At least that’s what the New York Times reports as being the current joke in Silicon Valley. But a joke didn’t derail the largest PC manufacturer’s business. HP’s (NYSE:HPQ) CEO Leo Apotheker says that “the tablet effect is real.” Now they’ve abandoned the tablet business altogether. He wants to say the iPad effect is real, but he simply can’t say that word.

I’d like to recount two tales about the iPad. One is about its (short) history, its place in the market today and its future. The second is about numbers, from basic mathematics to those kinds of numbers that directly help investors’ decisions.

**Qualitative tale**

These are very exciting times in the tech industry. Innovation and economic disruptions seem to accelerate. The PC matured in about two decades. The Internet went mainstream in about a decade. The iPod took about five years to change the way we buy and listen to music. In just two years, the iPhone redefined the smart phone, how mobile software is created, distributed and used, and pushed most of the established phone makers into low or negative profit margins. And it’s eating into established markets, MP3 players and handheld game consoles.

In about five quarters, the iPad defined a new industry and pushed the largest PC maker out of its decades old business. Additionally, if the iPad is considered a portable computer, Apple (NASDAQ:AAPL) takes the crown in worldwide market share.

**The iPad is taking us into ****the post-PC era****. **The competition has been warned since the beginning. The press and competitors dismissed the iPad as an ill-named useless fad, appealing to fanboys only. Read some entertaining quotes here, here and here. Come the second and third quarter of sales (and the by-then evident decline of the netbook), everybody jumped on the bandwagon of the “tablet market.” The saga of “killers” (iPod killers and iPhone killers) was on again. Not only it was too late, but they attacked it wrong: USB ports, card readers, Adobe Flash, GHz, MB and GB. There were no “orifices” to push their *productions* into the hands of users. There was no ecosystem to support their tablets: accessories, music, books and apps, apps or apps. Apple solved the chicken-and-egg paradox initially with iPhone apps and the iTunes store.

Some promising tablets were released only recently. If the iPad didn’t already exist, they’d probably be excellent first iteration portable devices, but they all pale in comparison to the original. People don’t want tablets, they want iPads. Only three months ago, HP was going to be number one plus in the *tablet market*. And some manufacturers are still in a state of denial.

**Present market share estimates** put the iPad in the 60% to 95% bracket. A careful analysis of the distinction between shipped and sold products shows that we are very close to that upper bracket. It dominates the enterprise market. It’s the fastest growing gaming platform. The iPad is going to places the PC never dreamed about. And it appeals to every age, from toddlers to 99-year-olds.

**The best is yet to come****. **As observed in December 2010, there still isn’t much of a “tablet” market. Some analysts think Apple will be able to hold a tight grip on the market it created for a long time. The iPad is *cannibalizing *the PC market (which now sees more than 300M annual sales) and extends far beyond it. It may well exceed half a billion units in annual sales eventually.

**Quantitative tale**

We’ve seen *explosive* growth patterns in the tech market place. It turns out that this isn’t limited to tech nor to markets in general. Many natural, social and economic *phenomena* exhibit an *exponential* evolution—until some external factor stops it. For example, this factor may be limited space or nutrients for a microbial population, a disruptive technology or idea that renders obsolete the dominating meme, or market saturation for the sales of a product. I’ll try to explain why they all share this behavior using basic mathematics. Those who don’t enjoy the subject are advised to skip the next paragraph.

**Back to basics.** Let’s consider a quantity that grows with time. Call it a function f(t) of time (t). Its growth is its derivative f’(t). For many processes, the growth is proportional to the present size. (In cellular division or rabbit reproduction, for example, the offspring count is comparable with the size of the population; the spread of a meme in society is done by those who are already “infected”, etc.) That is, f’(t)=k f(t), where k is the proportionality constant. The only types of functions that satisfy this relation are exponential, that is f(t)=C exp(k t), where C=f(0) is a constant, the initial value of the solution. If we chart this function in logarithm scale, we get a nice linear graph, as log f(t)=kt + log C.

**In practice**, we observe growth curves that look something like this:

It’s quite hard to guess the inflection point, that moment in time when we start climbing the famous hockey stick. Modern spreadsheet software will compute an “exponential trend line” for you, but that’s much harder to believe than extending a linear trend line. So we could simply look at the logarithmic scale graph to get more reliable and reasonable forecasts for growth. We’ll use the iPod and iPhone sales as examples. As both are subject to seasonal variations, it’s better to consider four quarters cumulative sales.

Both iPod and iPhone 12-month cumulative sales are charted in logarithmic scale for the first 14 quarters of data, together with their trend lines (estimated with the least squares method). By mid-2006, the iPod market became saturated and growth slowed down. iPod sales are slowly declining today, mostly cannibalized by the higher margin iPhone (and probably by competing smart phones). The iPod still retains about 70% market share. We observe that during the starting quarters, both graphs diverge from the trend line. We should therefore be very careful analyzing iPad sales.

**iPad sales forecast. **We only have five quarters of data for iPad sales. There’s almost no point of looking at 12-month sales as we’d have only two data points. This will induce further uncertainties in approximating its growth curve. So we’ll try to squeeze the best out of the available data, being careful not to overestimate.

I add a *very* conservative forecast (at least 2M less than my best guess) for the current quarter to have six data points, but also to make up for the tragic Japanese earthquake/tsunami in the March quarter (this serious disruption arrived during the transition to iPad 2). I did quarterly forecasts for about two years and I got quite good at it. I use two trend lines: for all five quarters (green) and for all data points (including my prediction, yellow).

I take the minimum of both results for each future quarter (it turns out it is the green line) to obtain an estimate for the following two years: 73.5M iPads sold in FY 2012 and 176.6M in FY 2013. As we work with the exponential function, small errors are amplified. Also, to account for other risks in the marketplace, I would recommend that investors trim about 20% (the dashed red line in the chart) of these results (even more for option traders who are very dependent on precise timing; 40% discount is charted as the dotted purple line). For the aforementioned reasons, those numbers will turn to be quite imprecise but having a reasonable guidance so early in the game may present a real advantage for the adventurous investor.

For those who want to play with the spreadsheets and do their own estimates, I uploaded the Numbers file here.

**Revenue and profit forecasts.** Apple’s average gross margin is around 40%. Not having reliable data, we may use the same number for the iPad. iPad average ASP is slightly over $640. More than 60% of gross margins end up as profit. We conclude that every iPad brings around $154 as net profit. Discounting forecasted sales numbers by 20%, I estimate that during FY 2012, the iPad will bring $37.6B in revenue and more than $9B in profits. For FY 2013, we have estimates of $90.4B of revenues and $21.8B in profits. At P/E ratios of 12 and respectively 10, using estimated share count of 950M and respectively 965M, the iPad alone would represent about $114 (by the end of 2012) and respectively $226 (by the end of 2013) of Apple’s share price.

Those numbers are staggering, but the iPad is growing faster than the iPhone (steeper slope in the logarithmic chart) and had a much better start out of the gate (recall that we charted quarterly sales for the iPad and annual sales for the iPhone). The iPod was growing even faster but it stated with very low sales. With faster growth and smaller addressable market, it was bound to stagnate sooner. Both the iPhone and iPad are today small fish in large ponds, but the iPad has no known predator. It is bound to develop according to the natural exponential growth for the foreseeable future.

**Disclosure: **I am long AAPL. I leverage my investment with option calls.