Back in April I posted a couple of charts showing how my "fair value" and "target" forecasts compared to AAPL's price history over the last few years. Several readers have asked for an update, and I said I'd do one when AAPL made a credible move to catch up with its fundamentals, which is the basis for my FV and target forecasts. Seeing as AAPL has run about 80 points in 7 weeks, I was also curious to visualize how far towards a fair valuation has this recent attempt taken it.

I found I needed to make some changes to the chart, mainly on the vertical scale. The details from 2006-2007 were getting squished due to the scale now going up beyond $700, so I decided to use a log scale. Because Excel sucks at doing log scales, I've added a few custom labels and gridlines along the axis, which might seem odd if you're not paying attention (not every gridline is spaced equally in visual distance and some not even in the underlying values). Anyway, here's the chart (click to enlarge):

So there you have it, still way undervalued. Now, in case you haven't noticed from all of my quarterly earnings estimates, I should clarify how I come up with these FV and target values. It's quite simple, I have stuck with a 25-times forward-looking multiple on yearly EPS, as that has seemed a good mid-range valuation metric over the years of my analysis, except recently (as noted on the chart).

I also studied some relationships between DCF, PEG, and P/E valuation methods, and concluded that as long as Apple's estimated long-term future growth rate remained above 20%, using a 25 multiple on forward EPS seemed consistent with the more academic valuation methods. Needless to say, over the past few years Apple has in fact grown EPS significantly higher than 20%, anywhere between 40% and 70% (this is all just after the couple of years of iPod hyper-growth of 350% when EPS grew from a very low base). But the market has always remained skeptic of the sustainability of such high growth, and has kept the long-term, next 5 years growth estimate around 20%.

Thus, early on I decided I wouldn't argue with the market on which multiple was appropriate for AAPL, but instead I would try to beat the market by estimating a more accurate forward-looking EPS for the denominator. And this approach has worked relatively well for me, as shown on the graph above.

So, for the FV (the blue points along the blue curve), I take the next four quarters' EPS estimates, i.e. the annual EPS one year in the future, and multiply by 25. For the 12-month targets (the red points along the red curve) I do the same but with the following four quarters, that is, the annual EPS 2 years in the future.

In trying to assess the accuracy, reliability, and effectiveness of my attempts to beat the market, I can identify 3 sources of uncertainty. The chart above attempts to show the end result of the interplay of these three sources of uncertainty, with a clear visual of how my final goals of forecasting AAPL's price are being met (or not). First, the market expectations about AAPL could be wrong. And they have. Consistently. Way wrong. This is why AAPL can be held or tanked for months on end without regards to fundamentals, or how other times it can keep climbing, merely catching up, in the face of uninformed pundits rolling their eyes and flailing their arms in "things can't go up forever!" desperation. There's not much I can do about this, other than to take advantage of the opportunity and hope the market eventually corrects itself.

A second source of uncertainty, much harder to gauge, is that my views about the market's expectations could be wrong (i.e. my valuation methods, choice of multiple, targets, etc.). This is a field mired with land mines and controversy, from academy to practitioners, with wide ranging theories and practices from fundamental to behavioral finance to technical analysis and even esoteric stuff like astrology thrown in for good measure. I can't concern myself with any of it too much.

To me, market valuation is not much different than going to the grocery store and buying bread and milk: you look at the variety of offerings, check the prices, read a few labels, and pick the best deal in your subjective opinion. Some would say that price is always right, since it's the result of the interaction of all the market players coming together and agreeing on the best price. However, price is also always wrong, since it changes every day, every hour, minute and second. So at any given instant, yes that price was right, but the next second it's immediately proven wrong (not to mention in the next quarter, or a year or two, which is the timeframe I'm concerned with).

Anyway, my solution to this infinite complexity is to use a simple multiple, the one I see most consistently applied by the market over a long period of time, and intuitively assess whether any temporary deviation is justified. But that solution might no longer apply even in the long term, as suggested by the comment on the bottom right of the chart. Others have done a great job describing the current problem with AAPL's valuation and possible explanations seem quite elusive. See Asymco's Horace Dediu's excellent research on this over several articles. So I'll leave it at that.

