What are the chances my trademark application will be accepted if there is another TM with a similar name in the Fed registry?

Disclaimer: This answer is provided as a public service and as a general response to a general question, it is not meant, and should not be relied upon as specific legal advice, nor does it create an attorney-client relationship.

I was unable to find a federal registration for "THE PIG STY" in the PTO's database for anything involving pottery -- there were some pending applications for restaurant services, sauces, and clothing, but nothing involving pottery.

If there was a federal registration for THE PIG STY for pottery goods, and you wanted to registere PIG STY POTTERY for pottery goods, the PTO would most likely refuse registration. The term POTTERY would have to be disclaimed and would carry little weight because of its descriptiveness. So you are left with two marks that are nearly identical for identical goods. No chance at the federal level.

The state level is a different matter. Most states are not very carefuly at reviewing applications. So long as the same mark for the same goods is not already registered, they will typically just register. But then again, a state registration is often worth the paper its printed on. Such registrations are good for stopping other people from using the same mark in the same state -- but they don't really get you anything outside your state beyond what you would have under common law (which looks at your actual market penetration as well as the penetration of your reputation in those markets where you have not penetrated).

Is she selling the entire business or just the trademark? If she just wants to sell that name itself, but is not really selling the underlying goodwill of the business that goes along with the name, then not only is that a bad purchase by you but could also be deemed a naked assignment.

The amount that should be paid for the business (including the trademark) depends on the value that the mark has to the business. If its just a state registration and the business is pretty local (with some online sales), then it might not be worth that much. But if there is a federal registration, then that would be worth more -- again to the extent you acquire the goodwill that goes along with such mark. You should try to seek out the services of an appraisal company with experience in appraising trademarks and other intellectual property.

Notice: The below is for educational and informational purposes only, is not a reflection on or a representation of any views or opinions held by my employer, and should not be construed as legal advice. Nothing herein is meant to create an attorney-client relationship.

You should probably speak to a knowledgeable trademark attorney. Whether you risk potential conflict with the other company if you proceed with use and attempted registration of your own trademark depends on a number of factors. As a rule of thumb, however, if both companies' marks are strong (i.e. coined, fanciful or arbitrary), the dominant portion of your mark is identical to the other party's mark, and you provide virtually identical goods or services, there could be a fairly high risk of conflict. The USPTO will examine your application based on a number of substantive and procedural grounds, including likelihood of confusion with a prior pending application or registration. If the marks and goods/services are quite similar, the application could be refused.

In the real world, the owner of the U.S. trademark registration might also have a claim for infringement. Whether the other company will enforce its rights and go after you is another story. Nevertheless, if you already know that this company is out there, there could be an argument of bad faith if you proceed. If you have not yet invested substantial time, effort and money into your business, it might be easier to simply pick a new name. It might be beneficial to ask a trademark attorney to assist in the searching and clearing of the new name if you plan to use it as a trademark and potentially file a U.S. trademark application.

As to a fair price to pay for the other company's trademark, it is difficult to say. This is probably a business decision. How much is the mark worth to you and your business? I note that in the U.S., a trademark cannot be assigned separate from the goodwill it symbolizes. If you decide to purchase the other company's registered trademark, you will need to negotiate with the owner and obtain an Assignment of Trademark document which will assign the mark together with the goodwill of the business symbolized by that mark. Keep in mind that if you do this, you will then be responsible for using that mark with the identified goods/services. Otherwise, you risk eventual abandonment.

If the company is making $50K per year on average over the last 3+ years & the income is direclty tied to the trademark either by way of sale of trademark goods or by way of licensing fees then discount the $50K to a Net Present Value and pay 60 -80% of that amount.

You are effectively valuing the business by way of its income stream. This assumes that there is no inventory, A/R, or equipment that you will be purchasing. Just the TM.

Get a business lawyer to help you or a cpa.

Disclaimer. I am not your lawyer. The information provided is merely for educational use. Contact a lawyer in your state.

There is a good chance that your trademark application would be rejected. "Pig Sty" is the unique part of the name and if each business is in the same industry you will run into the "Likelihood of Confusion" dilemma.
I'd pick a different name.