Earlier this week, I took a brief look into the special one-time dividend being paid by Atlantis Plastics (NASDAQ:ATPL), and many of you wrote in to ask questions and tell me your thoughts on the dividend. First, thank you to everyone who did. It's always great to get feedback and different viewpoints.

However, the fact that a large number of the responses centered on whether Atlantis is a "good short-term income play" is a bit troubling. As a Fool, I'm primarily interested in the operations of businesses and whether I want to be a part owner of a business via the purchase of shares.

To put that in a context specific to Atlantis, the dividend is only a part of the equation. For me, the dividend is unappealing, although if I'd held shares before the dividend was announced, I think I'd feel differently. Those folks have seen a very healthy increase in the value of their shares, and even after the dividend is paid and the shares fall to reflect that payment, I suspect they will have come out ahead of where they were before the announcement. Whether they'll want to hold onto their shares is another matter entirely.

We'll touch on one-time payments a bit more later, but I'd like to clear the air on a number of other questions about what makes one dividend good and another bad. Let's take a brief walk through the world of dividend-paying companies and where the money comes from that pays the dividends -- after all, the two things that most influence the quality of a dividend are how the dividend was funded and the company's prospects going forward.

The many forms of dividends
Dividends can be paid in various forms, though most companies pay them in cash on a set schedule -- most often on a quarterly or annual basis. However, some companies pay dividends as they have the cash in the form of one-time payments, and still others pay dividends in the form of stock. Tootsie Roll (NYSE:TR) is well-known for rewarding shareholders with three shares for every 100 they hold each year.

Dividends you can take home to Mom (the good)
Let's first tackle the companies that pay regular dividends of a set amount and kindly drop that amount into your account each quarter or year. The best of them pay dividends that are a fraction of earnings or free cash flow and are still growing earnings at a healthy clip. For example, I prefer companies that pay less than 70% of free cash flow. These are the Pepsis (NYSE:PEP) of the world. A company like Pepsi makes more than it needs to fund its expansion plans, and instead of funding projects that have a perceived lower return or piling up cash that does no one any good, the money is returned to shareholders.

Occasionally, firms that have stockpiled cash and don't have a way to invest it will also pay a one-time dividend from cash, just as Microsoft (NASDAQ:MSFT) did last year. For the same reason, smaller companies will often make one-time payments from cash, or they will make payments after selling an asset of high value.

Perhaps the most important thing to note is that although the dividend may be adequately funded, the stock may still not be cheap. Performing valuation analysis is still important here, since the dividend, while a nice guaranteed return, is only part of the return. You still want to see your Pepsi shares increase in value over the years as Pepsi sells more beverages and salty snacks.

How long can they keep this up? (the bad)
The atypical bad dividend payer is a company in decline that has kept boosting its dividend too long. These companies are often wedded to the idea of paying a dividend even if change is really what's needed. A great example of this was Eastman Kodak (NYSE:EK) a couple of years ago, and today's best example is almost any U.S. telecom company. My Foolish colleague and lead analyst for Income Investor, Mathew Emmert, recently wrote a commentary about the many ills in the telecom industry and why, despite the large dividends, he'll pass.

This is too good to be true (the ugly)
Finally, we have what I call the ugly dividend payers. Companies like this will give you some income, but it's not pretty. These are the dividends that exceed free cash flow for years and are eating away at the safety net of cash on the balance sheet. Worse, the company needs to go out year after year and sell more shares or take on more debt to support the dividend.

This is also where I'm most likely to place one-time dividend payments that are funded with large sums of debt, because debt, like weight, is a lot easier to put on than it is to take off. Where this becomes a mixed bag is when a company has outstanding prospects going forward and is essentially recapitalizing the company. If management is right and things go well, shareholders who owned shares before the announcement of the special dividend can come out ahead. If management is wrong, however, and earnings fizzle, a company is more susceptible to going bankrupt.

Final words
Dividends offer some undeniable benefits. With the right mix of companies, you'll not only get returns on your shares, but also part of your return is guaranteed, and reinvesting the dividends is a proven path to supercharged returns. But a company is still a company with many moving parts, and the dividend is but one part of the equation. So, by all means, include those dividends in your decision-making process for investments, but don't make the decision whether or not to buy the dividend.

Fool contributor Nathan Parmelee has no financial interest in any of the companies mentioned. The Motley Fool has a disclosure policy.