AAPL: Ray Mertola. Good study of basics.


Apple, Inc. (AAPL) currently sports a trailing twelve-month P/E of 10X. Based upon the discounted cash flow principles underpinning the concept of the Price/Earnings multiple, this makes little sense unless one believes the company no longer has an ability to generate incremental earnings and cash.

This article will explore the thesis in four parts:

  • How the P/E ratio relates to Discounted Cash Flow methodology
  • What P/E multiple relates to a “no growth” stock versus a growing enterprise
  • How the Apple stock P/E has decoupled itself from past and projected earnings metrics
  • A summary and concluding thoughts as to what’s going on


The P/E Ratio Represents Simplified DCF Methodology

The P/E multiple concept is grounded in Discounted Cash Flow (DCF) analysis, more specifically determining the Present Value (PV) of a future series of cash flows. The DCF process discounts these future cash flow back to a single present value number.

The following formula represents this situation:

PV = E * (1 + g)/(r – g) where

PV = The present value stock price

E = Earnings for the stock

g = growth rate

r = required rate of return or discount rate

Assuming the cash flows are no-growth constant sums, the g variable drops out and the simplified formula becomes:

PV = E / r

If we now rearrange the formula to isolate the r variable, and rename the PV variable P for Price, we obtain the following:

r = E / P

Starting to look familiar? If we invert E / P, we get P / E, as in P/E ratio.

Therefore, the P/E multiple of a stock is the inverse of r, or the assigned discount rate.

P / E = 1 / r

Let’s proceed.

What P/E Multiple Corresponds to a No-Growth Company?

We still haven’t solved the formula. So now it’s time to plug in some numbers. First, let’s make some assumptions in order to solve the r variable, or the expected rate of return for equities in general.

Historically, investors have required equity returns that compensate them for the risk taken in lieu of investing in risk-free assets. The following formula captures this:

r = RFR + B (Rm – RFR)

RFR = Risk-Free Return; often benchmarked by the 10-year U.S. Treasury note. These notes have historically been pegged at approximately 5 percent.

B = Beta, defined as a measure of the volatility, or systematic risk, of a security in comparison to the market as a whole. To keep our work simple, we will assume the Beta is 1.0. For the record, it just so happens that Apple stock has a Beta of 1.0, too.

Rm = Historical market return. Let’s recognize that all DCF work requires assumptions. In this case, we will assume that over the long term, equities have returned a nominal 11 percent to the investor.

Solving for r, we get

r = 0.05 + 1.0 (0.11 – 0.05)

= 0.11 or 11 percent

Here’s a simplified explanation of the foregoing: over time investors have generally required the “risk premium” for stocks to be about six percentage points above a corresponding “no risk” investment. The ten-year T-note has traditionally been benchmarked as such an investment. The average yield on a ten-year T-note has been five percent. Therefore, a reasonable discount rate for equities is about 11 percent.

Now if we go back to the original equation, we can plug in the value of r and find that the P / E multiple for a no-growth stock should be

P / E = 1 / 0.11 or 9.1

Therefore, a P/E of 9X approximates the expected multiple for a stock with a constant return, but no growth, when discounted at 11 percent.

What About a Company that Grows Earnings?

The P / E multiple is designed to give the investor a rough guide to estimate the value of a stock given its earnings growth rate. It’s not an exact science. However, the concept is sure: the Price / Earnings ratio should relate to an expected Earnings growth rate.

Therefore, the better a company’s growth prospects are, the higher P / E can be afforded to it.

Let’s avoid a great deal of math and theory. We will cut right to the Graham valuation formula. This shorthand equation provides a practical application for handling a relatively complex DCF problem.

Benjamin Graham, the father of value investing, was known for his thorough financial analysis of companies, but he also offered followers simple rules of thumb to evaluate stocks. Here is a valuation formula adapted from The Intelligent Investor:”

P / E = 8.5 + 2G

P / E = a fair P/E ratio for a given stock

G = earnings growth rate

Note that if the growth rate is zero, the fair P/E becomes 8.5X. That’s not too far removed from our calculated zero-growth equity formula earlier.

