Buying shares in companies that are facing a challenging period can prove to be an exceptionally profitable strategy. Certainly, there’s the risk that the company in question fails to mount a successful turnaround but, if it does, then capital gains can be superb.

For example, Aviva (LSE: AV) endured several tough years that culminated in a red bottom line in 2012. But since then it has restructured, returned to profitability and has proved to be a major success for its investors, with its shares now 60% higher than they were at the start of 2012.

Despite their strong gain, Aviva’s shares still trade on a relatively low valuation. For example, they have a price-to-earnings (P/E) ratio of just 10.7 and, with earnings forecast to rise by 11% in 2016, there’s a clear catalyst for a major upward rerating over the medium term. Furthermore, Aviva’s acquisition of Friends Life is also progressing well and is set to deliver significant synergies as well as create a dominant force in the life insurance market. Therefore, while Aviva’s turnaround story is a success, there’s still more to come for new investors over the medium-to-long term.

Long road ahead

Meanwhile, Rolls-Royce (LSE: RR) is enduring a difficult trading period at the present time with the industrial major having released five profit warnings in the last two years. Looking ahead, the company’s profitability is set to fall at an alarming rate, with earnings forecast to have fallen by 20% in 2015 and then to decline by a further 43% in 2016.

Clearly, Rolls-Royce is at the very beginning of its turnaround, with a new management team recently being put in place to improve the company’s performance. And while its share price has tumbled by 37% in the last year, Rolls-Royce has maintained its premium valuation, with it trading on a P/E ratio of 18.4 (using 2016’s forecast earnings figure). Therefore, while it’s a high quality business that’s likely to make a strong comeback over the medium-to-long term, the risk/reward opportunity doesn’t yet appear to be appealing enough to merit purchase.

Faltering footfall

Also struggling at the present time is discount retailer Poundland (LSE: PLND). Its shares have sunk by 10% today after a disappointing update that stated the company expects pre-tax profit for the full-year to be at the lower end of market expectations. The key reason for this is sluggish footfall on UK high streets that has now been a feature of its first three quarters of the year.

Clearly, external factors such as declining footfall are difficult to overcome, but Poundland’s performance has been encouraging in parts. For example, its Halloween and Christmas performance was positive and with total sales in the third quarter rising by 29% versus the same period last year, it still seems to be moving in the right direction.

Moreover, with its shares trading on a price-to-earnings growth (PEG) ratio of just 0.3, it could be worth buying for investors who can accept a relatively high degree of volatility in the short-to-medium term.

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Peter Stephens owns shares of Aviva. The Motley Fool UK has no position in any of the shares mentioned. We Fools don't all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors.