With the shares of many companies in the oil and mining sectors trading at multi-year lows, there are potential bargain-buys around for patient, long-term investors.

At this stage, it’s all about survivability. Companies with onerous debt and insufficient cash flow to service it will go under (plenty already have, and there’ll be more casualties yet), while the survivors will emerge from the downturn fitter and stronger.

BHP Billiton (LSE: BLT), Hunting (LSE: HTG) and Hochschild Mining (LSE: HOC) are three companies with good survivability credentials, which bold investors may want to consider buying at around their recent lows.

BHP Billiton

Size, diversification and relatively low gearing of 26% give the world’s biggest miner BHP Billiton a strong position in the survival stakes. With the shares more than 60% below their 52-week high, and more than 75% below their all-time peak, the long-term upside potential for investors today is considerable.

Of course, the short-term could be stressful. It’s possible Billiton’s shares may fall further before turning north. And one thing investors today shouldn’t bank on is a continuation of the dividend at last year’s level, which gives a yield well into double figures. Billiton’s Board has so far been reluctant to tarnish the company’s proud dividend history with a cut. But I believe management will demonstrate it’s putting prudence ahead of vanity by at least halving the payout — and possibly suspending it altogether — at the interim results on 23 February.

Investors today shouldn’t be looking for an immediate substantial uplift in the shares and dividend, but to be rewarded with both over the longer term.

Hunting

Oil equipment firm Hunting has been around since 1874 and has a chairman of 25 years standing who knows a thing or two about charting a course through the ups and downs of oil prices.

Hunting drastically cut its workforce and other costs through 2015, and slashed its interim dividend for the half-year ended 30 June by 50%. At that date, Hunting had modest gearing of 12% and net debt actually came down a tad by 31 October.

Like Billiton, Hunting has recently seen its shares trading more than 75% below their all-time high. And while this is another company that could suspend its dividend when it announces its results next month, a strong balance sheet and veteran leadership provide investors today with every hope of big rewards in the longer term.

Hochschild

Silver and gold miner Hochschild has come through all manner of adversities in its 105-year history of operating in South America. The company, which suspended its dividends a couple of years ago, strengthened its balance sheet with a rights issue last October, bringing gearing down to 20%.

Hochschild has continued to invest for the long term and has guided on a 28% increase in production for 2016 to 32m ounces of silver equivalent, with costs pared to $12-$13 an ounce from $13-$14 an ounce in 2015.

Clearly, with silver at a multi-year low of $14 an ounce, there’ll need to be a recovery in the price of the precious metal for Hochschild to start making serious profits and for its crushed shares (down almost 90% from their all-time high) to start heading north. But the company appears robust enough to survive — and prosper when the silver price changes for the better.

Of course, there are also many other opportunities in the market today. It's times like now that can help long-term investors on the road to building a million pound share portfolio, with all the security and life options that brings.

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G A Chester has no position in any shares mentioned. 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.