One of my projects in college was to recreate a logo for a local business.
The professor picked the business and I do not believe the business owners know about it. Since my logo has won several recognitions, I thought it would be cool if the actual business would use it.
Since they did not ask for a new logo, how would I go about asking them if they would like to buy it?
I do not want to come out sounding like a cheesy business person trying to sell something or offend the owner if perhaps they are the one who created their original logo. I am having trouble with the wording in my letter to them.
There's many good answers for this.
One thing I can suggest is to simply present the logo to the real business by explaining it the same way you did here! The fact that your logo got a lot of attention already is something that might be appealing to that business.
This way, you won't feel like you're judging their logo; you're simply presenting them some work that was already done and you're offering them the opportunity to actually update their logo without having to go through all the process of actually creating one! That's kind of a good deal already and a huge time saver for an entrepreneur. They don't even need to search for a designer!
Regarding the price, it depends on your goal with this; that logo is already done and kind of served its purpose. Logo prices can vary greatly from one designer to another and also depends on the size of the business who will use it. Some business feel okay with paying $300, others will find a Fiverr $5 clipart perfectly fine, others will prefer the +$1000 budgets. If your main goal is to make money, then try the $600-1500 range. If your goal is to see your logo being used in real, then try to get something between $200-600. The worst that can happen is this logo will not be used in real and will remain a part of your portfolio.
My approach with this (since the logo is already done) would be to write to or even better call the company to get an appointment to meet the boss. Don't send the logo in your letter, keep some mystery and give yourself the opportunity to meet the boss and present your own concept. I think a phone call is more efficient or even visiting the company to get an appointment might get you faster results than a letter.
Then I'd show my logo and would ask how much they want to offer and if they want any revision to it. If the price is less than what you wanted, tell that person it's less than what it's worth. The boss will certainly ask you how much you want. You can mention your price and offer other services to upsell as a way to negotiate (and get more work too). For example, if the boss is interested in other marketing material, you can offer to lower the price of the logo if there's other projects (guaranteed and with down payment) you can work on. If you don't care about future projects then simply shake hands and tell the guy you'll think about his offer. Call a few days later to accept or refuse the offer. That will let him some time to think about it and maybe even fall in love with your logo after getting some feedback from other people too.
And yes you're right, some people do their own logo and are very proud of it. Don't compare your logo with the actual logo when you'll present it. Simply focus on your own concept and creation!