Then there's a third source of uncertainty, the most critical one to me yet very easy to quantify, which makes the basis or inputs for the valuation methodology, and that's my EPS estimates. How certain can I be about those 1-year or 2-year estimates that I come up with? The chart above doesn't show this. It's not clear which of those targets might have been derived from flawed estimates, and that the market might have deviated from them not because it was wrong about AAPL, but because my expectations for AAPL were off. Quantifying this is a very simple exercise, yet I have never seen a single analyst do it for more than the most recent quarter. Because in order to assess the consistency and accuracy of our forecasts, a full history of them compared to actual results is required. Yet no one does this. I've attempted this with my estimates a couple of times, here and here (lousy attempts, I know).

So for today's exercise, I went ahead and aggregated all the EPS estimates I've documented making, more than 100 data points on different focus points looking into the future, and compared them to the actual reported results, charting the deviation bias (high/low) and accuracy (best/worst), and highlighting their statistical dispersion and skewness/clustering through colors, over the last 6 years and then again over the last 3 years. Here's what it looks like in four charts (click on each to enlarge).

There's 22 quarters worth of estimates for the same and next (1Q) periods, 20 estimates for two quarters into the future (2Q), 18 estimates for 3Q out, 17 for one year out, and 11 for 2 years out. The white lines separate each decile (10% of estimates within each column) so each colored block represents at least one estimate, and sometimes two, and sometimes in between (there's some interpolation involved). I tried to highlight the quartiles (25% buckets) through similar colors and gradients, not sure if that helps or not. Because this post is already extremely long, please feel free to use comments for further descriptions, interpretation, discussion, questions, etc.

## 12 comments:

As usual, a magnificent tour de force. I wish I could add value to this, but I'm still catching up. My own forecast is multiplied by a P/E ranging from 15 to 20 and it still shoots the price above 500 in 2 years (at least). Will the P/E stay low? This is the real unknown. Earnings are easy to forecast. Sentiment impossible.

Profound, as usual. As Horace Dediu says above, sentiment is hard to forecast, and sentiment is indeed driving prices now.

The knock on Apple is that it is already #2 in market cap, could soon be #1 in market cap, and how can Apple be bigger than Exxon-Mobil.

The other fear is the fear of large numbers. PE matched to growth rate is easy to rationalize for a small company - one can easily visualize a $500M company to grow to a $1B. But people are afraid to assign a higher PEG for very big companies, I think.

After Friday's big explosion, Google now has a forward PE of 19.12, according to Yahoo finance. Goldman put out a $700 price target for GOOG.

AAPL fwd PE is only 17.46. Most analysts would likely agree that Apple is the better growth story. That means AAPL should warrant at least a similar forward PE as GOOG, if not higher.

My own take is, both AAPL and GOOG will probably see a forward PE of 20, perhaps a bit higher, but I get the sense that they won't let them rise up to 25.

Share prices could continue to slowly climb up over time, of course, but clamped to a forward PE or around 18-20, I think.

What Apple needs is for someone to make a back-of-the-napkin case for how Apple's revenues over the next 4-5 years could grow to $200B, when you add up everything Apple has going for it.

The biggest fear investors need to overcome is that there is still several years to go before worrying about Apple becoming a dividend play.

My 2 cents' worth ...

My take on what's happening with Apple:

During the depth of the Great Recession Apple's earnings remained stable even as their stock value submarined, causing the disconnect in 2008/2009. When it became clear Apple was not being hurt by the recession, that reversed starting around March 2009. At about $200/share, stock value "caught up".

But then something unusual happened. The stock market went into several months of "doldrums", corresponding with an Apple stock price of $250/share. But Apple earnings started to unexpectedly explode.

Now we have something very different from the "catch up" that happened in 2009. Now we have earnings looking to grow nearly exponentially - and the market is behind the curve on fair valuation.

I believe that your projections for future growth in earnings are actually quite conservative, particularly so because Apple is a target in motion. It's a fair bet that Apple has a stable full of innovative products making their way to market.

If true, then Apple may become a profit juggernaut such as the world has never seen. Over time, Exxon-Mobil may well pale in comparison.

Nice work, Daniel.

I do wonder about the 25x metric. As Roy suggests, the market cap can tend to hold down the PE; are there historical precedents for a top-five market cap company having a PE 50% higher than the market P/E? (Perhaps GE a few years ago.) Another factor is the derivative of growth rate for Apple is declining despite its high nominal rate. And, of course, we can always point to the fact that Apple is not understood by Wall Street.

