Apple's Residual Enterprise Value is less than 7x Earnings

In his third “The Critical Path” podcast, Horace Dediu explained how Apple’s cash can be viewed as a strategic option, an opinion that resonated also with other analysts [1]. Cash is one of the most flexible resources as it can convert quickly into other resources such as brands, companies, technologies, people and even processes. More cash means more strategic flexibility. The large cash reserve Apple has accumulated provides high flexibility for future investments. These characteristics of cash already imply an intrinsic option value. But how big is this value?

Calculating Option Value

To help us determine, I will apply the Black-Scholes model. The model has two key characteristics that are applicable to valuing the option character of Apple’s cash. First, the simple form of the calculation excludes dividends and, as far as we have seen, there is no new information available that would suggest that Apple will pay dividends in the near term. Second, it implies that the option can be exercised at any given time until the end of the option exercise period – just like any buying or investment decision made by consumers. Lastly, we will assume that Apple’s cash (including short-term and long-term cash as well as financial investments) is instantly available. Although large amounts are held by foreign subsidiaries or are invested in maturities longer than one year, we can overcome these practical issues by borrowing against it. As we are interested in the value of the whole pile, we use the latest reported figure of $81.6 billion as the strike price (or exercise price).

What other inputs do we need to determine the option value of Apple’s cash [2]?

  • Volatility: A measure that determines financial risk of a certain asset. Apple’s share has shown a volatility of 26,1% over the last year.
  • The risk free rate determined by the 10 year US governmental bond interest rate: 1,96%.
  • A timeframe in which the option can be exercised. Let’s assume a 10 year timeframe in line with the risk-free rate and an imaginable horizon for mere mortals.
  • The value of the underlying (or what Apple is investing in):

The return of the investment exercised with the cash at hand should yield a higher Return on Capital Employed (RoCE) than previously achieved to increase shareholder value. On the other hand, such a high cash pile also provides the flexibility to invest into lower return ventures. Such an investment would be taken if a certain technology or trend has been missed by management or becomes suddenly more important in the priorities of the company. In defensive moves or moat creating ventures, the expected return would be significantly lower or can even be negative. For the last twelve months, Apple has returned 106% in terms of operating income over its capital employed [3]. I use the return to value the underlying. For example, investing $81.6 billion in assets that yield 106% return equals a underlying value of $168 billion.

The chart below shows the option value of the cash as a percentage of enterprise value of Apple (at the time of writing $310 billion) based on the range of the expected return on capital employed. Or in other words, how much of Apple’s current value is explained by the option value in holding such a large cash reserve.


Therefore, with the assumptions above and a RoCE from -10% to 110%, between 8% and 35% of Apple’s current valuation is explained by the option value of cash. We can see that even with large variations of the key input variables, Apple’s enterprise value is partly explained by the option value of cash which, in turn, is attributable to the sheer amount of cash at hand.

If we look at the option value explaining 25% of Apple’s enterprise value then 75% or $232 billion is the “Residual Enterprise Value” (REV) representing the value of Apple’s cash flow generating operations. That puts Apple’s valuation at 6.9x REV/EBIT 2011 or 6.5x REV/EBITDA 2011 — fairly low relative to recent performance. EBITDA and EBIT have been growing at a rate of 70% for the last two years and at a rate of 84% over the last year alone.

  1. It’s good to be king ( , Apple: Behold The ‘iEndowment,’ Says Wedgewood (
  2. For more information regarding option pricing see
  3. Operating income of the last twelve month of 33.8 USD billion divided by capital employed of 31.8 USD billion defined as total assets minus cash (or sum of all asset excluding cash)
  • Anonymous

    It should be possible to produce a firm upper limit on the option value by examining the cost of an equivalently sized revolving syndicated loan facility.

    • Eduardo, could you elaborate a bit so I can reply in proper form?

      • Anonymous

        Ok, I’ll try to explain my thinking. The question that we’re really trying to answer here is, what is the value to an investor of the cash being on Apple’s balance sheet, over and above the value of the cash itself. One way to measure that value is to look at it from the other angle – how much would it cost Apple to get an equivalent option in the market? Logically if the option value to Apple of additional cash is greater than the premium that it would have to pay – ie. the cost on an undrawn syndicated loan line – then it should load up on such options – which to the best of my knowledge it has not done.