However, since Graham proposed his formula back in 1949, it has shown a tendency to provide fair P/E multiples that are a bit too high. Therefore, I suggest we modify the formula to make it more conservative. The following formula tends to work very well.

P / E = 9 + 0.5 G

The details outlining the rationale around this modified Graham formula can be found on this web link.

If one accepts this formula as a rough guide, a stock that grows at 4 percent a year, for example, should command a P/E of 11X.

So How Does this Relate to Apple Stock?

Apple stock currently trades at a ttm P/E of 10X. We have established that a stock with no growth should trade at a P/E of about 9X. Furthermore, we outlined how it is reasonable to premise that a stock with an expected two percent earnings growth rate should trade at 10X.

Yet AAPL has grown operating earnings at 33 percent a year over the past 15 years. Street analyst consensus five-year forward EPS growth estimate for Apple is between 15 and 18 percent depending upon the source. Wall Street believes that after a flat FY 2013, growth will resume. Here’s a link to one such consensus.

Wall Street says Apple EPS will grow at a mid-to-high double digit rate. Yet Mr. Market assigns Apple stock a P/E implying a 2 percent forward growth rate.

Some Additional Color on the Subject

Are Earnings the Same as Cash?

No, earnings are not the same as cash. Therefore, if Apple, Inc. is growing earnings it does not mean that it is necessarily growing cash flow. If a stock were earnings-rich, but cash-poor, it could explain why a stock can deserve major P/E compression.

A review of past financial filings indicate that this is not an issue. Here’s a summary of the past five years; comparing AAPL earnings versus free-cash-flow (FCF). FCF is operating cash less capital expenditures.

Apple Earnings per Share and Free Cash Flow (FY 2008 – 2012)

FY 2008 FY 2009 FY 2010 FY 2011 FY 2012
EPS $6.78 $9.08 $15.15 $27.68 $44.15
FCF per share $9.57 $10.02 $18.11 $35.81 $45.33

While past performance is no guarantee of future returns, I did find the chart incredible. Indeed, Apple clearly has not had an earnings-to-cash conversion problem. The company actually generates better FCF per share than EPS. Remarkable.

The Bottom Line

Granted, the P/E ratio is more of a blunt instrument than a surgical knife. Like any DCF or financial multiple analysis, the underlying assumptions make or break the results.

However, in the current case of Apple stock, even conservative DCF assumptions don’t jibe with the Street’s projected earnings and cash expectations. Hence, there is an apparent anomaly.

Wall Street forecasts a company growing earnings at high double digits, yet the market assigned a Price / Earnings ratio that implies about two percent future growth.

Please note this analysis doesn’t purport to make any demands upon the market. Stocks behave as they will based upon buyers and sellers. They don’t behave as we expect them to.

Nevertheless, it does seem like AAPL Street earnings growth expectations and market multiples are unusually disjointed.

So What’s Going On?

There are any number of theories as to what’s going on, but here’s my take on a few of them:

  • Market Sentiment / Negative Momentum: AAPL stock price may have separated from earnings and expected growth due to a simple lack of buyers. The stock had been touted via buy-side analysts for a long, long time. At some point, the buyers are exhausted and sellers take charge. The multi-year run up in price and tax considerations at year-end 2012 may have provided a catalyst for shareholders to begin to take profits. They did. Negative momentum ensued: Selling begets more selling until equilibrium is reached again.
  • Transition from Growth to Value Stock: Apple had been recognized as a tremendous growth story for years. The law of large numbers makes it nearly impossible for a stock to continue to grow so rapidly year after year after year. Large growth-company money managers may have decided that the jig was up on the AAPL growth story. They started unloading the stock, creating a vortex of other managers to follow suit and do likewise. At some point, the value money managers will move in and begin to buy shares based upon fundamentals and the dividend. If true, the process can take awhile.
  • The market is correct: Perhaps my thesis for this article is entirely wrong. It is possible that the market has properly handicapped Apple stock. It “deserves” a 10X multiple. Most analysts indicate that Apple EPS will be flat in FY 2013. If the company earnings were to stay flat to low single digit growth for an extended period of time, then a low P/E is warranted. While I find this a low probability thesis, it cannot be dismissed.

