Shares of mining giant BHP Billiton (LSE: BLT) are worth 30% more than they were in January, but 40% less than they were one year ago.

The firm’s shares trade on a 2016 forecast P/E of 47, but a trailing P/E for 2015 of just 6.6! These numbers show how hard it is to value a cyclical business using just one year’s earnings. So, are BHP shares cheap or expensive?

One ratio which can be useful in these situations is the PE10. This is the current share price divided by average earnings from the last ten years. A low PE10 suggests earnings are below historic averages, and are likely to rise. A high PE10 suggests a stock may be overpriced.

A mining bargain?

I’ve calculated a PE10 of 5.2 for BHP. Although this figure may still be flattered by the long boom in demand from China, I think it suggests that BHP is now at a fairly low point in the cycle. I believe BHP’s profits are likely to rise significantly from here.

City brokers are also turning positive on BHP. Earnings per share forecasts for the year ending 30 June have risen by 26% to $0.24 over the last three months. This figure is expected to double next year. Current forecasts suggesting BHP will generate earnings of $0.47 per share in 2016/17.

These earnings are expected to help support a dividend payment of $0.32 per share, giving a forecast yield of 2.8%. In my view, it’s not too late to invest in BHP’s recovery.

Debt risks change picture

At first glance, oil and gas firm Premier Oil (LSE: PMO) offers a similar opportunity. My calculations suggest Premier Oil currently trades on a PE10 of just 3. However, I believe this figure could be misleading.

Premier Oil currently has net debt of $2.68bn. This dwarfs the firm’s market cap of just £355m. When you factor Premier Oil’s debt into its valuation, the firm’s shares trade on a debt-adjusted PE10 of 19.5.

A more serious concern is that Premier Oil has already had to renegotiate the terms of its loans twice with its lenders. The group is due to start making repayments in late 2017. Any further problems could result in Premier Oil being forced to raise fresh cash from shareholders.

In my view, the risks associated with Premier’s debt make the stock a ‘sell’.

Outlook may soon improve

Most investors agree that the outlook for Asia-focused bank Standard Chartered (LSE: STAN) is uncertain. Based on historical earnings, Standard Chartered shares do look quite cheap. My calculations suggest that the shares currently trade on a PE10 of just 4.6.

What’s less clear is whether Standard Chartered will be able to return to historical levels of profitability. Low interest rates have crushed returns in the banking sector. Standard Chartered’s profits are also being weakened by relatively high levels of bad debt among its customers.

On the other hand, tougher regulation means that UK-based banks do have stronger balance sheets than before the financial crisis. A more conservative approach is being taken towards possible losses from bad debts. So far, Standard Chartered’s loan impairment rates have been in line with the bank’s forecasts.

City analysts expect 2016 to be the low point for Standard Chartered. In my view, these shares could soon be a contrarian buy.

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Roland Head owns shares of BHP Billiton and Standard Chartered. 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.