      • Interesting take. I think coming from that side, we run into the same problem: what is the value of the underlying? In this article I went through the backdoor with the return on investment. As you said, it may be implied (by Apple’s action/inaction) that such options would be pricier than holding cash.

      • Anonymous

        The entire point of this approach is that it circumvents the need to fix on an underlying. Instead we depend on Apple’s nature as a rational value maximizer – and their superior information.

        It’s not implied by Apple’s actions that such a facility is pricier than retaining profit -it’s implied that such a facility is more expensive than the marginal benefit. Thus the marginal benefit of additional available cash, must be less than the marginal cost of such cash, allowing us to determine an upper bound.

        If we assumed a very conservative 100bps for the cost of such a facility then that would indicate an upper limit to the additional ‘option value’ of 8BN over 10 years, or 88BN including the actual value of the cash. Given how low current dollar rates are, and Apple’s superlative credit rating it seems likely that the true cost would be far less.

        One could argue that there is a problem that the marginal benefit varies as the amount of cash increases. This is almost certainly true, fortunately we have the advantage of knowing that Apple has been debt free for years and there have been no announcements of credit lines in all that time.

  • Dirk, congrats to that great blog post. I really like the idea of not just looking at Apple’s cash balance at face value, but rather treat it as an option.

    Couple of comments / thoughts on the above:
    1. Do you think it would make sense to discount the option value of the cash with an assumed tax burden? From the recent earnings release call I understood, that a large part of the money is abroad and cannot be transfered to the US or put to any other productive use without taxing it.
    2. I’m afraid Apple will not be able to make the 70% RoCE assumed by the 25% explained value applied above. Unfortunately… 😉
    3. I think you mixed up the REV/EBIT and REV/EBITDA numbers above. EBITDA > EBIT and therefore REV/EBITDA < REV/EBIT
    4. Using the face value of cash instead of the option value, I get the below:
    – EV/EBITDA (LTM): 8.2x
    – EV/EBIT (LTM): 8.7x
    – P/E (LTM): 11.3x (though excluding cash on P/E level is technically incorrect; would be 14.5x incl. cash)
    Still rather low multiples given the growth path, profitability, positioning, and industry outlook.


    • 1) I suggested Apple could borrow against the cash at hand. If the cash is abroad, Apple could ask a foreign bank in the same jurisdiction as the currency to provide financing.
      2) Apple just made an RoCE of over 100%. But the range is more of a thinking exercise.
      3) Thanks a lot!
      4) My numbers from when the article was written (in USD billion):
      Mcap 391.5
      Cash 81.57
      EV 309.9
      EBITDA 2011 35.6
      EBIT 2011 33,8
      The market cap of the time when the article was written to mcap now most likely explains the difference.

      • 1 & 2) Understood.
        3) You’re welcome
        4) I guess you got me wrong. Didn’t want to point out any differences. Just wanted to share what the multiples look like if face value of cash was used. I used the same numbers as you did (with a slightly lower mcap back than). All good.

      • Alright.

  • Anonymous

    There is presently a very strong correlation between price and earnings per share from almost exactly three years ago. Price was almost exactly 25% of what it is today, and earnings per share are almost exactly 25% of what they are today. Note that almost exactly three years ago, Apple bottomed after the huge market drop due to the onset of the Great Recession. This strongly impies that all growth in Apple stock since that time has been driven directly by investors tying the stock price to materialized rather than projected earnings per share. If this is true, then going forward we should be able to predict Apple’s future minimum stock price. If the earnings go up 100% per anum, the stock price will go up a minimum of 100% per anum. Since the P/E ratio presently stands at a little over 14, we can say that any P/E less than 14 is not likely to stand for long.

    Note that the huge Apple cash position appears to have no direct bearing on the stock price, other than perhaps coincidentally growing at the same rate as earnings per share.

    • On the contrary, the only thing that has a bearing on the stock is cash. Earnings have no bearing. See:

      • Anonymous

        Are you saying that it’s just a coincidence that EPS and stock price have both gone up almost exactly 300% over three years? Also, see my other clarifying post below.

      • Yes, of course cash-based pricing is entirely coincidental or at least I hope so. But my point is that the stock price certainly has is no correlation (and hence no hope for causation) with earnings growth.
        Valuing Apple at 5x cash has been a remarkably consistent rule of thumb and a rule that has held for years now.

