tag:blogger.com,1999:blog-4057266811973629846.post2172594899850777489..comments2024-07-02T09:17:38.734-04:00Comments on deagol's AAPL model: Mobile Apple: The Limits to Growth (Part 3)Daniel Tellohttp://www.blogger.com/profile/18356162909901960817noreply@blogger.comBlogger24125tag:blogger.com,1999:blog-4057266811973629846.post-12046018091293451362012-04-20T00:42:17.219-04:302012-04-20T00:42:17.219-04:30"Here's an eyeball fit of the two curves ..."Here's an eyeball fit of the two curves for the iOS adoption data up to Dec-2011, assuming saturation at 1b for both"<br /><br />Daniel, That is quite impressive. I have to learn to use WolframAlpha like that. Great work. In this little corner of the web, true innovative analysis is going on. Thanks Daniel.<br /><br />Just as a sidebar, I saw some growth curves for Amazon. My first reaction is,"Ah..tehre is an S curve"!!<br /><br />-ChandraAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-4057266811973629846.post-41829822050817600112012-04-16T11:08:11.093-04:302012-04-16T11:08:11.093-04:30Great reply to my query, Daniel. Excellent analysi...Great reply to my query, Daniel. Excellent analysis and very helpful. Let me mull over this and digest. Thanks.<br /><br />-- ChandraAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-4057266811973629846.post-22869549054297400862012-04-12T13:44:32.243-04:302012-04-12T13:44:32.243-04:30Daniel, what can I say, just awesome. Quite thrill...Daniel, what can I say, just awesome. Quite thrilled that you took the time to write a detailed response to my question. You did see through correctly a few things I had in mind when I asked that question. I understand what you are saying and that makes sense. Yes, it helped a lot. I will digest further and if I have any further questions/comments, I will post here. You can consider elevating the above three part comments as addendum to the main article. Thanks.<br /><br />--ChandraAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-4057266811973629846.post-36588784831047073872012-04-11T11:25:05.041-04:302012-04-11T11:25:05.041-04:30Having said all that, I'll try to illustrate t...Having said all that, I'll try to illustrate the answer to your question by graphing some sensible fits to the historical iOS adoption data (perhaps I should've started with this). The biggest problem in choosing Gompertz or logistic or any other model to the data <i>before</i> the inflection has occurred is that it's practically impossible to differentiate between them until you're very close to the inflection, or already there. <a href="http://www.wolframalpha.com/input/?i=Plot%5B%7B1000*E%5E%28-E%5E%28.33%282013+-+x%29%29%29%2C+1000*%281+%2B+E%5E%28.75%282013.5+-+x%29%29%29%5E%28-1%29%7D%2C+%7Bx%2C+2007%2C+2020%7D%5D" rel="nofollow">Here's an eyeball fit</a> of the two curves for the iOS adoption data up to Dec-2011, assuming saturation at 1b for both (Gompertz in blue and logistic in red). The logistic fit finds the inflection in the middle of next year while the Gompertz finds it by the end of this year. Here the Gompertz curve is a better fit for those comparatively small differences observed up to 2009.<br /><br />If we relax the 1b max capacity constraint, and instead fix the inflection of both having already happened by the end of last year, then there's <a href="http://www.wolframalpha.com/input/?i=Plot%5B%7B657*E%5E%28-E%5E%28.4%282012+-+x%29%29%29%2C+483*%281+%2B+E%5E%280.92%282012+-+x%29%29%29%5E%28-1%29%7D%2C+%7Bx%2C+2007%2C+2020%7D%5D" rel="nofollow">this possibility</a> in which the final saturation for Gompertz is 657m (e*241.6) while for the logistic it's only 483m (2*241.6).<br /><br />As you can see by these two arbitrary examples, any number of decent fits can be found before or even a bit after the inflection point occurs. The reason for this is that up until shortly before the inflection all we see is simple exponential growth, and neither model can decisively discriminate out of it. Which means there's no reliable way to estimate the maximum saturated level of adoption, nor the real shape of the curve until after the inflection is observed. This fact gives away the flaw in any analyst's pretense in currently projecting a limited growth model solely from internal historical adoption data. And that's precisely why in my analysis I rely mostly on external market share penetration assumptions to inform the possible saturation levels of each product line, and arbitrarily aim inflections around the end of next year to try to entertain a bit of the pro analysts' collapsing growth predictions by then.<br /><br />Phew, that sure was a mouthful! Hope it helped.Daniel Tellohttps://www.blogger.com/profile/18356162909901960817noreply@blogger.comtag:blogger.com,1999:blog-4057266811973629846.post-40492856235331106312012-04-11T11:18:53.189-04:302012-04-11T11:18:53.189-04:30Third, under the methodology I've used in thes...Third, under the methodology I've used in these 3 articles (strict 2yr replacement cycle, see other comments here for explanation) the iOS installed base as of Dec-2011 is 241.6m and not 300m. Still, it's quite likely that we get to a 350-400m installed base by the end of this year. So if we assume a $1b saturation capacity and a Gompertz curve then that's still a likely inflection within this year.