LONDON -- One sector in which I've been reluctant to invest over the last few years is big miners -- giants like BHP Billiton (NYSE: BBL)Rio Tinto (NYSE: RIO), and Anglo American (OTC: AAUKY). These behemoths of the resource industry have been supremely profitable but a little expensive for my taste, thanks to booming global demand for their commodities. However, slowing growth in China means that is all starting to change, and these shares are starting to show me two key buying signals.

Let me explain.

Thanks, China
China's growth rate has slowed slightly this year, causing widespread falls in the share prices of the world's biggest mining companies. Despite this, China's GDP is still expected to grow by about 7% this year -- and from a much larger base than in previous years. This means that global demand for commodities like coal and iron ore will remain strong, but it does mean that the commodities industry is likely to move from flat-out expansion into a more mature "cash cow" phase.

The big miners seem to have anticipated this quite sensibly, with Rio and BHP both announcing scaled-back, more focused investment plans over the last few months. I reckon this good news will give investors who didn't get onboard before the commodities boom a second chance to gain access to these companies' earnings at an attractive price.

Covet thy earnings
Earlier this year, the world's third-richest man, Warren Buffett, ignored market sentiment and increased his holding in one of the U.K.'s biggest companies to more than 5%. He did so because he thought it looked cheap and wanted greater access to its strong, long-term earnings. (You can find out the name of the company Buffett bought and the price he paid in this free Fool report.)

Buffett's logic is the reason I am currently so attracted to big mining shares.

In 2011, BHP Billiton made operating profits of 19 billion pounds on turnover of 44 billion pounds. Most of the big mining projects BHP and its peers undertake have lifespans measured in decades, virtually guaranteeing a strong, reliable stream of earnings.

As the table below shows, access to mining companies' earnings has become a lot cheaper over the last year, falling much further than the FTSE 100. This mouthwatering cheapness is my first buying signal:

Company

Price-to-Earnings Ratio

12-Month Change

BHP Billiton

7.1

(23%)

Anglo American

6.6

(27%)

Rio Tinto

5.5

(31%)

FTSE 100

14.2

(5.5%)

Source: Digital Look; Yahoo! Finance.

Here come the dividends!
My second buying signal is income. BHP, Rio, and Anglo American are all expected to start paying out a greater share of their earnings in dividends over the next few years. As the table below shows, they all have a much higher level of dividend cover than the FTSE 100 average and can easily afford to give shareholders a pay raise:

Company

Yield

Dividend Cover

BHP Billiton

3.63%

3.9

Rio Tinto

3.25%

5.6

Anglo American

2.23%

6.8

FTSE 100

3.8%

2.85

Source: Digital Look.

These figures suggest to me that a 4%-plus yield will soon be within the reach of shareholders in BHP and Rio, taking their yields above the average for the FTSE 100 -- one of my criteria for buying. Indeed, as I write, BHP offers a 4.1% yield based on its current share price and forecast total dividend for the current financial year.

Ready to buy?
Shares in Rio and Anglo American have now fallen to 2006 levels, and while BHP remains a little more expensive, I believe that all three now offer very good value. My choice will be BHP or Rio -- probably the latter -- but I've got a feeling they might all be cheaper still later this year, so I'm going to keep my powder dry for a little longer yet.

In the meantime, you might be interested to know that the Fool's own team of analysts has also singled out the mining sector as one of the best places to invest in 2012. You can find out which mining shares they are tipping in this free report, "Top Sectors for 2012," which I highly recommend.

Where is the U.K.'s leading dividend stock-picker investing today? The identities of Neil Woodford's favorite blue chips are revealed in this free Motley Fool report: "8 Shares Held By Britain's Super Investor."

Further investment opportunities: