How much are you willing to pay now for a great long-term growth story? And how much volatility can you stand?

Those are the current questions for owners of shares of Baidu (BIDU), China’s leading search engine.

The stock has been on a tear since December, climbing to $143 on April 4 (before pulling back to $139 today, April 7) from $97 a share on December 31. That’s a gain, as of today, of 43% in a little over three months. And the intraday high at $143.48 marked a new high for the stock.

The shares now trade at about 90 times trailing 12-month earnings per share, and 55 times the projected 2011 earnings per share.

Pricey? Well, the shares aren’t as expensive as they seem, considering Wall Street projections for the company’s earnings growth. The median estimate from the 25 analysts who follow the stock calls for 45% earnings growth in 2012.

You should never stop with a consensus estimate, however, especially with an ultra-fast growth stock like Baidu. The consensus hides a huge difference of opinion. The most optimistic analyst is looking for 71% earnings growth in 2012. The most pessimistic, just 25%.

Quite a difference.

No one thinks that China’s market for Internet search is about to top out. And no one sees a rival about to seriously challenge Baidu’s dominant market share: the company has 70% of the paid-search market and an even bigger share of the search-query market.

But the big question for Baidu is, how quickly it can capitalize on that huge market share?

Even in the company’s core search market, that’s not as easy as it seems. In the fourth quarter, Baidu doubled revenue on a 24% increase in the number of customers. But that represented growth from the previous quarter of just 1.5%.

The problem, Morningstar conjectures, seems to be that many Chinese companies are only marginally profitable—and as competition drives up the selling price for many search keywords, many less profitable customers drop out of the market. That leaves Baidu facing the need to launch expensive campaigns to acquire new customers and to retain the old ones.

In 2010, traffic acquisition costs as a percentage of revenue fell to just 9.6%. That’s way below the 15.7% in 2010, or the 12.4% average since 2005. The lower cost in 2010 isn’t likely to be sustainable, given the company’s plans for spending on customer and traffic acquisition.

Of course, Baidu isn’t dependent for growth on its core search-engine business. With its market presence, the company is looking to expand to other areas, such as music distribution and e-commerce.

For example, the company is starting a service called Ting, currently in testing, that would let users download or stream licensed music. Baidu currently allows users to search for pirated music. (The company was named to the US Trade Representative’s “notorious markets” list this year.)

How quickly a licensed music service will generate substantial revenue from a customer base accustomed to pirated music is an interesting question.

Baidu has already demonstrated that turning market share into revenue growth won’t be without hiccups.

For example, Baidu has announced that it will move merchants from its Youia e-commerce site to e-commerce site Yaodian100.com and to Rakuten China, a Web site run by Baidu’s joint venture with Japan’s Rakuten. (Baidu invested in the operator of Yaodian100.com back in November.)

This kind of change isn’t anything unusual in the fluid world of e-commerce. But it can play havoc with quarterly results.

That’s not a big deal with a stock that’s trading at 20 times earnings. It sure produces massive volatility when a stock trades at 90 times earnings.

I don’t think you have to sell Baidu here, as long as you’re able to put up with the intense short-term volatility that comes with this long-term growth story. It might not be a bad idea, however, to sell part of a position and take some profits. And then wait for the next slightly disappointing quarter.

There will be one. It comes with the growth story.

Full disclosure: I don’t own shares of any of the companies mentioned in this column in my personal portfolio. The mutual fund I manage, Jubak Global Equity Fund (JUBAX ), may or may not now own positions in any stock mentioned in this column. The fund did own shares of Baidu as of the end of January. For a full list of the stocks in the fund as of the end of January, see the fund’s portfolio here.