<br /><br />However, the assumption that the max carrying capacity of iOS is 1b devices is enough to fix the max earnings extracted from such a saturated market, regardless of the shape of the curve to get there, and which similarly fixes the stock price given some P/E ratio. In other words, if you assume iOS saturation is 1b, and that implies zero EPS growth and a constant P/E from then on, then the stock price at that point would be the same regardless of Gompertz, logistic, or any other diffusion model used to get there.<br /><br />The only difference is that the slowdown in adoption for the Gompertz model is much more gradual than for the symmetrical logistic model. The time it takes to reach saturation after the inflection is 2 to 3 times as long as the time of increasing adoption up to the inflection. This may allow sufficient time to devise new product and/or service strategies to further monetize the still growing installed base after the inflection.<br /><br />Finally, consider the earnings power of commanding a huge installed base (even if saturated) which is conditioned into a frequent and loyal replacement cycle. Even if you're right about the stable P/E (at 12 or 10 or whichever figure the market decides to apply), such a loyal customer base would provide a practically unlimited flow of "E" into the P/E equation. If the share price were to remain constant, as your premise implies, that means all of the "E" would have to be distributed through dividends to prevent the cash balance from accumulating indefinitely and eventually surpassing the share price, which would be absurd.<br /><br />continues in next comment...Daniel Tellohttps://www.blogger.com/profile/18356162909901960817noreply@blogger.comtag:blogger.com,1999:blog-4057266811973629846.post-91011662822212352212012-04-11T11:18:03.631-04:302012-04-11T11:18:03.631-04:30Ok there's a few assumptions in your reasoning...Ok there's a few assumptions in your reasoning that need to be made explicit, just to make sure we're clear on your argument. This comment will be pretty long so apologies in advance.<br /><br />First, you assume the max P/E is tied to the max iOS adoption. This would imply that iOS adoption is the sole driver of earnings growth. It may be a very good approximation currently, but things can change. I would suggest that in the extreme hypothetical case that iOS reaches 100% of the world's population (zero or minimal adoption from then on), Mac OS X would not have reached even half, and most likely no more than 25% of the traditional PC worldwide installed base, and thus that could be an important growth potential to tap from even in the face of no growth from iOS. Obviously new product categories would be another source, and likely would have stronger needle-moving power than the old Mac line in reigniting growth after iOS saturation.<br /><br /><br />Second, it's not the case that P/E expansion must go on as long as customer adoption rate is increasing, nor is it the case that the P/E ratio should start declining when adoption slows down. Curiously, for all of 2010 and 2011 there was PE compression despite accelerating iOS adoption and EPS growth rates. Most recently the P/E ratio has recovered just in time for a most likely deceleration of EPS y/y growth over the next couple of years. So the opposite of your assumption may seem to be the case? I don't know. Obviously other factors are in play.<br /><br />In my preferred approach there isn't any long-term consistent directionality in P/E in relation to increasing or slowing growth, but instead I assume that a 10 P/E (or use your 12 or any other that may best fit the data) is the fair long-term multiple when assuming some sustainable long-term EPS growth rate. Then any deviation from that "fair" multiple by the market, regardless of the current short-term growth cycle trend, would be an opportunity to adjust one's exposure to AAPL and benefit in the long term.<br /><br />One distinction that needs to be made is between the relative y/y growth rate and the annual incremental adoption (the derivative of the s-shaped curve). These are not the same, and neither would their peaks coincide. In fact for the simplest logistic and Gompertz theoretical models in my examples, the relative y/y growth rate is always declining, so the peak occurs at the very first growth point computed (the second year).<br /><br />There are more flexible theoretical generalizations of the logistic and Gompertz dynamics which allow for relative growth rates that expand for some time before declining, with a max rate of growth inflection. It turns out that this max rate of growth inflection moment always occurs before the inflection on the incremental adoptions (the derivative).