Perhaps a a variant of PE would be a useful metric. You might put the Apple PE as the numerator and the the S&P500 PE as the denominator. This does not mitigate against the market cap issue, but could help in other ways. Also, I have found it useful to have two or more indicators when determining buy or sell signals.

Mostly just thinking out loud here. Your work is outstanding just as it is.

-capablanca

Daniel,

Very nice work. Ironically, I wrote a similar, but less sophisticated piece, on Friday. I'd be delighted to have your feedback.

http://sewardtotty.blogspot.com/2010/10/apples-valuation-conundrum.html

Thank you.

Great comments.

Roy and Capa, dig up some of MSFT's 10-year-old annual reports. Compile a few data points for '97 through '01: revenue, net income, Y/Y growth, shares out, cash, EPS, share price, P/E (fwd and ttm), and market cap. Was the market afraid of granting a 50 P/E to a $300b cap? What about going north of $500b? What was the P/E then? What was the expected long-term growth, 50% forever into the future? 20%? Where did their actual growth came at, even after the post-2001 "reset" of expectations? How high did their market cap go post bubble, even after years of continued disappointments? I wont bother looking for any documented expectation of long-term growth, but the valuation sure suggests there was no "law of large numbers" in effect. Not even allowing for the tech bubble hype.

I think it's undeniable that MSFT should take most of the blame (popped bubble notwithstanding) for the massive destruction of shareholder value. AMZN, the poster child for stratospheric valuation during the bubble, is now at all-time highs (and still gets to keep a high multiple, even if lower than those days). AAPL of course went through their own issues, but promptly took the ball and ran for a touchdown (or three). Along came GOOG and stole MSFT's mojo, seemingly overnight. Looking at those same metrics for MSFT 10 years later, after the destruction of hundreds of billions of value, and I still see room to fall.

Not a single investor from back then ever complained at market caps greater than $500b. Nor they immediately tacked on a "law of large numbers" compressed multiple to companies reaching those levels (except after the failures were made evident in almost every such case, by MSFT, CSCO, GE, XOM, C). Nor ever questioned the 20% or higher estimated long-term future growth rates for such ailing behemoths trumpeted by broker-analysts selling them these shares as safe-for-retirement vehicles.

Investors seem to have finally learned a lesson in big-cap valuation moderation under the "new normal." But, as always, it gets codified in these simplistic market adages and platitudes. Is the market saying that the last decade's appalling performance from the few tag-teaming top dogs in market cap is inevitable? Is the fear that "AAPL2010=MSFT2000" the reason behind this idiotic "AAPL=15xEPS" valuation? Is that bleak scenario priced in?

Is the market's new-found "wisdom" for moderation justified, or is it just one more example of such simplistic market adages, same as blindly betting on the "best-in-breed" horse, no matter what, was proved wrong? Is it inevitable that Apple will fail as this "new-normal" law guarantees? Would the market reconsider if sometime next year AAPL is at $450 and still hasn't dropped the ball, posting EPS growth of 45% and expected to grow north of 30% in 2012? Will the dumb masses of "investors" (pension funds, etc.) only place their bets then, sending AAPL to $650 for a fwd PE of merely 22, supposedly commensurate with expected long-term 5-year growth?

Who knows! I'm not in a hurry, I'll take it year by year. As long as I get 25% annual gains, I think there's no better or safer investment anywhere for the next 5 years. BTW, 25% annual gains roughly means $400, $500, $625, $780, and $975 for each of the next 5 years. Maybe then it'll be fairly priced, if growth has slowed to 15% (hope I'm still here to let you know if my model agrees). I do think we should get more, but I'd be happy with that. Anything less and I'd be disappointed.

Are you holding any options ATM Deagol?

I personally have just shares right now, but family members do have deep ITM Jan11 calls acquired in Feb and Aug on my advice.

Daniel - you are absolutely correct about the peak market cap in MSFT and CSCO in 2000. But as you know, the markets are notorious for not consistently applying a standard. Case in point: the valuation of AMZN vis-a-vis AAPL.

The rationalization for MSFT in 2000 would be that it was a bubble then. The implication is, of course, we are much smarter now, lol.

Well, the sell off on the morning after is probably not a bad thing. It shakes loose some weak hands, and possibly, attracts a few new short sellers who will be fuel for further rallies. The next pause should come in the $400s. I am salivating at fiscal Q4.

