Now that the stock has finally broken through the $400 barrier, how high can it go?

Click to enlarge. Source: Seeking Alpha

Last summer, when Apple (AAPL) was trading for $260 a share, we ran an item on some analytical work by Nicholae Mihalache, a Romanian mathematician who teaches at the University of Paris. He had prepared a series of charts tracking Apple's performance using various criteria, from the familiar P/E (price to earnings) ratio to the more obscure P - $EG (the difference between share price and cash holdings per share divided by annual growth rate).

He concluded, based primarily on Apple's PEG (price over earnings divided by growth), which at the time was 0.25, that Apple at $260 had considerable room to grow. (Traditionally, any stock with a PEG less than 1.0 is considered undervalued.)

Mihalache returned to the subject Tuesday, exactly one year later, with an article in Seeking Alpha that asks whether Apple at $400 is still undervalued.

In fact he concludes that, based primarily on the PEG ratio, Apple's shares are even more undervalued now than they were a year ago. The company's earnings over the past 12 months have grown at the rate of 90% per year while its stock is up about 50%, moving Apple's PEG from 0.25 to 0.17.

On that basis he makes some forecasts:

"In order to be conservative and to avoid ridiculously high valuation predictions," he writes, "I will assume further P/E compression (12 and 10) and earnings growth cooling off in 2012 and 2013 (respectively, 80% and 60%). Barring any market meltdown, I predict that one year from now AAPL will be at $550 or more, $650 by the end of 2012, and at least $850 by the end of 2013."

[The stock closed Tuesday at $403.41, up $4.91 (1.23%) for the day, having traded as high as $404.50.]

Mihalache tends to set high bars for Apple. But in our most recent earnings smackdown, in which we compared the Q3 2011 estimates of 48 Apple analysts -- professional and amateur -- Mihalache's were, by a large margin, the best.