<br /><br />In other words y/y growth rates for EPS or at least unit sales peaking might be taken as a warning of an impending inflection of adoption (though it may be avoided), which would in turn depress investor enthusiasm toward the stock, impacting the P/E ratio, all of it without any actual inflection in incremental adoption having occurred and possibly never occurring (for example avoided through an incremental product refresh that boosts the growth rate back to investors' expected levels).<br /><br />continues in next comment...Daniel Tellohttps://www.blogger.com/profile/18356162909901960817noreply@blogger.comtag:blogger.com,1999:blog-4057266811973629846.post-555203569382100312012-04-09T23:27:47.707-04:302012-04-09T23:27:47.707-04:30THanks Daniel. So, if Apple iOS adoption follows G...THanks Daniel. So, if Apple iOS adoption follows Gompertz, then the peak addition will happen this year. That sounds too soon. What do you think? I did not realize Gompertz predicts a considerably lower value for the inflection point than Gaussian<br /><br />Which one fits iOS adoption better, Gompertz or Gausssian? More than just theoretical, that inflection point may also signify as a point of (approx) the maximum P/E ratio for Apple before it starts a steady contraction to 12. In my mind that 12 will be the PE when the growth curve reaches the right most point.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-4057266811973629846.post-18509062901017651992012-04-09T20:46:46.759-04:302012-04-09T20:46:46.759-04:30That's correct if you assume the bell curve is...That's correct if you assume the bell curve is symmetrical (e.g. logistic or gaussian). If instead it ends up looking like the right-skewed Gompertz curve, then the peak additions to the iOS installed base would occur at around 368 million (1 billion/e).Daniel Tellohttps://www.blogger.com/profile/18356162909901960817noreply@blogger.comtag:blogger.com,1999:blog-4057266811973629846.post-45371441385697391502012-04-09T19:17:45.507-04:302012-04-09T19:17:45.507-04:30Daniel, amazing work. I learned a lot from the thr...Daniel, amazing work. I learned a lot from the three parts.<br /><br />One question. Let us assume 1 Billion iOS devices as the top of the S curve. Can I then assume that 500 Million as the mid point of the first derivative bell curve?<br /><br />If so, we are currently at 300 million. In 18 months they can reach 500 Million. Does that then point to the peak growth point for iOS?Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-4057266811973629846.post-17152612542020864442012-03-27T13:28:42.488-04:302012-03-27T13:28:42.488-04:30Daniel,
Amazing oeuvre. Many may have the instin...Daniel,<br /><br />Amazing oeuvre. Many may have the instinctual notion that Apple is many years away from slowing down, but here you have provided statistical proof. <br /><br />Now stop teasing us and give us your fair share price estimate for the next 5 years. We know the market will lag 2 to 5 years behind the fair value, but eventually will get there.<br /><br />The biggest disruptive threat I see is the antimonopoly busybodies in US/Euroland forcing a break up of the company, and not understanding that the company is OSX/iOS.El-Visitadorhttps://www.blogger.com/profile/08823897085882597971noreply@blogger.comtag:blogger.com,1999:blog-4057266811973629846.post-74425536102337858362012-03-11T13:40:06.913-04:302012-03-11T13:40:06.913-04:30Daniel... my apologies. You are correct in your co...Daniel... my apologies. You are correct in your comments. You see I first read about LOL in part 1 of your blog and then I read several other articles by other authors during that period. By the time I read part 2 I had forgotten about first reading about LOL in your part 1 blog. Oh, the aging brain is a terrible thing. Personally I can't see anything stopping Apple for a long time. The new ipad launch has generated initial numbers that are off the charts pushing back pre-orders. We'll see new thinner Macbooks, iphone 5, possibly new MacPros all this year. I can only see another amazing year of growth.JavaJackhttps://www.blogger.com/profile/03263943961526019485noreply@blogger.comtag:blogger.com,1999:blog-4057266811973629846.post-60353594711080651022012-02-29T20:30:26.978-04:302012-02-29T20:30:26.978-04:30Jack, I'm sure you saw my comment about the so...Jack, I'm sure you saw my comment about the so called LOL numbers in <a href="http://aaplmodel.blogspot.com/2012/01/apple-limits-to-growth-part-1.html" rel="nofollow">part 1</a>.Daniel Tellohttps://www.blogger.com/profile/18356162909901960817noreply@blogger.comtag:blogger.com,1999:blog-4057266811973629846.post-47651871337161857902012-02-25T12:46:21.375-04:302012-02-25T12:46:21.375-04:30What do you think about the Law of Large Numbers? ...What do you think about the Law of Large Numbers? Seems like everyone is trying to get press by putting Apple down these days.JavaJackhttps://www.blogger.com/profile/03263943961526019485noreply@blogger.comtag:blogger.com,1999:blog-4057266811973629846.post-20128422007851798762012-02-13T21:22:50.967-04:302012-02-13T21:22:50.967-04:30Once again, I am in awe of your work.
