Yup charge them for the logo design. You did the work, if they want the logo, they should pay for it.
But in the future, set up a way to deal with logo work as a separate product/service than sign work. AND THIS IS KEY: never do design work without a down payment, unless you want to deal with people trying to take your design work elsewhere. If you collect down payments before you do design work. 99% of the time they will want you to do the job from start to finish because they have already invested in you. And that 1% of the time you didn't get the job, at least you got paid for your time.
If a customer wants a sign with a logo on it and they don't have a logo, you need to sell them on a logo. If they don't want to pay to have a logo developed then they won't get a logo. It is very important to tell them that the sign layout they are getting is not a logo and can't be used as a logo.
We then tell them that sign design files do not leave our shop, but logo designs will be released on a CD in multiple file formats. That is why logos cost more. We also tell them if they want to use their sign design as a logo at a later date, we do offer a "sign to logo design package". Usually if you add up the cost of the original sign design charge with the "sign to logo design package" it usually ends up costing a bit more than if they would have went with a logo in the first place.
Some people out there are clever. I think they purposely try to get sign makers to develop a logo for them without actually buying a logo. They figure that if you did the design work for their sign, that simply handing it over to them should be free. You need to set up a strong policy on this type of thing and clearly state that this is not the case before you do any work.
