Millions of investors are scurrying to find stocks that pay dividends. Inevitably, some of those dividend stocks aren't going to work out as well as they hoped. Are you prepared enough to know what you'll do if a stock you own makes a major cut to its dividend?

Far from a sure thing
Over the long haul, dividend stocks have a lot going for them. Countless studies have shown how much better dividend-paying stocks do with long-term performance compared with their non-dividend-paying counterparts.

But before you run out and by just any dividend stock, you need to realize that there's always the risk that the stock you choose will have to cut its dividend. If it does, you'll have to figure out whether you should dump your shares and move on to another high-yielding stock or hang on in the hopes of seeing an eventual recovery.

To get an idea of what can happen when a stock cuts its dividend, I decided to look at several examples of popular dividend stocks that have cut their payouts in recent years and what happened to them in the months and years after their dividend cuts.

Case 1: Making a big buy
In early 2009, Pfizer (NYSE: PFE) was a dividend lover's dream. With a yield of more than 7%, the drugmaker compensated shareholders fairly for some of the uncertainties it had in its future.

But when the company decided to buy out Wyeth in a whopping $68 billion takeover bid, it slashed that attractive dividend in half in order to help finance the buy. Shares sank along with the rest of the market into the March 2009 lows.

Since the end of January 2009, though, the stock has risen more than 50%. Pfizer has upped its dividend twice, although it's still far less than what it paid before the buyout. In contrast, Merck (NYSE: MRK) and Eli Lilly (NYSE: LLY), which have kept their payouts stable for years, have risen far less than Pfizer since the 2009 lows. Diverting dividend money to a buyout may have spooked investors in the short run, but the rebound shows that those who stuck with Pfizer got paid off in the end.

Case 2: Plowing money into the business
Last year, Frontier Communications (NYSE: FTR) decided to cut its long-standing dividend by 25% to save more cash to invest in broadband and to acquire more rural-line assets from Verizon. Yet unlike many stocks announcing dividend cuts, the move didn't really spark a sell-off.

The reason may have been that investors believed in the necessity of Frontier's business expansion. Although Frontier is a cash cow, its core assets are a throwback to technology that's quickly becoming obsolete. By investing in its future, Frontier is trying to guarantee dividends for decades to come. Even if it means smaller quarterly checks, that's good news for long-term investors.

Case 3: A sign of things to come?
In their most recent quarters, both Annaly Capital (NYSE: NLY) and Chimera Investment (NYSE: CIM) cut their dividends. The cut for Annaly was modest, accounting for only 3% of its previous dividend. But Chimera saw a bigger dividend cut, with March's $0.14 payout representing an 18% reduction versus its fourth-quarter dividend in 2010.

Mortgage REITs such as Annaly and Chimera pay dividends based on income, and so the small reductions signal a slowdown in the underlying profitability of these businesses going forward. With their highly leveraged business models particularly sensitive to changes in interest rates, it's entirely possible that even the most subtle changes in rates could send them plummeting. Chimera has already seen a big drop, down 15% in price since the end of January.

Case 4: A matter of trust
At the end of 2008, former Canadian royalty trust Precision Drilling (NYSE: PDS) decided to cut its dividend and then eliminated it entirely just a few months later. With a buyout of a competitor and a tough environment for its drilling operations, the company made the moves to preserve cash.

That's proven to be the right call. Since then, shares have risen almost fivefold. The company has benefited from increased interest in drilling, and despite weak natural gas prices, demand for its rigs has jumped with the economic recovery. Those shareholders who stayed in are glad they did.

Be smart
Dividends are great rewards for owning a stock. But knowing whether you'd want the shares even if the dividend went away is important. Think about a contingency plan for a dividend cut now, and you won't find yourself panicking if that payout actually goes away sometime in the future.

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Tune in every Monday and Wednesday for Dan's columns on retirement, investing, and personal finance.