      • gbonzo

        “the stock price certainly has is no correlation with earnings growth.”

        Do you realize that if the reported earnings growth matches the estimated earnings growth, then the stock price should not move much.

        Example: market estimates earnings growth at 100%. The growth comes at 100%. The stock price should not move much as a result. Certainly the stock price should not rise 100% because of this.

      • Of course. If the growth is foreseeable it will be discounted and will not cause the stock price to move. Stock owners are only rewarded for unforeseen growth.
        But that has not happened. Apple’s growth has not been foreseen. At least judging by analyst estimates (both buy- and sell-side). The unexpected growth has not been discounted and the price of the equity has not reflected unforeseen growth. Not only have estimates been too low, but they have been typically too low by a huge margin, with beats measured in dollars per share. Analysts have predicted 20% growth and the result has been 70% to 80% growth for years. And yet, the stock is valued at a single digit multiple of FCF.
        One could maybe argue that the massive beats have become predictable and therefore foreseeable and therefore should be ignored. I can no longer imagine how this logic follows. I can only see the possible absurdity of a high-growth company valued below book value. The consequence would be that it would become an easily financed takeover target.
        When I said the stock price has not responded in any way to earnings growth it is to suggest that it has not responded to unforeseen earnings growth.

      • Sacto_Joe

        Exactly, Horace. My premise is that earnings growth for Apple is only believed after it is seen. (Amazon, OTOH, is being bid up on expected future earnIngs.) That is why I contend that Apple stock is being driven by earnings, but in a totally backwards manner. Investors are being dragged into buying Apple stock kicking and screaming all the way.

      • “Investors are being dragged into buying Apple stock kicking and screaming all the way.”

        LOL! No judgment – just love this visual of people being cattle-prodded into handing over cash at some sort of bank-teller counter in exchange for stock-certificates, looking like chastised 3 year olds w/ pouty lips the whole time!

      • gbonzo

        “the price of the equity has not reflected unforeseen growth”

        Not true. Apple stock price has beaten S&P500 by a huge margin.

      • Anonymous
      • Anonymous
      • Anonymous
      • Sacto_Joe

        BTW, just for grins, I went back 5 years. Talk about a divergence between stock price and earnings!

    • Anonymous

      When I say Apple’s cash position has no bearing on the stock price, I don’t mean it doesn’t correlate with its stock price. I mean that, subtracting Apple’s cash, presently at about $80/share, from Apple’s stock price, however one wishes to do it, would submarine Apple’s effective P/E far below 14. Thus, investors are not pricing Apple’s cash position into the stock price. They are valuing Apple today at the same P/E they did three years ago, right after the Great Recession market crash – and totally ignoring its vastly improved cash position.

      • Anonymous

        Actually, the cash position may be relatively about the same when compared to EPS three years ago and EPS today. But there’s a huge difference between $20 billion in cash and $80 billion in cash, when the number of outstanding shares hasn’t changed much!

  • MOD

    Instead of computers, Apple is starting to build … solar panels. And … office buildings. This is the beginning of the end.

    A foole and his monie be soone at debate,
    which after with sorrow repents him too late.

    That is an early version of the proverb “A fool and his money are soon parted”.

    • Anonymous

      Not sure why you see these as poor investments. Solar is a hedge against a probable future increase in the price of fossil energy. That’s why I’ll be installing it on my house. And a campus that puts all workers within close proximity of one another, which this design accomplishes, is a smart business decision. The assumption is, of course, that they will grow the number of employees sufficiently to fill that huge building. I personally see no reason to doubt it.

      In short, these seem more like nits you’re pcking than serious reasons to call out Apple for wasting money. But perhaps I’m wrong….

      • Anonymous

        Lets face it – that solar plant is a hedge against protests by Greenpeace, it’s nothing to do with power prices. It won’t supply nearly enough of the datacenter’s power requirements to matter except as greenwashing.

      • jawbroken

        Do you have a calculation that supports the claim in the second sentence?

      • Sacto_Joe

        From the first AppleInsider article:

        “Apple’s solar farm will be placed on 171 acres of vacant land on Startown Road. It will power the $1 billion data center that opened earlier this year and helps to power Apple’s online services, including iCloud and iTunes.”