Not only ...Once again, I am in awe of your work. <br /><br />Not only is it telling of Apple's massive future growth, it is so obviously low-balled by the beyond-reasonable-low estimated consensus estimates, which you so obligingly employed.<br /><br />Your closing comment, of your own conservative 2013 estimated growth rate of 3# TIMES the street's consensus, leads to growth that boggles the mind.<br /><br />If I were but young again, I'd be urged to have almost all my holdings in AAPL, while reminding Britney that the cause of most growth spurts is <i>stimulating experience</i>!JohnStetnoreply@blogger.comtag:blogger.com,1999:blog-4057266811973629846.post-5238619433461893332012-02-12T17:58:22.228-04:302012-02-12T17:58:22.228-04:30Anon #2, thanks for the appreciative words. Glad y...Anon #2, thanks for the appreciative words. Glad you like it.<br /><br />Anon #3, yes log scale can reveal some things but can hide other things, the patterns are just different and require extra attention to interpret correctly. Some people do get confused with the extra layer of abstraction. I mainly went with linear scale to show the bell and sigmoid patterns as described in <a href="http://aaplmodel.blogspot.com/2012/01/apple-limits-to-growth-part-1.html" rel="nofollow">part 1</a>.Daniel Tellohttps://www.blogger.com/profile/18356162909901960817noreply@blogger.comtag:blogger.com,1999:blog-4057266811973629846.post-36073741586880713222012-02-12T17:49:57.618-04:302012-02-12T17:49:57.618-04:30Unknown, I do try to keep them simple, but yes I s...Unknown, I do try to keep them simple, but yes I sometimes tend to overlay too much on the same chart. There's not much complex data in Apple's financial reports. Perhaps you might like <a href="http://aaplmodel.blogspot.com/2010/12/apple-financial-floor-plan.html" rel="nofollow">this one</a> from about a year ago?Daniel Tellohttps://www.blogger.com/profile/18356162909901960817noreply@blogger.comtag:blogger.com,1999:blog-4057266811973629846.post-27038565943585564282012-02-12T17:43:51.700-04:302012-02-12T17:43:51.700-04:30Anon #1, the 'new' user data is directly d...Anon #1, the 'new' user data is directly derived from the sales data and the 5y life cycle rule: the sales from 5 years ago (or 2 years for iOS or adjust with your own) get flagged as replacements, and any excess in the current quarter (or deficit) is flagged as 'new' (or defections) i.e. just subtract the 5-yr old sales from the current sales.<br /><br />That is of course a very simple rule, but the resulting estimate doesn't contradict what Apple has always said, that they get <i>more</i> than 50% new-to-Mac in their retail stores (I'm getting mid 67-68%).<br /><br />The reason it may come out lower in Apple's survey data could be that kids who've originally received hand-me-down Macs from their parents or older siblings and later go to a store and upgrade wouldn't characterize themselves as new-to-Mac when the store employee asks them, but under this model, that being their first direct purchase indeed makes them a new user.Daniel Tellohttps://www.blogger.com/profile/18356162909901960817noreply@blogger.comtag:blogger.com,1999:blog-4057266811973629846.post-13968901449034828202012-02-12T15:54:37.107-04:302012-02-12T15:54:37.107-04:30Great analysis. Seems like using a log scale would...Great analysis. Seems like using a log scale would be more revealing.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-4057266811973629846.post-41291147788854445432012-02-12T15:42:19.277-04:302012-02-12T15:42:19.277-04:30Daniel, this is utterly fantastic work you have do...Daniel, this is utterly fantastic work you have done here - worth every minute you put into it. There are people like me who appreciate this kind of analysis more than we can express, people who are just as into it as you are, but lack your analytical skills.<br /><br />Kudos!Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-4057266811973629846.post-36869148967939102242012-02-12T12:23:17.717-04:302012-02-12T12:23:17.717-04:30I love the analysis. I would love to see simpler ...I love the analysis. I would love to see simpler charts, based on complex data. Very tough request, I realize.<br /><br />You've probably seen this, but here is an example.<br /><br />http://www.edwardtufte.com/tufte/postersUnknownhttps://www.blogger.com/profile/16189533526806338115noreply@blogger.comtag:blogger.com,1999:blog-4057266811973629846.post-44226701004573263962012-02-12T09:50:23.167-04:302012-02-12T09:50:23.167-04:30Those are incredible charts! Works of art.