I believe that over time, undervalued stocks either demonstrate that they deserve to be priced as such (the proverbial “value trap”), or the market eventually recognizes the disconnect and bids up the shares to reach normalized valuation. It may not happen when we want it to happen, but it does.

Having bought Apple shares some years ago, I plan to hold for the time being. I do not intend to buy more, nor cut my current position. My view is that the shares are undervalued.

AAPL’s management discussing earnings
  • Share this article
    Short URL:


Comments (34)
Track new comments on this article
  • BUY BUY BUY at these levels and sleep wonderfully if you have a long term view of investing. AAPL at this price may be the deal of the century.

    27 Feb, 10:54 AMReply! Report AbuseLike5
  • What’s going on? Your gave the answer. A stock with a 2% growth rate should have a ttm PE of 10, right?Given that Apple’s PE is lower, the market is saying they don’t think Apple is going to be able to grow earnings at 2%. If you think the market is wrong about Apple’s future earnings, then buy up. But I think there’s a good chance the market is right, so I think I’ll wait for a better safety margin before I jump in.

    27 Feb, 11:09 AMReply! Report AbuseLike3
  • Therein tombo, is the big question. Is Mr. Market “right,” or has he over-reacted to short-term or other-than-fundamental circumstances?If the market is “right,” then the legions of Wall Street analysts are pretty far out of line given their EPS projections past 2013.

    This is what makes a market.

    27 Feb, 11:58 AMReply! Report Abuse1
  • This is the most thoughtful and well-written synopsis of AAPL that I have read in a long, long time.Insightful, level-headed, and without bias or sentiment — a rarity.

    Thank you.

    27 Feb, 11:10 AMReply! Report Abuse12
  • Thank you Tap16I appreciate the kind words. When I write, it forces me to think critically and then share it on the record, so to speak. That is a great motivator.

    All the best.

    27 Feb, 12:01 PMReply! Report AbuseLike0
  • Your analysis is welcome and compelling, and thanks for setting out the assessment so clearly and candidly. I share your plan to hold for the long term.

    27 Feb, 11:11 AMReply! Report Abuse6
  • Let’s hope we have this handicapped correctly!

    27 Feb, 12:02 PMReply! Report AbuseLike0
  • Your analysis was insightful ! thank you.I think your beta assumption of 1 is skewing the results too much. Historically AAPL’s beta has been 1, however the market cares more about recent volatility than historical volatility. If I were to guess, AAPL’s 2 yr beta is closer to 2 than 1.

    27 Feb, 11:13 AMReply! Report AbuseLike3
  • @karthi89 – “If I were to guess, AAPL’s 2 yr beta is closer to 2 than 1.”Yahoo finance says that AAPL’s beta = 0.75. That is not the 2-year beta that you’re guessing about, but it has the advantage of being factual rather than a guess.

    The problem with beta is that it is backward looking and provides no guidance for the future.

    27 Feb, 11:53 AMReply! Report AbuseLike0
  • Valid point, karthi89. Beta isn’t a fixed point, but can vary.

    27 Feb, 12:03 PMReply! Report AbuseLike0
  • I obtained the 1.0 Beta from the TD AmeriTrade site. Indeed, the number can move around. As an earlier commentator noted, I suspect the near-term Beta may be different than a longer-term one.

    27 Feb, 12:04 PMReply! Report AbuseLike0
  • Good article and tutorial. I am long AAPL, I’m a DGI that believes the stock is underpriced and hopes that the div will be aggresively advanced.

