Value of work is tricky, though I know that larger companies seem to have it nailed.

I've pretty much always based my pricing by my hours worked. It's hard to convince my clients otherwise.

I would talk to her about budget if I were you. Everyone should have one and it i reasonable to ask for it. Some people would say as cheap as possible, some might have a real figure.

You want to give her the best work you can within her budget.

Welcome to IMdesignworks, GDF. I'm sticking my nose in to ask you to please read these important threads posted here. They will explain a lot about how the forum runs, from the rules and regulations to frequently discussed topics to the background on some of our lingo and inside jokes.

Just a little caution: We're not allowed to discuss specific pricing here.

You could work out a fair hourly rate for yourself and times it by however long you think it will take, only giving the client the price per project (rather than your hourly rate). The hourly rate you base your quote on should reflect the value of your work. Definitely ask about the budget, and have follow up questions and a price in mind in case they just say "i dunno".
A good tool might be this rate calculator: http://freelanceswitch.com/rates/
Good luck

This part unclear. Are you saying that 1.) she has only given the non-profit a quote for the coding portion of the site and will give them a separate quote (based on your fee) for design, or 2.) she has already given the non-profit a quote for everything and now needs to know what percentage of her quote will need to go towards design? Hopefully it's the former, but in either case someone should have some sort of budget in mind—if no one does, then I see headaches in your future because not having a budget indicates lack of planning.

This is excellent advice and exactly what I used to do when I freelanced. Your quote should also include time for emails, phone calls, revisions, etc.

Be SURE you define scope of work in your quote and get a signed agreement before you begin any work. Is the coder is going to be the one communicating with the client? If so, since it sounds like you haven't worked with her before, you need to be sure she has good communication & project management skills because if she doesn't and the project turns into a train wreck, your name gets dragged through the mud along with hers.

Digi

Also when you are dealing with any corporation, non-profit or not, you'll need to figure in the "committee" aspect of designing. Everyone wants an opinion, and you may go through several revisions to get your design to their liking. So that 3-4 hours of work may actually triple with the revisions.

And yes, get a contract with how to handle revisions in it.

Jade

Are you supplying only sketches? No final work in Photoshop or other programs that she will code from? Should make that clear.

The Graphic Artists Guild Handbook covers cost questions like this. You may be able to find it in a library, even an older copy would help. Regional prices have to be taken into consideration. Here is their site
http://www.graphicartistsguild.org/handbook/

Yes I would have a set price for web site design, not hourly. Mine is based on 5 pages and anything over that is extra.