How to manage timesheets & cashflow of service business?

Hope someone can share a good practice or app on timesheets management for service businesses. Web agency in particular.

Let me explain how we work (I guess it's typical but still). Each project manager is in charge of X number of clients. For each client, we need to log every estimate we send over. Later on, we track if estimation is confirmed, then if service is delivered, if it's invoiced, if it's paid, when etc.
For new projects our payment terms are usually 50 - 30 - 20. Right after signing the contract, PM creates 3 entries in the timesheet and updates the progress during the project.
Same goes for daily support & change requests. Estimate is provided and logged into timesheet right away.

Account manager, CEO etc have insight into timesheets. When time comes, based on this timesheet we create invoices, cash inflow etc.

Now we do all this via Excel - each PM has its own Excel, each client is a sheet in excel. Once per month Excels are merged into "master".

This Excel-based setup used to work fine but it's not good solution as we grow. Cashflow is a separate excel (so we have to manually copy the data), no rights can be set for different users, cannot automatically create invoice out of selected timesheet data...

Is there a software to handle this elegantly? I found a bunch of time tracking tools but that's not what we need...