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Social-media enthusiasts with eyes on the stock market bought into Facebook's initial public offering May 18. Now those who clung to the stock are wondering: When will shares of Facebook climb back to their IPO price of $38 a share?

My answer: About 32 quarters -- or eight years.

Here's why:

I did an analysis August 1, when Facebook closed at $20.88 a share. That's right about where the stock is currently trading. This puts Facebook's price-to-earnings ratio based on the last 12 months (LTM) earnings at 72.4.

I compared this to the median P/E -- also based on the last 12 months of earnings -- of Apple, Yahoo, Microsoft, Google, and LinkedIn, a composite of tech leaders. Apple and Google have proven revenue-growth stories, and LinkedIn (like Facebook) is a newcomer as a reference point. Like Facebook, Yahoo has a huge user base and struggles with the amount of revenue it makes off each user. For this composite of tech leaders, the median P/E ratio is 18. So let's use a P/E of 18 as a benchmark.

That's when I arrived at our first piece of sobering news: If Facebook were valued comparably to this group on a P/E basis, its stock would be $5.22 a share, not $20.88.

Facebook's earnings-per-share will grow at 26.2 percent per year, which is the projection from Capital IQ .

Profit margins stay where they are.

Assuming those two things happen, for Facebook to get its sales and earnings at a level that justifies a $38 stock, it will take 32 quarters, or eight years.

The math is simple: Facebook needs to increase its current earnings per share of 29 cents to $2.11, a more than sevenfold jump. And it would need the same sort of annual revenue boost, from $4.3 billion to $31.3 billion. If it pulls that off, our stock price of $5.22 (based on that 18 P/E) returns to $38 ($5.22 x 7.28).

Let's look at a key metric, Facebook's average revenue per user, or ARPU. As of the latest quarter, Facebook's ARPU was $1.28 in the last quarter. Annualized, that would be $5.12, a penny increase from the ARPU of $5.11 it reported at the end of 2011.

But to meet the $31-plus billion in annualized revenue, the company would either need to have 6.1 billion users at the current ARPU, or make a lot more money off each user -- theoretically increasing ARPU to $33.15. More realistic would be a combination of an increase in ARPU, plus an increase in users to meet that $31.3 billion mark.

What does this mean for Facebook and its investors? While the U.S. economy is facing a possible fiscal cliff , Facebook is facing a tsunami. Here's why: