Since the start of the year, shares in diversified mining company Anglo American (LSE: AAL) have more than doubled. This comes after a hugely challenging period for the company that saw its financial outlook come under considerable strain, with investor sentiment towards the wider mining sector weakening severely as commodity prices fell sharply.

However, investors now seem to be much more upbeat about the future returns from mining companies such as Anglo American. And in this respect, Anglo American seems to have turned the corner.

Furthermore, as a business Anglo American is making excellent progress. For example, it has streamlined its operations, made asset disposals and is seeking to become increasingly efficient. And with it trading on a price-to-earnings growth (PEG) ratio of just 0.4, it seems to offer a wide margin of safety as well as considerable upside potential.

Certainly, there’s scope for a worsening in the outlook for the wider mining sector. However, with such a keen valuation and an improving financial outlook, now seems to be a good time to buy Anglo American for the long term.

Take another look

Also posting gains since the turn of the year has been Rolls-Royce (LSE: RR). Its shares are up by 7% following a very challenging period for the business, with it releasing multiple profit warnings in recent years. Certainly, those profit warnings were at least partly due to general weakness in the defence sector. But they caused a fall in Rolls-Royce’s bottom line of 10% last year and with a further decline of 58% forecast for this year, investor sentiment could come under pressure in the short run.

However, with a new management team and the prospects of the implementation of a new strategy, Rolls-Royce could be about to turn a corner. Its forecasts certainly suggest so, with Rolls-Royce expected to increase its earnings by 36% next year. And with it being a high quality business with a relatively large economic moat, Rolls-Royce’s PEG ratio of 0.5 suggests that while its shares may be volatile, now could be a sound moment to buy them.

Long-term play

Meanwhile, Centrica (LSE: CNA) continues to endure a challenging period. Its shares have fallen by 6% since the turn of the year and while investor sentiment following its fundraising announcement has been weak, Centrica appears to have a bright long-term future.

Central to that is its new strategy. Centrica is seeking to move away from its oil and gas operations to become a more focused domestic energy supplier. While this may not prove to be a perfectly smooth transition, it should create a more robust business that benefits from major cost savings over the medium-to-long term.

With Centrica trading on a price-to-earnings (P/E) ratio of 13.5, it seems to offer good value for money. And due to its shares having a yield of 6%, they remain a very enticing income option. Therefore, while further volatility can’t be ruled out, Centrica seems to be a sound income and value option for long-term investors.

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Peter Stephens owns shares of Anglo American and Centrica. The Motley Fool UK has recommended Centrica. We Fools don't all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors.