At the Fool, we love dividend stocks. Having a strong income stream is one of the best ways to build long-term wealth in your portfolio. And when dividend stocks go on sale, it makes them even more attractive.

Cheap dividend stocks offer a one-two punch of excellent income and the potential for the stock price itself to rise. Here are three stocks that pay great dividends and are trading at a nice discount right now.

Mortgages can be very lucrative
One of my favorite cheap dividend stocks is American Capital Agency (AGNC 0.99%), which pays out a tremendous 12.1% dividend yield. Yes, a lot of volatility and uncertainty come with mortgage real estate investment trusts, but the valuation here makes it worth it.

As of the most recent quarterly report, American Capital Agency's book value per share was $26.26, and the stock currently trades for less than $22. In other words, you can buy the company's assets for $0.82 on the dollar right now. That should help you stomach the volatility.

And the volatility might be less than you think. The company has reduced its leverage ratio from 7.2-to-one to just five-to-one since last September, and interest rate uncertainty seems to have calmed down, at least for the time being.

I especially like the company because when mortgage REITs get cheap, American Capital Agency's management has a history of making savvy moves, such as aggressively buying its own shares for less than they're worth, and even buying the shares of competing REITs if the valuations are attractive. And now that the shares have dipped, I wouldn't be surprised if the company did it again, creating another leg up in net asset value.

A diverse basket of loans lowers the risk
Apollo Investment
 (AINV 2.00%) is a business development company, or BDC, that essentially makes its money by financing the debt of small- and medium-sized companies, and receiving a higher than average rate of return.

While each individual business BDCs invest in is generally a bit on the risky side, the diversity of the portfolio means shareholders' income isn't too dependent on any one company. In Apollo's case, the portfolio is spread among investments in over 100 different companies, including such household names as BJ's Wholesale Club, Del Monte Foods, and Molycorp.

Apollo pays a dividend yield of about 9.7% per year, and currently trades for a 5% discount to the book value of its assets. The BDC sector has experienced some headwinds during 2014, such as being taken out of Russell and S&P indices, which have driven down valuations across the sector. So, if the next year or two provides smooth sailing for the companies, we could definitely see a nice rebound toward the historical average valuations, which in Apollo's case is closer to 1.1 times book value.

Invest with the big dogs
Transocean
(RIG 2.16%) has been beaten down lately, thanks to the low price of oil and legal concerns surrounding the company's involvement in the 2010 Deepwater Horizon disaster. In fact, the company has lost nearly 40% of its value so far in 2014.

Transocean owns oil rigs for a variety of oil drilling applications, and leases them out to oil companies such as BP. The company's fleet consists of 79 drilling rigs, and it has another 12 under construction.

Activist investor Carl Icahn holds a 6% roughly stake in the company, and was perhaps the main reason Transocean agreed last November to raise its dividend to $3 annually per share. The stock price has plummeted since then, so that dividend has ballooned to a sky-high 10% annual yield. And, although earnings are expected to decline in 2015, mainly on sector weakness, the consensus estimate of $3.07 per share will still cover the payout, should Transocean decide to keep the dividend constant.

Cheap, but for how long?
All three of these companies pay double-digit yields, or very close to it, and all trade for less than their book value.

RIG Price to Book Value Chart

None of them come without risks -- otherwise they wouldn't pay so well. However, these are three well-run companies that are trading at a nice discount right now and probably won't be this cheap forever.