    27 Feb, 11:15 AMReply! Report Abuse3
  • I suspect that pressure on AAPL management will eventually force them to offer a clearer plan for their cash hoard. I believe it’s become so big it’s more of a psychological liability than an asset.

    27 Feb, 12:08 PMReply! Report Abuse1
  • Great article. I believe AAPL is a good buy. You may want to buy it and thank the author in 3 years. It is a value stock in many metrics. Most value stocks take some time for its value to be realized by the market.—-
    P/E is one of the many metrics to consider. PEG is another one. Market outlook is another one. Even for P/E, I would like to compare the following:

    P/E (forward) to its 5-year average.
    P/E to the industrial average.

    27 Feb, 11:17 AMReply! Report Abuse4
  • There are two related chapters in my ebook Myths
    http://bit.ly/131Oaa5The abstracts:

    Based on data of 10 years, P/E has 3 values: High (< 4), Mid (<10) and Low (> 40).

    In general (with many exceptions), the stocks with P/E greater than 40 will lose money in a year.

    Stocks less than 4 would be hidden gems but could be problem stocks (such as lawsuits pending).

    Apple is within a good range at 10.

    The following is a long discussion of P/E:

    55 Mysteries of P/E

    P/E is the most misunderstood indicator. However, it could be the most useful one.

    * Better definition.

    P/E should be inverted as E/P, which is termed as Earning Yield. Earning Yield is easy to compare and understand. It takes care of negative earnings for screening stocks and ranking. If you sort P/E in ascending order, your order is wrong with negative earnings but right with E/P.

    It is usually compared to a 10-year Treasury bill yield (or 20 or 30 years) or a CD rate. If the stock has 5% and your one-year CD is 1%, then it beats the CD by 4% in absolute number and many times better percentage wise. However, the CD is virtually risk free and the future earning yield is an educated guess and it may not materialize.

    * Many ways to predict of E/P.

    • Based on last 12 months. Project it to future E/P. It is also called last twelve month E/P.

    • Based on analysts’ educated guesses. Guesses may not materialize. From AAII screens based on data for 10 years for expected PEG and historical PEG (cannot find for P/Es), the expected usually predicts better than the previous one that is based on last 12 months. This is the one I use most and many investing subscriptions provide this expected P/E.

    • Based on last month or quarter. Latest information could be better for prediction. However, they are not good for seasonal businesses such as retail where most sales are done in the Christmas season.

    * Best E/P could not be the best.

    Very high E/P could be sign of troubles ahead like lawsuit pending, fraud, etc. You can find companies E/P over 50% and it means two years’ profits could equal to the entire cost of the company! I can tell you right away they smell fishy as there is no free lunch in life.

    However, from time to time, some bargains exist due to certain conditions or Wall Street is just wrong about the company. You need to find out whether they are bargains or traps. When the E/P is low (sometimes even negative) but it is improving fast, it could mean big profit for you. During a recession, a good company should not concentrate on sales as it is the most expensive time to market products in particular on new products, but it usually is the least cost to develop products. In this case, there is no alarm even with negative earning. The only alarm is the high burn rate.

    * E/P and PEG.
    For value investing, E/P is usually used, the higher the better but not extraordinary high as described above. PEG measures the rate of improving E/P. For growth investing, PEG is usually used. Select one that favors the current market conditions whether it is value or growth.

    In a secular bull market, growth is usually better than value. Value (opposite to growth) is better in early recovery stage of the market cycle – the best result is selecting top stocks sorted by Value/Timing. Value and Timing could be one composite metric classified by some investment newsletters / subscriptions.

    * Fundamental metrics.
    E/P is one of the metrics you should use but not exclusively. If the earning yield is high but the % of debt is too, then a good bargain may not be as good as it appears to be. See next chapter on other metrics.

    Some other metrics may not be easily found in the financial statements like the intangible, insider buying, pension obligation, losing market share, etc.

    * P/E variations.
    There are other P/E variations like Cape. Personally I like to compare its current P/E to the average P/E for the last 5 years and/or compare it to the average of the companies in the same sector.

