Book deal - how much do I charge?
Their budget is irrelevant, what is relevant is how the images will be used - in this case how many copies of the book are being made and sold. If they are going to make 100 books and sell them at small gigs that is far less valuable than if they print 10,000 and sell them on their world tour.
They may not be big yet but just in case they suddenly land a great record/tour deal charge them a modest upfront for the first X number of books and then Y additional payment for each extra X they have printed.
You could go for a % of sales but be aware that that means you get paid a lot later (if at all), requires the hassle of them reporting sales and may result in money only coming in in dribs and drabs. Its also possible that the books might not sell in which case you don't get paid. I have done a lot of royalty deals in my (non-photography) day job and frankly they are a pain. Better to get an upfront if at all possible.
I love my girlfriend, my dog and my canon 5DIII - even though none of them ever do what I tell them
I am learning photo graphee - see the results at www.danmarchant.com