Shares of Medical Properties Trust (MPW 4.61%) and AGNC Investment (AGNC 0.22%)have been beaten down so far that the stocks now offer eye-popping dividend yields above 11%. Let's look at some of the reasons why the stocks have fallen to see if they could be smart buys at recent prices.

Medical Properties Trust

Medical Properties Trust is a real estate investment trust (REIT) that owns 444 hospitals and acute care facilities spread across 31 states and 10 countries. Its stock price has fallen by half over the past year. Now the stock offers an enticing 11.2% dividend yield.

Rather than run its own hospitals, this REIT generally has hospital operators sign long-term net leases that transfer the variable costs of building ownership away from the REIT and onto the operator. This leads to hyper-reliable cash flows as long as its operators can pay their bills.

Medical Properties Trust stock is down sharply this year because an operator that rents 1.2% of the REIT's portfolio, Prospect Medical Holdings, has imploded. In the fourth quarter, Medical Properties Trust recorded a $171 million impairment related to four Prospect-run properties in Pennsylvania. It also wrote down $112 million worth of rent it doesn't expect to receive this year from a hospital in Delaware that has been ordered to close due to a lack of staff.

Public demand for hospital beds doesn't go away just because a particular hospital operator can't manage its business and Medical Properties Trust is confident it can quickly find new operators for its underperforming hospitals.

While rising interest rates could limit the addition of new facilities to this REIT's portfolio, it doesn't look like the company will have a problem maintaining its dividend payout. Management expects normalized funds from operations (FFO) to reach $1.50 in the unlikely event it can't recover any lost revenue from Prospect this year. That's more than enough to cover an annual dividend payout currently set at $1.16 per share.

AGNC Investment

Like Medical Properties Trust, AGNC Investment is a REIT that can avoid paying income taxes as long as it distributes nearly all its profits in the form of a dividend. Instead of a quarterly dividend, this stock pays shareholders every month and at recent prices, it offers a 13.2% annual yield.

AGNC Investment is a mortgage REIT that's more interested in buying long-term debt than real estate. The vast majority of mortgages on AGNC's books are backed by federal agencies in the event of a default. This makes its cash flows easily predictable most of the time. Unfortunately, soaring interest rates are presenting the company with an unusual challenge.

Mortgage REITs earn a living in the margins between interest paid on short-term loans and interest received from long-term mortgages. The Federal Reserve has raised rates so quickly over the past year that interest rates on new short-term debt are actually higher than rates on long-term debt. Economists call this an inverted yield curve and while inverted yield curves have always been temporary, they can quickly cause a lot of trouble for rate-sensitive businesses.

AGNC reported FFO that fell to negative $2.22 per share in 2022. On the bright side, at the end of 2022, the average rate received from loans in its portfolio rose to 4.13% from 3.8% just three months earlier.

Are these stocks worth buying?

AGNC Investment can only report losses for so long before it will have to lower its dividend payout. Investors considering the stock should know it had to lower its payout in 2019 and again in 2020. Shareholders who bought the stock five years ago are receiving 33% less these days. With this in mind, it probably isn't the best option.

The past five years haven't been easy ones for hospitals but this didn't stop Medical Properties Trust from raising its payout four times. With a proven ability to overcome challenges, this looks like a great stock to buy now.