Oftentimes, depressed valuations can accompany fat dividend yields, especially if we're talking about the shares of a company that have been under enough pressure that the yield has swelled to the higher end of the historical range.

Indeed, truly troubled firms that have shed north of half of their value may sport yields that are close to double that of historical averages. And while it's always nice to get shares of a company at a much lower price of admission, the supercharged dividend may not be as safe and sound as it once was when the firm wasn't crumbling under the weighed of headwinds or idiosyncratic issues.

In this piece, we'll check out two cheap Canadian blue chips that have been down and out for well over a year now. After sagging even lower for 2024, contrarian investors may be interested in checking out the two names to play a potential bounce-back year in 2025.

TD Bank

Indeed, when it comes to crises that are specific to certain companies (think TD Bank (TSX:TD) and the painful aftermath of the money-laundering fiasco, which haunts shares to this day), there tends to be a massive haze of uncertainty that could make valuing shares that much more difficult.

Undoubtedly, the big banks tend to be quite hard to value already, even without factoring in big management changes (a new chief executive officer coming in very soon) and the unanswered questions surrounding how TD Bank will grow with restrictions in place.

It's not hard to imagine TD's peers are gaining a leg up while TD seeks to iron out the remaining wrinkles in its now highly hazy long-term growth story. Either way, I think TD Bank stock is shaping up to be a fantastic high-yield dividend play to buy and hold for the next three years.

Going into 2025, there's going to be somewhat higher expectations in place for Canada's big banks. For TD, though, which hasn't gained as much as its rivals have in 2024, it won't take nearly as much to spark an upward move, at least in my opinion.

With the stock down close to 31%, there's already so much damage dealt to the name—arguably too much damage. Perhaps a big announcement and some words from the new CEO could be enough to help beckon value hunters back into the stock in the coming months. With fellow Canadian bank stock Bank of Montreal recently upgrading TD shares while noting the "steep discount," it's hard not to want to be a huge buyer while TD's dividend yield is over 5%.

Nutrien

Nutrien (TSX:NTR) has been another hard stock to own in 2024. Year to date, shares of the fertilizer firm are down 16%, putting it nearly 53% off from its all-time highs. Understandably, agriculture demand has fallen into a serious slump. And while it's hard to tell when agricultural commodity prices will soar again, I do view Nutrien as one of the best players in the industry.

While the fertilizer market is anything but exciting, I do see ample value to be had for investors willing to wait things out as they take in the 4.7%-yielding dividend. Like with TD, the future is cloudy, with a chance of further showers. That said, if value and yield are what you're after, the name looks incredibly tempting for those looking to start the new year on the right foot.

Just don't expect Nutrien to turn a corner anytime soon. The turnaround and bottoming-out process could really drag for some time.