I am a little puzzled by Steve Jobs' appearance in the earnings call, however. I especially loved his comments about Nokia ("We don't aspire to be them... they are good at being who they are, but we want to be us" - as best as I can paraphrase) and about the iPad ("We've got a tiger by the tail").

But it is a little uncharacteristic and I did not see a need to voluntarily take shots at RIM and Google. Just do as you've been going, why talk?!

Perhaps Steve felt the need to sprinkle a little cold water on Wall Street's rediscovered enthusiasm for GOOG on Friday.

Any thoughts on Steve's appearance?

Rgds,

Roy

One way to look at Apple PE is as follows ( back of the envelope calculation ): Zero or meager growth P/E is around 12. When will Apple reach that stage. Let us say in the next 5-6 years. Today's P/E is 20 can be theoretically justified with the following growth rates for the next 6 years : 20-25% for the next 4 years and 10-15% for the next 2 years and then who knows. Let us assume it will reach that zero/meager growth state then. Such a story deserves only a P/E of around 20. Apple's revenues will reach $185 billion with a EPS of around $42. To achieve this, they have to selll in the outer most year around 160 Million iPhones and 70 million iPads per year. At this rate we will be targeting close to 3/4 a billion iOS devices. At that time, the P/E will shrink to 12 for a share price of 504.

So today's price with a P/E of 20 really projects a price of 504 in 5 to 6 years. That is not bad but it is not explosive as some people tend to assume. And all the positive expectations about Apple have to come to fruition for this to happen.

At this stage in the Apple growth story, what matters more is the peak EPS and not too much when Apple reaches it. I picked a period of 5 to 6 years. Some might say that is too conservative and that Apple may reach that in 3-4 years. "peak" implies the years following are not similar growth years which causes the P/E to contract. As we approach that point, you will see a gradual contraction of the P/E to the 12 range even though the earnings are growing up. But the price curve will not necessarily mimic the growth curve. That is the P/E contraction effect. I would say Apple is currently in that half way stage of P/E contracting. That is, a P/E of 20 is sort of mid-point of this contraction from 30 to 10-12 range.

I tested a model with a bit more juicy growth rate. 30-35% for the next 3 years, 20-25% for 1 year and 10-15% for another two years. In that 'what if' scenario, a current P/E of 25 is justified with a peak EPS of around $60 with earnings in the $265B range. Then a zero/meager growth stage sets in with a contracted P/E of 10-12 which amounts to a price target of 600-720. It is going to be gargantuan task to be selling $265B and an EPS of $60 each year after that, in the midst of shrinking Average Selling Price and lowered Gross Margin. That is why the market is not quite going to a current P/E of 25 but stuck around 20.

My prediction is, Apple P/E would hover in the 20 range for a while before taking the path of contracting P/E to 12.

( I posted this at asymco, I thought I will do it here also to get some feedback if I am directionally correct )

Chandra

Thanks Chandra. There were 5 duplicate comments with slight variations from you, which I deleted. I tried to pick the one that included everything you had to say.

I think your figures have a lot of wiggle room in them. For example, using your top growth ranges results in very different outcomes than using your bottom ranges. What do you mean by zero/meager growth? 0%, 5%, and 10% are quite different things.

AAPL fwd PE 17, next 5y growth 19%

GOOG fwd PE 22, next 5y growth 17%

ORCL fwd PE 15, next 5y growth 15%

IBM fwd PE 13, next 5y growth 13%

CSCO fwd PE 14, next 5y growth 13%

GE fwd PE 15, next 5y growth 13%

RIMM fwd PE 9.5, next 5y growth 12%

INTC fwd PE 10.5, next 5y growth 12%

XOM fwd PE 12, next 5y growth 12%

NOK fwd PE 14, next 5y growth 11%

HPQ fwd PE 10, next 5y growth 10%

MSFT fwd PE 11, next 5y growth 10%

WMT fwd PE 14, next 5y growth 10%

MCD fwd PE 17, next 5y growth 10%

WFC fwd PE 12.5, next 5y growth 9.5%

BAC fwd PE 11, next 5y growth 9%

PG fwd PE 16, next 5y growth 9%

BHP fwd PE 24.4, next 5y growth 9%

KO fwd PE 18, next 5y growth 8.5%

JPM fwd PE 10, next 5y growth 7.5%

DELL fwd PE 11, next 5y growth 7%

BRK-A fwd PE 18, next 5y growth 7%

T fwd PE 13, next 5y growth 6%

JNJ fwd PE 13.6, next 5y growth 6%

BP fwd PE 7, next 5y growth 5%

MOT fwd PE 24, next 5y growth 5%

PFE fwd PE 7.8, next 5y growth 2.7%

All these are according to Yahoo! Finance (don't trust them much). Notice some mega caps there with much bubbly valuations than AAPL. Only RIMM and INTC show a better valuation (shaky fundamentals), and I know AAPL will beat that growth estimate, as well as beat EPS for a lower real fwd PE than that; not sure about any of the others. I looked at AMZN, AKAM and NFLX and I won't even bother putting them up, ridiculous comparison.