    P/E is more reliable for a group of stocks like SPY instead of individual stock which has too many other metrics to deal with.

    Shiller P/E is one way to track the current market valuation. It is controversial and its value is easily misinterpreted. Hence, use it as a reference only unless you understand all its issues.

    When you compare the total return of an ETF, you need to add the respective dividends of an index to ensure a fair comparison with total returns. Currently, S&P500 is paying about 2% dividend.

    You may want to take out the cash per share from the P to have a better indicator. Some cash-rich companies like MSFT and CSCO could have a better P/E than with the cash.

    EV/EBITDA is another way to measure the value of a company. This metric has both advantages and disadvantages over P/E. Click the above links for more information which is beyond the scope of this article.

    * Garbage in, garbage out.
    I do not trust in most financial statements of emerging countries especially the smaller ones. Watch out for fraudulent data.


    Again, one metric should not dictate the reason to trade a stock. Most metrics can be manipulated and give different prediction in different market conditions.

    27 Feb, 11:25 AMReply! Report Abuse3
  • Good points all, Tony Pow.

    27 Feb, 12:05 PMReply! Report Abuse1
  • Nice analyses, clear and complete! I sent this to a retired friend who (hasnt studied) isnt comfortable with technical or quantitative analysis because he doesnt understand the methods – formulae. This article is a Great walk-thru of the P/E discipline!
    Good luck & Good investing!! JTL

    27 Feb, 11:17 AMReply! Report Abuse4
  • Thanks JTLowlorGlad I could help, even a little bit!

    27 Feb, 12:09 PMReply! Report AbuseLike0
  • As both a long term Apple shareholder and a long term owner of its products, I thoroughly appreciate your thoughtful analysis. I too wait for the market to correct back to a fair valuation. I also await their new products, as well as their upgraded/refined products.At some point the Board and management at Apple will also address the low valuation through dividend increases, buyback increases, and perhaps even a stock split. Any one of these should bolster the stock and help with regaining momentum. Or else we just wait for Apple’s next quarterly profitable, cash generating, growth quarterly report.

    This is one of the great growth stories on the planet and it keeps on going. Let’s commit to be aware of real information and metrics, and at the same time ignoring all of the noise.

    27 Feb, 11:22 AMReply! Report Abuse4
  • Indeed, you have outlined an investor’s general thinking versus a trader. All the best.

    27 Feb, 12:11 PMReply! Report AbuseLike1
  • Great article Ray. Nice to see someone take a sound, mathematical (not emotional) approach to valuing Apple. This is definitely an article I will be adding to my investing toolbox.As you mentioned these are conservative valuation estimates. Would be interested in seeing a more aggressive valuation, and one that includes the discounted value of future dividends. I expect the results would be nothing short of astonishing.

    I am long Apple and intend to go longer after the probable stock price hit coming later today/tomorrow if Apple does not announce a new product or dividend increase.

    27 Feb, 11:22 AMReply! Report AbuseLike1
  • Appreciate the comment, RyanI believe that AAPL shares will work out for the patient. I bought several years ago and plan to stay the course on this one.

    Following up on your comment about Apple valuation, I was astonished to put the last five years of EPS versus FCF on paper, then think about what it means. I did a double-take!

    27 Feb, 12:13 PMReply! Report AbuseLike1
  • You might want to see what is coming out this year.
    http://read.bi/13khDxTThe iPhone 5 is just beginning to sell. People were buying the 4S because it was cheaper. The 5 is so much better. This is going to be a good year for the iPhone 5 sales. You have to talk with someone who has really used both phones.

    27 Feb, 11:31 AMReply! Report AbuseLike0
  • Thanks MomintnI read something along those line just the other day. We shall find out soon enough!

