I have limited Freelance experiance as I was hired shortly after graduation. However my standard pricing was based on information I was given in school on freelance pricing.
First you have to consider the project and map out the phases it will take to complete, and estimate the time that each phase will take.
Now take that time and multiply it by a billing rate, gennerally $75-$100 an our for Industrial Design services. This is because @ 1/3 for taxes (including sales tax that you will have to pay on delivered goods), 1/3 for Insurance, and 1/3 is the hourly rate that you want to make. I would say $75 for first couple of jobs…I was able to pull $90 but for midsized client.
Then if you have to build somthing like a model or prototype, if you approximate the cost do so with about a 30% markup to cover any price increases in matterials. If you can not, leave this as a TBD price and list seporatly in the proposal
When you prepare the proposal only show the Cost of each phase, not the hours you feel it will take, just give a general project time like 3-4 weeks, always estimate slightly higher as it will make you look like a hero who worked late on the project when completed ahad of schedual.
This is usually done prior to starting a project so this will be helpfull on your next project. On this one I would sugest you get atleast your hard costs( materials and outside services) covered upfront, and take the rest upon compleation. The other option is to get 1/2 upon initiation, and the remaining 1/2 upon compleation. I would also start by charging only a flat project cost as, these are for their use and will not be resold, so there is no back end percentage.