Apple (NASDAQ:AAPL) stock is up about 20% in the past three months. Zooming out a bit further, it's up about 55% in the past year. But this industry leader sill trades at a price-to-earnings ratio of just 15.3. Compare that to the S&P 500's P/E ratio of 19. Is the stock still a buy, even after the run-up?

Image source: Apple.

While I made the case a few weeks ago that Apple stock was worth $120, based on a conservative discounted cash flow analysis, probably one of the best ways to illustrate the stock's story is through charts. On that note, here are the three most relevant charts that show why the stock is a buy.

Apple's hot China market
The smartphone market is still growing rapidly. In 2013, for instance, global smartphone shipments hit 1 billion, up from 725 million in 2012, according to data from IDC. But one of the greatest opportunities for smartphone manufacturers is undoubtedly in China, the world's largest smartphone market.

And combining smartphones and tablets, the potential for smart devices in the country is simply monstrous.

Data for chart retrieved from Umeng's 2013 report on smartphones and tablets in China.

Of course Apple's smartphone and tablet businesses make up a whopping 74% of the company's total revenue, so the big growth in China in these two markets is especially encouraging for Apple investors.

But is Apple popular enough in the country to benefit from the opportunity? Absolutely. Chinese app analytics firm Umeng (via Benedict Evans) says that 27% of all smartphones sold in China in 2013 were in the $500-plus price range, and 80% of these devices were iPhones.

A conservative valuation
Almost any way you slice it, Apple stock is cheap. Even though analysts predict Apple earnings per share to grow at a rate of about 15% per year, on average, over the next five years, the stock even trades at a discount to other slow-growing cash cows in the tech sector, like Intel and Microsoft.

To illustrate, consider these three stocks, compared on price to free cash flow. The price to free cash flow metric is a useful metric to use because it levels the playing field -- especially for mature companies like these three tech giants.

AAPL Price to Free Cash Flow (TTM) Chart

AAPL Price to Free Cash Flow (TTM) data by YCharts

An aggressive share repurchase program
To help boost earnings in the coming years, Apple is putting its strong cash flow to work in repurchasing its own shares. Consider the difference Apple's repurchases have made so far.

AAPL Average Diluted Shares Outstanding (Quarterly) Chart

AAPL Average Diluted Shares Outstanding (Quarterly) data by YCharts

Fortunately, Apple looks poised to continue repurchasing shares over the long haul. The company announced in April that it had authorized a second significant increase to its share repurchase program, boosting it from $60 billion to $90 billion. Even more, Apple said it planned to utilize this cash by the same end date the program had when it was first announced: the end of calendar 2015.

With a huge opportunity in China, conservative valuation, and aggressive and shareholder-friendly share repurchase program, Apple stock is an excellent bet for long-term investors.