To actually know, you will need your companies overhead rate (expenses/payroll); but, you might not be privy to the year end statement which will give you the company expenses.
The overhead rate may take into account other employees (accountants, secretaries, CEO's, etc) that do not work directly on projects; but, still play into the picture.
If the firm works for certain government agencies (DOT's), they may have an audit done by that agency which sets the overhead rate allowed for that agency. That may be close to the actual; but, sometimes these agencies do not allow for certain expenses which lowers the rate.
If you have your companies actual overhead rate and you know how much time was placed on the project (by every billable person involved), you can calculate the actual expense for the project and the remainder is profit.
Most times the charge out rate is based on the overhead rate x 1 hr x profit (10-15%). As mentioned above, the project cost estimate can be dependent on a number of variables which affect the bottom line based on the employee's efficiency.
Also as mentioned above, different firms have different overhead rates and some firms even calculate different overhead rates for different departments (people).