Without getting into the ins and outs of this particular case, a very common mistake that people make when first becoming self-employed contractors is to under-estimate overhead costs.
If you come from an employed background and your used to being paid $X an hour people often cost up jobs at a bit more than $X per hour whilst you really need to cost them up at more like four times $X per hour.
If you're doing work on a commercial basis (rather than as a favour for a friend) you've got to account for all the hours it takes to do things that are done by others if you work in a large company such as
i) marketing (i.e. spending time finding work and persuading people that you are capable of doing a good job)
ii) admin/legal stuff i.e. determining exactly what the job entails, agreeing specifications and some sort of contract and what the position is should requirements change,
keeping time sheets,delivering the final product/design and getting it accepted,
iii) travel and meeting time and associated costs
iv) idle time - i.e. time between contracts when you're looking for the next job
v) holidays/vacation
vi) time and money spent on accounts, tax returns
vii) rent, insurance, secretarial services (maybe you need to be in shared offices where there is someone to answer the 'phone though of course you can just use your mobile)
perhaps even legal services if you want to get any contracts checked over (insurance might include liability insurance should your design have some major flaw which costs the customer money).
If you've not run a small company or been self-employed before it is very easy to under-estimate what it will cost you in time and perhaps other expenses to deal with all the boring stuff.
It gets even worse if you start expanding beyond just yourself and perhaps start to employ others even if it is just part time admin help.
Of course when you first start out you probably will do things on an ad hoc basis and work from home and not bother too much with contract details etc but it is difficult to put up prices so it is best to charge a sensible rate from the outset.