Could you point me to another mega cap (>100b) with a better valuation than AAPL would have in 5 years @ $504 (12x $42 EPS) and a similar solid-growth business for the following 5 years? (15% growth then will be easy: 160M iPhones will still be <10% share of all mobile phones, 70M iPads <15% share of PCs) INTC, TM, C? (gag) If there are no others (and there's probably about 50 companies this big) then one of two things must happen: either the market got them valued wrong (wrong PE) or the growth estimates are wrong.

Either way AAPL must catch up to their valuation. Only question is, will they all tank to meet AAPL (and AAPL holds $500), or will AAPL deserve that 15x multiple on 15% growth, and go from $600 to $1000 in the second half of the decade? In either case, where would you invest now?

Sorry about those duplicate comments. I tried the non-anonymous route a few times and Google gave me an error every time.. Then I posted with the anonymous option.. Thanks for cleaning it up.

For a long time I used to use the thumb rule of 12 + Growth rate as the fair P/E. During the .com bubble I could not find any growth stock whose P/E was less that this. That is indeed the definition of a bubble. Now, after the recession, there are a lot of "growth" stocks that trade below this 'fair PE'. So to a large extent, the market tends to over or under reward the PE depending on the overall market sentiment. That is fine, in fact that is what is useful to decide whether to buy or sell a stock. But of late, I have switched to this 'peak earnings' method to get a better feel for where the stock is headed. The math behind is the same except I do not assume a perpetual growth rate. That is a flaw in discounted earnings model which always bothered me. It does not take into account the resistance every company faces when saturation occurs. So one can not assume a growth rate for ever. Since we are interested in what the market's view of the stock in 5 years, we really need to take into account what the same calculation will look like in 5 years. As a proxy for all this, I am now using the 'peak earnings hypothesis' and using a P/E of 12 ( it can be 10 as well ) as the future P/E when such a a state is inevitably reached.

You are right in your observation that my numbers have a lot of wiggle room. Given the unpredictability and irrationality of the market at any time, it is better to have a fuzzy description since all we care about is guessing the direction of the stock correctly and if there is some fuzziness in the actual price number,that is OK. Also, there is this huge garbage-in garbage-out in all these calculations. The growth numbers are speculative, the discount rate used is speculative, the overall bearish/bullish mood that is going to prevail in the next couple of years is speculative etc.

First, on where to invest other than apple, I do not have an answer. I am an Apple share holder and I am probably over-weighted on Apple. I am a bit reluctant to add more money to it now... But if I believe my own numbers of 315-500+ in 5 years, I may be better off in a wilshire5000 index because of the reduced volatility..

>What do you mean by zero/meager growth? 0%, 5%, and 10%

In that range. I would not rule out some contraction also along the way since there is not much room for error at such high sales rates. A good example is like Microsoft of today in terms of growth rate.

>would have in 5 years @ $504 (12x $42 EPS) and a similar solid-

>growth business for the following 5 years?

>(15% growth then will be easy: 160M iPhones will still be <10%

>share of all mobile phones, 70M iPads <15% share of PCs)

All true. But there will be more and more head wind to maintain that year after year. We will have more competition, slowing ASP and slowing Gross Margin.

I have a probabilistic model which can take high and low end for the growth rate. In this simulation, for the first 5 years 20-30, next 5 years 15-15 and then 0. So, the peak earnings will happen at the 11th year. Assuming current earnings are $15.00, that comes to $90.00 for a price of 90 x 12 = 1080 in 10 years. For this to happen, Apple

should generate revenues of around $400 billion per year. And the market should believe that they can keep doing that for every year after that. And with that high expectations, the stock is going to 1080 in 10 years. That is the risk reward ratio we need to keep in mind.

p.s thanks for the data on all those companies.. that is lot of effort in collecting them. Thanks.

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