    27 Feb, 12:14 PMReply! Report AbuseLike0
  • Excellent article. I think that you and the above commenters are correct that despite what the analysts say, the market is concerned about the ability to grow earnings in the face of Android/Samsung competition. My personal view is that there is a lot of room for growth in established products like laptops, as well as new products like iwatch or television. And very few companies get design like Apple does or have the brand insistence.

    27 Feb, 11:35 AMReply! Report AbuseLike3
  • Yes, AdamThis is the question. The current P/E indicates that Mr. Market say that Apple is done growing; basically washed up. While that is a possible scenario, and I understand that Tech moves rapidly, I just don’t think that’s the probable scenario.

    27 Feb, 12:16 PMReply! Report AbuseLike2
  • Thanks for the enjoyable read!

    27 Feb, 11:39 AMReply! Report AbuseLike2
  • Thanks AshrafI appreciate you taking the time to comment. Likewise, I enjoy reading your S.A. work, too. All the best.

    27 Feb, 12:16 PMReply! Report AbuseLike0
  • while I agree with your analysis of the fundamentals, I just don’t trust a logistics and operations guy like Tim Cook to lead Apple – a company whose competitive advantage has always been innovation.

    27 Feb, 12:09 PMReply! Report AbuseLike1
  • The assumption that Apple isn’t innovating is just an assumption.
    Apple is spending a great deal on new product development but they are secretive for a good reason. The idea that Apple must “innovate” and produce new products to market every year is not realistic. Jobs always had products under development for years before they were released.
    Can anyone name another company that is innovative? Not Samsung or Microsoft. Google tries hard but really bought the Droid OS, they didn’t develop it.

    27 Feb, 12:20 PMReply! Report AbuseLike1
  • Respectfully – your DCF formula is wrong: “PV = E * (1 + g)/(r – g)”
    The correct formula would have Dividends ( not Earnings) in the numerator. Growth requires re-investing a portion of the earnings – which is why dividends are generally lower than earnings.
    The other problem with this formula ( even corrected to include dividends) – is that it assumes growth continues to infinity – forever. This is a particularly troubling assumption for a company like Apple – which is in the fast moving consumer tech business. I fondly remember Amdahl, Convergent Systems and Atari from the 1980s.
    That is just for starters – the discount rate is the other big issueP/E can be very misleading especially when comparing very different types of businesses.

    27 Feb, 12:16 PMReply! Report AbuseLike1
  • Great article. However in reality we cannot assume either a 2% growth or a 6% growth on a constant basis in the future. How about a revenue decline of 10% in the first year then a 25% growth the following two years then followed by a 10% decline the next year?If we take the past as the basis, we always anchor our expectations based on the past. Even when we try to be extremely pessimistic, we do that relative to what has happened in the past.

    I wonder whether it would be possible to do some Monte Carlo simulations of various combinations of revenue growth and revenue decline scenarios and look at how the stock is valued.

    27 Feb, 12:26 PMReply! Report AbuseLike0
  • What was RIM’s projected growth rate 5-6 years ago? They owned the smartphone market. What happened? What would a DCF valuation on RIM looked like – say in 2006? Would that exercise have been helpful in actually trading RIM stock over the past 5-6 years?
    If not – why use the same failed approach to yet another company in the smartphone business?

    27 Feb, 12:56 PMReply! Report AbuseLike1
  • It’s all about risk. When one discounts future earnings of a company whose future earnings might be much less predictable and much more vulnerable than other companies in other sectors, then one applies a much higher discount rate. Hence, Apple’s apparent “low” P/E.

    27 Feb, 01:06 PMReply! Report AbuseLike0
  • The real anomaly is not AAPL’s P/E but rather its level of earnings over the last years since it has introduced the I-Phone. They have absolutely no hope of sustaining it. In fact it is all down here from here. Two simple reasons: 1) Loss of Market Share 2) Massively Decreased Margins, both as a result of the rise of worthy competitors. AAPL earnings will not be growing or even flat in the next five years. They will be in decline. Hence the 9X-10X multiple!

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google+ photo

You are commenting using your Google+ account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )


Connecting to %s