I do ...Those are incredible charts! Works of art. <br /><br />I do think I’m missing something however. What is the source of the ‘new’ user data? I have always thought that each quarter new users make up about 50% of the sales. Yet, when I look at your stacked bars, I see a far greater proportion of Macs sales coming from new users? Thanks for the explanation.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-4057266811973629846.post-7003924919701709502012-02-11T17:12:24.936-04:302012-02-11T17:12:24.936-04:30Thanks Walt. I agree with the uncertainty aspect, ...Thanks Walt. I agree with the uncertainty aspect, which is why I try to remain on the conservative side.<br /><br />I believe what you're seeing for the upcoming iPad upgrade cycle is not only the smoothing effect of the trailing 4 quarters aggregation (which for the initial points does give some inconsistent comparisons), but also the strict enforcement of the 2-year lifecycle condition for upgrades. Under this simple replacement rule, only those units sold precisely two years earlier get to be upgraded if there's enough sales in the current period. If there's not enough sales to cover the 2-year-old sales then you get declines in the installed base as in the iPod case.<br /><br />So for the iPad upcoming upgrades, by the end of this quarter there will be zero iPads that are 2 years old. By the end of next quarter in June, there will be exactly 3.27 million (sold in 3Q2010) units that are 2 years old, and thus all of them will get replaced because Apple will sell way more than that, and the excess is categorized as new users.<br /><br />So, you see the total height of the bar for the current quarter (2Q2012) at about 47m units, that is for the trailing 4 quarters up to March, which implies about 11m for this quarter alone. There are no replacements being modeled since every single iPad bought up to March is less than 2 years old. Then you get to the next stack combined height at a little over 54m over the trailing 4 quarters up to June, which implies about 17m for the June quarter alone. Of those 54m, only the 3.27m that became 2yo are up for replacement, thus you get the slightly over 50m in new users over the 4 quarters up to June.<br /><br />Notice then you're seeing a comparison of 4 quarters worth of new users and only one quarter worth of upgrades stacked on top, when the true quarterly comparison of new vs. replacements is actually about 14m new vs. 3m replacements. Give it another year and the comparisons become consistent being all annualized replacements: 1 year worth of sales from 2 years prior against 1 year worth of current (ttm) sales.<br /><br />Of course, in reality much more than 3m iPad users will actually upgrade by June, just as many original iPads were upgraded to iPad2 regardless of them not being "old enough". But then you have some others who wont upgrade after 2.5 years or 3 years. Over the long term, the true average lifecycle would come through the data (simply divide the estimated installed base by the estimated annual replacements in the following year and you get the implied average lifecycle) and then one could consider recalibrating the simple 2y assumption if needed.<br /><br />As described in part 2, this is quite a simplified rule for modeling upgrades and installed base size, but it's still quite useful particularly over longer periods of time. I wanted to keep things simple.<br /><br />Hope this helped.Daniel Tellohttps://www.blogger.com/profile/18356162909901960817noreply@blogger.comtag:blogger.com,1999:blog-4057266811973629846.post-28551765499817126202012-02-11T15:33:25.844-04:302012-02-11T15:33:25.844-04:30First: GREAT work!
Long term matters a whole lot,...First: GREAT work!<br /><br />Long term matters a whole lot, but I'm glad you cut off the projections before they could dominate the visuals. There are a LOT of issues around substitutions — e.g., whether biz types who love iPads might go for WinSlates — and straight-up competition — esp the increasingly hardball patent litigations — that would require some huge confidence bands around the numbers.<br /><br />But the most curious thing to me is your oh-so-conservative baseline number for short-term iPhone and iPad growth. Per your insights above, Apple has been building out its infrastructure in China. Looks to me that in a quarter or two, US share of iPhones could fall from ~ 35% to ~25% in the best possible way: an explosion of new international users. And regardless of whether recent rumors are correct, an upgraded iPad would seem inevitable, and with it, another huge explosion or replacements atop a “fast as they can make 'em” new user curve.<br /><br />Or am I misunderstanding the charts' Trailing 4Q feature? If you showed Quarterly at Annual Rate, would your data show this?Walt Frenchhttps://www.blogger.com/profile/00873789914522579055noreply@blogger.comtag:blogger.com,1999:blog-4057266811973629846.post-78789390919672706952012-02-11T12:04:09.921-04:302012-02-11T12:04:09.921-04:30Thanks Daniel. It's very exciting to watch App...Thanks Daniel. It's very exciting to watch Apple grow and read your analysis. Thanks for quoting Britney Spears. Made me laugh.JavaJackhttps://www.blogger.com/profile/03263943961526019485noreply@blogger.com