In a very simple view,
You should first consult your architects and developers as how long would it take for them to
design and implement the whole system
While that's done, include the test efforts and reworks (if any part of your system is faulty you need to spend time to fix them). Always try to be realistic and include vacations, holidays, etc
At this stage you should increase the total by a bit (using the parameters and metrics specific to your department and whatever process you have) and you will end up with a rough time estimate
Once you got the time, use the cost per head and you will end up with what you will need to spend to make the project done,
Add the amount that you want to charge your customer for support and maintenance
Then based on your local market and prices, provide a price to your customer (this means to include your benefit)
Costs are not always the engineer’s payments; you should include equipment repairs, rentals, etc
i.e. cost per head per hr = 100
Total time 20 staff months (including design, development, testing, people’s holidays, etc)
1 day = 9 hrs -> 9 * 100 = 900 per day,
20 * 22 = 440 days -> (440 * 900) + (other costs i.e. equipments, rental, etc) = (total cost)
Total cost + (%commercial price expectation for web application) = what you tell to your customer
This was very very high level, simple view, and only to give you a rough idea
If "commercial price expectation for web application" is not available, then you should do a research and add whatever benefit you expect and then use that instead
I hope I haven't done any stupid mistake in my calculation :)