just had to start working and keep incrementing as the decisions and assets were sent over in order to meet the deadline.
We are now in the position of being a few days away from the deadline with most of the work done, finally at the point where we know the total scope, but we have no formal agreement beyond our initial estimate, which is about 70% of the total project since some parts increased in complexity.
What's the best way to approach this? Obviously we'd like to get paid for the full amount. Should we update the estimate and send it over? Simply send over our final bill when done based on day rate? Cut our losses and just bill the estimate?
It's a medium size company with 30-50 employees. We're two people.