        From the link to the AppleInsider article:

        “Apple prides itself on using sustainable energy for its facilities, which include data centers. According to the company’s website, just 2 percent of Apple’s energy footprint comes from its facilities around the world. Currently, facilities in Austin, Texas; Sacramento, California; and Cork, Ireland use 100 percent renewable energy, saving as much as 21,500 metric tons of CO2e emissions.”

        I’d echo jawbroken; do you have information to the contrary? I will say that it’s not likely that all energy produced will come from the solar farm. I’m not sure what the rules are in North Carolina, but in California if you produce more energy than you use it becomes free energy to the power company. So typically you “size” a solar unit so that it produces most of the energy required, and you don’t pay for “overproducing”.

        But in a farm that’s as large as this, it’s more likely that they’d have clean-burning generators that they can bring online to avoid the problem of “overproducing” and thus avoid relying on the “dirty” energy produced by Duke Energy. That’s obviously important as well if you want to be able to power the plant when there’s insufficient sunlight or insufficient stored energy.

      • jawbroken

        Some further information suggesting it could provide a significant portion of the facility’s power here

        Difficult to call it greenwashing, especially at a point in time where they haven’t promoted it at all.

      • The economics of solar are not as simple as that. Much of the value of the solar plant is in moderating peak costs. Solar’s value for commercial properties is in smoothing loads and hence reducing uncertainty of pricing.
        It actually makes a lot of sense for data centers as they increase their load during peak solar hours. Solar makes little sense for residential use due to the poor overlap with weekday consumption patterns. I’m sure a good ROC case can be made for solar in this particular site.

      • Anonymous

        Actually Horace, so long as you can sell back excess power, solar makes fine sense even for residential (at least in California). We have time of use metering here and earn a 10% ROI on our residential solar. A return that is in cost savings and therefore is effectively after tax.

      • That’s a valid point.

    • You should know better than to read the stuff from those Wall Street types. I covered capex spending in great detail. If you would read my posts on the subject you’d easily recognize the flaws in the piece you linked.

      • gbonzo

        What if the truth is somewhere in the middle? For example that a small piece of the increasing capex is related to office project?

      • Of course there is a budget for office space. The argument is whether buying solar panels for a data center is the “beginning of the end”.
        I’ve heard the argument that “vanity buildings” and extravagant campuses are the signs of hubris and imminent demise. This can be easily disproved with a list of prominent landmark corporate headquarters for long-standing successful companies. I’ve gone through this more than once.
        The $8 billion will not be spent on new stores (that’s a separate budget) and given previous patterns, new construction projects are unlikely to be “significant chunks”. The land and both the data center and the campus have already been purchased. The data center construction is complete and the campus will be built gradually and take until 2015.
        The vast bulk of the spending will be as it always has been since 2007: machinery and manufacturing equipment and servers to support iOS.

      • davel

        I don’t see solar panels being an issue at all.

        1) I doubt building them is that hard. In fact I read a piece about a kid who built a farm from scratch.
        2) I have read that Apple has looked into solar powered devices, so this is just an extension of that.
        3) Any knowledge of issues with solar will help it as it explores solar for consumer electronics.

      • Anonymous

        Solar is cost competitive with other electrical anyway as prices on panels have cratered and there is a 30% investment tax credit on it. I fail to see how that is even a marginal concern. The energy from the solar panels will cost the same in 30-50 years as it does in 2011. Good luck achieving that with grid power.

    • Pinczower

      Funny – I remember “Instead of computers apple is starting to build music players” that worked out OK.

  • Westechm

    I would like to see this type of analys appilied to

    • I might be working on it, but may I ask for your motivation to pick Amazon?

      • Westechm

        Sorry to take so long.

        First some basic facts

        Amazon and Apple are in two distinctly different businesses. Apple is a high tech manufacturer of hardware and software. is a high growth company, huge margins, very profitable, and has a mountain of cash. Amazon is an on-line supermarket, razor thin margins, high volume, solid growth (until the last quarter), fairly good cash flow and cash position.

        Over the last two years Apple’ revenues have increased 2.5 fold, and profits by more than 3 fold. Amazon had shown a steady growth in revenues and earning, but not nearly as fast as Apple’s, but in the last quarter their profits dropped dramatically.

