The Right Price comes out of the Identify and Specify procedures. And sometimes out of the Design procedure if the design leads to Identify and Specify revisions.
Until the project is finished, all predictions are based on estimates. If you do not have a collection of statistics about your past projects, how can you estimate with any confidence? The answer is NOT "you can't"!
The first thing you do is search for published statistics for producing content in the field or industry where you are working. There will be data somewhere on the Internet.
The second thing you do is make use of the societies and forums you have joined. (Or will join!) Ask if anyone knows of industry statistics for producing your kind of work.
Between those two, you will find numbers you can use, and references, to show your estimates are not based on wild guesswork.
The third thing you can do is to promise to start collecting data from your own future work:
If you cannot estimate properly, you are doomed to work long hours to make your deliveries and not make much money (if you are working for yourself).
The irony is you are quite good at estimating:
Why are you able to make reasonable estimates about these things, but not about producing documentation? Because you have a lifetime of experience estimating height, weight and speed.
So all you need is either your own historical statistics or at least a reliable source of industry statistics.
The Right Price is the amount our company or our customer will pay. That means every now and then, no matter how well you can estimate, the price will be more than the amount in someone's budget.
Always remember, you can bring a high price down (but you can rarely put a low price up). So if you want to bring a price down, despite your estimate, the question is: how much of your own time do you want to risk as extra, unpaid hours if your estimate is more guesswork than science?
In that situation, you either need to re-examine your Identify and Specify work. Can you find another way? What can do differently, or cut out? Have you over-specified the content for the documentation project? If have no good reasons to change your estimates, don't be afraid to walk away from that particular job.