## Tuesday, January 31, 2012

### Mac: The Limits to Growth (Part 2)

To give full growth to that which still doth grow?

(this post is a continuation of this one)

If you haven't read the first part of this exercise, please at least skim through it so you can take better advantage of whatever insights might come from the analysis presented here.

I'm going to try to observe the evolution of the size of customer installed bases, which should gradually expand (or contract) in typical s-shaped patterns (aka sigmoid, logistic or other similar functions) when plotted over time. This derives from the notion that significant, long-term changes in customer adoption driven by innovative technologies require time to play out, as different segments of customers react differently to change, even assuming immediate information transfer about the innovation (which is not the case even in the internet age).

I'll tend to focus the charts around easily visualizing the yearly variation of the customer bases considered (y' continuously but ∆y given our discrete data) which should roughly fit a bell shaped curve. The shapes don't need to be exactly as the figures shown previously since those were just two very simplified examples given arbitrary theoretical assumptions on how the relative growth rate y/y should moderate as y gets bigger (notice the subtle distinction between y'/y=relative rate of change refers to the continuous modeling notation and "y/y=year over year"or "q/q=quarter over quarter" as the discrete modeling shorthand for the same measure).

So, for this second part I'll start with a broad historic view of all computing, and later dig into the adoption of traditional personal computers highlighting Apple's participation of such adoption, while aiming to give some perspective on the Mac's potential opportunity for expansion within that market. I'll leave a more detailed scrutiny of the recent mobile revolution for a later post.

## Sunday, January 29, 2012

### Apple: The Limits to Growth (Part 1)

‘Rule Forty-two. All persons more than a mile high to leave the court .’
Everybody looked at Alice.

"Population, when unchecked, increases in a geometrical ratio, Subsistence, increases only in an arithmetical ratio."
–Thomas Malthus

"Evolution is the result of a sequence of replacements."
–Elliot W. Montroll

Over the last 8 years Apple's revenue has grown from \$6.6b in calendar 2003 to \$128b in calendar 2011, a 19.4x increase, or an annualized compound rate of 45% per year. Most astonishingly, EPS (including some substantial share dilution) has grown from 13 cents in 2003 to a whopping \$35.11 in 2011, a 270x increase, or annualized to a compound rate of 101% per year. That's more than the equivalent of doubling every single year for eight years (2^8=256 times).

In light of such an impressive long-term performance, last quarter's 73% and 116% Y/Y growth, in revenue and EPS respectively, may seem like par for the course. Indeed, this is the way many "savvy" yet uninformed investors characterize Apple and AAPL: as a momo growth stock bound to fall off a cliff (so many examples from last year: NFLX, RIMM, FSLR, APKT, SINA, just to name a few) as soon as the scorching growth cools down a bit (and it will sooner or later, that's an undistputable fact).

## Monday, January 9, 2012

### Fiscal 1Q 2012 Final Estimates

Apple shares today are flirting around the record all-time intraday high price of \$426.70, yet that still represents a record low valuation of 8.6 times my forward-looking EPS estimate (6.6x ex-cash).

A cash balance of \$409 per share is estimated by June 2016, and \$432 by the end of that Fiscal Year in September 2016, still surpassing the current market price within 5 years from now (this assumes no dividends so if you're reading this in 2016 remember to add back any of those plus interest).

As for the most recent past, and immediate future:

```3mo ending Dec-2011   Rev(\$M)   EPS(\$)
-------------------   -------   ------
Apple guidance         37,000     9.30
Analysts consensus     38,280     9.87
Deagol estimates       41,895    11.58
```