        The two measures for the value of a company are Market Capitalization and EV (enterprise value). Apple’s value by either measure is about four times that of Amazon.

        The P/E ratio under most conditions is a rough measure of how much growth investors anticipate. Apple’s P/E is around 12-14, while Amazon’s is about 100. As generally interpreted this means that investors expect a lot more growth from Amazon than from Apple. Amazing. As Apple has grown wildly for the last four or five years the ‘market’ has not expected it to continue.

        I was hoping (but not really expecting) that your analysis might reveal something we have missed.

      • Anonymous

        Investors believe that Amazon is a “safe” investment. It’ll be interesting to see how safe it is if the Kindle Fire bombs….

      • Westechm

        Safe investments usually have a P/E of ten to fifteen, like Microsoft.

        I believe that the Kindle Fire is an e-reader with features It is not a competitor of the iPad. Amazon is stepping a bit outside of their field of expertise which is always dangerous, but they probably are not stepping very far. The biggest question is why did Amazon’s margin drop so abruptly before the new Kindle, which supposedly will sell at a loss. Maybe they used some kind of accounting gimmick to take at least a part of the loss before the Fire went on sale? More likely their expenses got out of hand, or their pricing is out of hand. I will have to take a close look at their financials when I have a chance.

      • Sacto_Joe

        Every term, like “safe investment”, is relative. I should have been more clear about the context.

        I was really focusing on this issue of why Amazon seems to have a high P/E while Apple’s is much lower. My conclusions parallel what I think I see as yours, in that, even though the two companies are distinctly different, taking this into account it’s hard to countenance Amazon’s P/E being nearly 8 times larger than Apple’s.

        To me, it’s an issue of investors missing the obvious in both cases, but for different reasons. For Amazon, there’s no doubt that it has been growing handily during the economic turn-down. Also, investors in Amazon have been amply rewarded for their perseverance. And as my wife pointed out, every investor uses Amazon’s services. They know the “product” and literally endorse it with their usage of it.

        It’s also a fact that investments that are perceived as safe (there’s that word again) can offer, in this day and age, very little return and still be considered attractive. I was just reading a story about how banks have so much more cash than they can use that they are actually in some cases charging customers to keep their cash with them! That’s the level of fear that’s out there!

        But if the Titanic is sinking and everybody rushes to a given lifeboat, there comes a point when adding more people to the lifeboat makes it increasingly liable to sink as well.

        Anyway, that’s my take on the reason for Amazon’s ultra-high P/E ratio.

        Apple’s story is kind of the reverse of this. Apple’s earnings are not believed in – until they become real. I can say until I’m blue in the face that Apple’s EPS will go up 100% within a year and a half, but people won’t believe it – until it goes up 100% a year and a half later. The reasons for this lack of belief are many and varied, and frankly don’t really matter. What matters is that it’s real, and that it’s drastically affecting the P/E of Apple.

        Consider: If I’m right and Apple doubles its EPS a year and a half from now (if not sooner) to about $55/share, and the P/E ratio stays around 14, the price of Apple stock would have to go to almost $800/share. That is literally unthinkable to most investors. So they won’t gamble that it will.

        So what happens? The stock bumps up every quarter when the earnings indeed turn out to be stellar, but only grudgingly. As a result, the P/E sinks lower and lower. Two years ago, the P/E was at 20. Today, it’s at 14.2. A year and a half from now, it might be at 10. If it is, then Apple stock won’t be worth $800/share, it’ll only be worth $550/share.

        The problem with this “kick the can” approach is that Apple’s earnings are consistently growing at very high percentages, year after year. So three years from now, the EPS will likely have doubled again to $110/share. But to maintain a P/E of 10, that means Apple’s stock price would have to double – from $550/share to $1,100/share – in a mere 1 1/2 years.

        And if it doubles again a year and a half later, then once again to maintain that P/E of 10 Apple’s stock price would have to double – to $2,200/share.

        That’s the kind of insanity that’s building into Apple stock right now.

        It’s also why I’m holding Apple long, and for as long as possible….

