As I put fingertips to keyboard today, I'm overwhelmed by a Groundhog Day sort of feeling. Am I really penning a bear argument on Apple (NASDAQ:AAPL) again?

A bit of history
Way back in February 2006, we held a similar duel on Apple, in which my Foolish colleague Tim Beyers played the bull, and I the bear. I made the centerpiece of my argument the growing consensus that Apple was overvalued, as calculated by yet another Fool, Nathan Parmelee; by Tim himself; and -- of course -- by me.

Back then, Tim called Apple "richly valued by almost any measure" (and remember, he was arguing for the stock). Nathan even put a number to the overvaluation, arguing that at $87 per share, Apple could be 30% overvalued. To justify that price, Nathan suggested the firm would need to grow "20% a year for the next five years, 10% for years six through 10, and 5% for years 11 through eternity," and that falling short would precipitate a significant fall in price. (By the way, all this was before Apple reduced its earnings guidance, and before it discovered "irregularities related to the issuance of certain stock option grants made between 1997 and 2001.")

Enough history. What about today?
Good question. And I'd answer that the more things change, the more they stay the same -- at least with respect to Apple being overpriced. Regarding the business, I'll grant that the company has an impressive portfolio of products, from iMacs and iPods today to iTVs, iPhones, and for all I know, iMicrowaves and iVacuumCleaners tomorrow.

But put the press releases aside for a moment and focus on the numbers. Ask any value investor whether a hypothetical stock trading at 39 times earnings, with long-term growth projected at 20%, is a bargain, and you'll get laughed out of the room. It's only when the name "Apple" is substituted for "hypothetical" that investors become willing to suspend their belief that valuation matters.

But it does
Personally, when I look at those numbers -- 39 P/E, 20% growth, PEG of 2.0 -- I recoil in horror. "Too high," I cry. Even so, let's take a closer look at the valuation on Apple, and see what expectations investors have built into the stock price.

Unfortunately, thanks to Apple's stock-option backdating imbroglio, the firm hasn't filed a cash flow statement since May 2006 (and that one showed the firm running free-cash-flow negative for the first fiscal half). Lacking accurate cash flow statements, I cannot reproduce Nathan's free-cash-flow-based calculations. But the company has filed "preliminary" earnings reports, showing that it's generated net profits of roughly $2 billion over the last 12 months. Using those GAAP net profits as a proxy for Nathan's free cash flow, and plugging the numbers into Motley Fool Inside Value's discounted cash flow calculator, here's what I came up with.

To calculate what expectations investors have priced into Apple's stock, I used a generous 11% discount rate to approximate the growth that an investor could receive from investing in the S&P 500. I plugged in the firm's $2 billion in trailing-12-month earnings, subtracted Apple's net cash per share from the share price, and hypothesized possible growth rates for the company. Result: For Apple shares to be worth the $88 and change they're currently selling for, the company needs to grow its reported earnings at 20% per year for the next five years, 10% for the five years following that, and 3% from then to eternity.

Doable? Perhaps. After all, Apple exceeded 20% growth in each of the last three years. But that was still "iPod growth," in which it created a new market and faced only weak competition within it. Going forward, the firm will encounter entrenched competition to its iPhone from the likes of Nokia (NYSE:NOK) and Samsung. And in the TV set-top box market, it's coming late to the race, trailing Motorola (NYSE:MOT) and Cisco (NASDAQ:CSCO). Personally, I doubt Apple can continue growing at 20% as its iPod market matures and it struggles to break into existing markets against well-funded, established competitors.

Foolish takeaway
Unless it does grow at 20%, Apple is overpriced.

Wait! Think you're done? You're not! Go back and read the other arguments, then vote for the winner of this Duel.

Fool contributor Rich Smith has no position, short or long, in any company named above. The Motley Fool has a disclosure policy.