Is Apple undervalued at $260?

Yes, says a Romanian mathematician. But not as much as Microsoft.

Having run-up an even $100 (62%) over the past year, it's hard to think of Apple  as a bargain at $259.10 a share. But that's how you should look at the stock, according to a historical analysis of Apple's share price sent to us over the weekend by Nicolae Mihalache Ciurdea, a Romanian mathematician who teaches at the University of Paris and was one of the blogger-analysts who participated in last week's earnings smackdown.

He charts Apple's (AAPL) performance over the past 12 quarters using a series of criteria, the most familiar being its trailing price-to-earnings ratio, which fell during the financial crisis from a high of 51.5 in Q4 2007 to a low of 12.8 in Q1 2009 before recovering to just under 19.6 today.

But he quickly moves beyond P/E to more sophisticated measures, namely

• P - $/E = The ratio of share price minus cash holdings to earnings
• PEG = Price over earnings divided by annual growth rate
• P - $EG = PEG after Apple's cash holdings are taken out of the share price

The last two criteria, he argues, are the best way to measure the value of a stock, because a company that is growing rapidly and has a huge cash hoard should be more valuable to investors than one that isn't growing and carries a lot of debt. Historically, a PEG (or P - $EG) less than 1 is considered undervalued.

That sounded reasonable to us. So we took Ciurdea's analysis one step further and applied it not just to Apple, but also to Google (GOOG), Amazon (AMZN), Hewlett-Packard (HPQ) and Microsoft (MSFT). We used Friday's closing price and the most recent quarterly earnings to measure growth year over year.

Can you guess which of the five stocks, by this measure, is the most valuable, and which the least? Answers below the fold.

All five stocks have PEGs below 1, so can be considered undervalued.

But measured by P - $EG, Microsoft at $25.81 is the best bargain and Google at $490.06 is the worst.

Apple is close behind Microsoft -- twice as valuable at $259.94 as HP at $46.5 and three times as valuable as Google.

UPDATE: At the request of several readers, I've taken another crack at the spreadsheet, this time using forward-looking EPS and P/E ratios, cash and marketable securities (not just cash) and long-term growth estimates from Thomson Financial. Here's what that looks like:

In this version -- which uses different data than Ciurdea's model --  things have tightened up considerably. Google has zoomed ahead of both Apple and Microsoft, and Amazon has moved into overvalued territory.

In the end, Daniel ("deagol") Tello, who helped me work through several iterations of the spreadsheet -- each with very different results -- had this to say:

"I'm sure by now you realize how futile this exercise is. The conclusion of who ends at the top or the bottom in the PEG column is only as good as analysts consensus for next year's EPS and the LT growth. AMZN and GOOG used to beat analysts handsomely, except for the last couple of times when they've come soft or even missed. HPQ and MSFT tend to beat only by a small margin.
AAPL is almost always a huge blowout. Consecutively for the last 27 quarters. That's almost 7 years."

See also:

• Earnings Smackdown: The best and worst Apple analysts
• Ballmer's is still bigger than Jobs'
• Apple blow-out: Profits up nearly 78%

[Follow Philip Elmer-DeWitt on Twitter @philiped]