      • We can look into this as well (time is my limiting factor). Maybe comparing this analysis to Amazon may be not the most suitable approach. I am not an up to speed with Amazon’s valuation at the moment. When I read the latest 10Q, I noticed two things
        1) a one-time increase in fulfillment capacity
        2) a permanent increase in “Technology and Content” costs

        There are several factors that contribute to difference in P/E ratio. You pointed out growth, I would also add business model including margins, cost of capital, etc.

        One nugget I found looking at Amazon was the historically stable P/Book ratio of around 12x. A very reliable measure for the past years.

        Sorry, that I can only sporadically point out things to this topic.

      • Westechm

        Gross margins haven’t changed, so the decrease in profits all must come from increased operating expenses. The details behind fulfillment costs are rather opaque so its hard to say what will happen going forward.

        If Amazon sells one million Kindle Fires in the current quarter, and if indeed they lose $50 on each, that would be $50,000,000. If they net 2% of sales at the bottom line they would have to increase sales by $2.5 billion to offset it. Their current media sales are about $4.1 billion. Doesn’t make sense to me.

        This should be an interesting quarter for Amazon.

    • Me too.

  • brainless

    Pretty charts notwithstanding, I just don’t see how Black Scholes is appropriate here. As someone once said, I’d rather be approximately right then precisely wrong.

    I more insightful, but less mathematically precise, analysis would indicate that the value of Apple’s cash at these levels is clearly “negative” to the company valuation.

    Even Ben Graham back in his 1936 Security Analysis demonstrated that….and it is just as relevant now as it was back then.

    • I will read up on this, but I do not see cash holding as such, as a problem. Happy to here your approach to the topic.

      • brainless

        Yes, Ben Graham has a whole section on this subject, laying out bare the negative consequences of hoarding excess cash and consequences to shareholder value. I am only pointing to this, because folks would rather believe an “expert” then think for themselves. In any case, Ben Graham’s treatment on the subject is about as clear and no-nonsense observation as I’ve ever seen and one that stands the test of time…

        Clearly there is no point convincing the “believers” here on on similar boards that hoarding un-investable cash leads to massive destruction to shareholder value (as is the case with Apple), because they will always point out the seemingly logical, but pointless observations:

        – Look how much the stock has gone up
        – Look what happened to other stocks of companies that re-purchased shares (i.e. plently that have not done well)
        – Growth companies don’t pay dividend
        – Apple is “using its cash” for supply-chain investments
        – …and many other platitudes that belong to the same league as “Apple can not grow, because of law of large numbers…”

        Oh, well. The only saving grace is the current policy is keeping the stock vastly undervalued, allowing for continued beneficial purchase points – good for future investors….

        p.s. And the Black-Scholes excersise..that’s like trying to fit a square peg in the round hole…:-(

      • davel

        Would you care to summarize why cash is a drag?

  • Anonymous

    “Volatility: A measure that determines financial risk of a certain asset. Apple’s share has shown a volatility of 26,1% over the last year.”

    That seems awfully short-sighted and more in line with looking at a company such as General Mills on a historical level. Apple would seen to be near triple digit. Also, average volatility doesn’t work well for Black Scholes, one would be better using Heuristics to value options better than Scholes.

    Though we are a boutique private trading group, mostly options, futures and certain derivatives, we do not use Black Scholes. For better reasoning, please refer to research done by Espen Gaarder Haug and Nassim Nicholas Taleb.

    We treat cash as a liability depending on the business. Such a case would be a business where future legal or IP obligations are possible, deferred taxes or revenue, AR or inventory; basically any potential future claims on cash (whether now or possible in the near future).

    • Here are my volatility stats:

      10 days 16.89%
      20 days 22.13%
      60 days 32.76%
      120 days 27.42%
      150 days 26.66%
      180 days 26.21%
      200 days 25.14%
      260 days 24.20%
      1 year 26.10%
      162 weeks 37.45%
      Maximum 37.45%
      Median 26.15%
      Average 26.50%
      The average is a good representative.

      I can see the benefit of a heuristic approach, but in this article it would add one more variable that can not be observed or derived.

      I will also catch up on the mentioned research.

      There are good reasons to assume material liabilities outside operations as liabilities reducing cash at hand. I would not include items that drive operations like NWC, taxes only when not due to business model.

      • Anonymous

        Hi Dirk,

        Here is something else you might like to look at, and thank you for the posts. I do not read many blogs, but I have come to appreciate Asymco and the two authors.

        “Modelling the implied volatility surface: an empirical study for FTSE options
        Author: Amadeo Alentorn ( PhD in Computational Finance
        Centre of Computational Finance and Economic Agents University of Essex
        Supervisors: Dr. Sheri Markose & Dr. Kyriakos Chourdakis”

      • Thanks, I shall read this too.

  • JZ

    If Apple were to return some of the cash to share holders in the form of a special dividend, share holders will have options to invest the cash as he or she see fit. There are options values for each individual share holders ( different tax rates, ages, risk aversions, and other investment opportunities). I for one have no problem to have Apple invest the cash on my behalf because i presently don’t have a more compelling alternative (no opportunity cost for me). But some investor may have opportunity cost. can you incorporate opportunity cost for individual investors into your analysis? Maybe take into account of difference return of SPX index and AAPL return? I bet AAPL’s cash still has option value, but it is not as big?

    • Anonymous

      Actually you still have an opportunity cost, you could invest the cash in Apple. While it might seem that this is the same as not receiving the dividend in the first place, in fact it is, since you will end up owning a larger percentage of Apple, and thus a higher proportion of their future earnings and growth will accrue to you.

      • JZ

        you are double counting here.

      • Anonymous

        Apple is two businesses right now, a world leading consumer electronics firm and an $80Bn dollar fixed income fund. A special dividend would allow you an opportunity to invest more in the world leading part, and less in the stodgy world of fixed income.

      • JZ

        not really, if i use the cash dividend to buy more shares, it is the same as Apple investing the cash in insanly great opportunities and my existing share price would go up. just look around, few hedge funds are actually making money if not loosing money? I’m just not a better capital allocator than Apple at this point.

    • JZ

      Upon further reflection, I think Apple’s cash option value is not that of traditional financial options as modeled by Black-Scholes, Rather It should be modeled as REAL options. let me explain:

      If Apple sees an attractive investment (call it investment X) and if the investment X is a publicly traded company, there is really no difference between Apple using its cash to buy X and Apple paying out the cash to shareholders who then buy X themselves. perhaps this is why we rarely see Apple buying publicly traded companies.

      If Apple sees an attractive investment in private market (call it investment Y, think Siri or potentially twitter, etc), there is little chance that individual investors will be able to invest in Y with cash payout from Apple, Apple has a much greater chance to buy Y. That’s a REAL option which cannot be modeled by traditional Black-Scholes. There was no way for me to buy Siri, but because Apple bought Siri and it will sell a lot more iPhone 4S because of Siri, I rip the benefit as a shareholder. That’s the option value.

      Apple can also invest in supply chains, obtain discount due to large orders, pre-pay component manufacturers in exchange for lower prices and guaranteed supply, etc. , these are all examples of REAL options that can not be modeled by Black-Scholes.

      My conclusion: Yes, Apple’s cash does have large option value but its value is not the same as financial options modeled by Black-Scholes.

      • Actually there are different models to value real options. Black and Scholes may not be the best, but it is very established.

  • The value of Apple’s cash is about $80 per share, corresponding to 20% of its current stock price ($400) and hence 20% of its valuation. Do we really need a more complicated analysis to estimate the value of Apple’s cash? Given the wide range in the presented result I have doubts about it and would consider the presented result as an indication that the simple calculation in sufficient.

    • Well, I’ve just read in another comment from a financial expert that he considers cash to be a liability so I think we can use all the education we can get.

      • Guest

        Hi Horace,

        I am referring your earlier article about apple trading 5X cash and that AAPL will touch $500 when cash on BS is $100. When do you see that happening.

        Also, BS cash seems to grow exponentially as well & not linearly! Based on that what is your thought on an equation to model cash growth? That is when will cash hit $120B, $150 B etc..


      • I believe Cash will reach $100 in two quarters. I can’t really predict much further out.

  • Anonymous

    Thanks for reminding me of my quant class in grad school! Anyhow, wouldn’t an option price value for Apple’s cash be more valuable in determining a purchase value for a company like Apple, rather than a share price value?

  • i am an option trader and this is BS.
    first volatility should be the one of your ‘potential investment’
    second ‘real option’ theory does not take into account the fact that you are short the other guy’s options.

    this theory is a monument to gullibility of the executive layer

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