The Law of Large Numbers: Has Apple Hit a Wall? (Featured Article)

The article featured below was contributed by fellow Apple investor Bhagwan “Bags” Motwani. Bags is an ex-CPA with a graduate education in financial markets and eight years marketing experience in the consumer wireless space. Bags also creates interactive Apple earnings calculators (access his latest 1Q2013 calculator here). You can reach him at

Has Apple Hit a Wall? (by Bhagwan Motwani)

January 15, 2012 (11:00 am)

Will Apple ever see $700 again? Has it hit the wall because it ran into the Law of Large Numbers? Is Apple yet another victim of history repeating itself?

Within the last dozen years, this history has had Microsoft see its market capitalization decline from $642 billion in 2000 to $226 billion today. Cisco reached its market capitalization peak of $557 billion in 2000, only to fall to $108 billion today. Does more pain await Apple as its market cap drops from its high of $661 billion in September of 2012 to $489 billion today?

Naturally, there are some key differences between Apple today and the Microsoft’s and Cisco’s of the tech bubble days, first and foremost being the insane PEs of these two giants (Cisco’s PE was 120x at its peak). Not to mention the animal spirits or irrational exuberance that goosed the market in the dot-com era.

But, do the market cap comparisons above tell us that there is an inevitability to gravity re-asserting itself and could what we have seen with Apple over the last quarter be indicative of this? And, worse, could it presage a continuing drop in Apple’s market capitalization (and by extension its stock price)? After all, earnings growth has and continues to decline as we look at decelerating and perhaps even negative earnings growth over the next few quarters.

This phenomenon, whereby market capitalization reaches a nadir and then declines precipitously, is commonly referred to as companies confronting the “Law of Large Numbers”.

In this article, we will weigh both sides of the argument as to whether the Law of Large Numbers will stymie Apple’s market capitalization and, by extension its share price, or whether the Law of Large Numbers is irrelevant and Apple’s market capitalization will be determined by other more germane factors.


Before we delve into this topic, however, some definitions may be useful.

The Law of Large Numbers is really a statistical term which states that the number of times an experiment is repeated, the average of the results will revert back to the mean. A perfect example would be the case of coin flips, where an increasing number of coin flips will result in something increasingly closer to a 50-50 split between heads and tails.

The financial markets and analysts have taken this term and modified its definition to represent the concept that a company cannot keep growing at a constant incremental rate for extended periods of time. A perfect example is Apple. The table below shows what happens when revenue and earning grow at 20% and 40% rates over 5 years.

AAPL Growth

If Apple were to successfully grow at 40% per year for the next 5 years, the company’s revenue would see more than a five-fold increase, EPS would reach $226 and the stock price, assuming a PE of 12x would reach $2700, for a market capitalization of $2.5 trillion. Just to put in in perspective, the value of the entire U.S. stock market is $15 trillion. A 20% growth rate over 5 years is also shown, and while more reasonable still represents a significant stretch. Clearly, compounded growth rates of this nature are both unrealistic and unsustainable and highlight the limitations that the Law of Large Numbers espouses.

Some very simplistic assumptions are employed in this table (for example Gross Margin remains the same, number of shares outstanding for the market cap calculation remains consistent). This was done intentionally to highlight the magnitude of change that compounding growth rates can drive, even over a relatively short period.

By the way, the Law of Large Numbers doesn’t necessarily mean that once a company’s market capitalization hits some kind of a theoretical wall, it is automatically going to slide back and never breach it again. All it says is that companies cannot afford to grow indefinitely at any given rate because the absolute incremental numbers for revenue and profitability get so big that they, in all likelihood, can never be met. Remember, nothing grows to the sky.

As for the definition of Market Capitalization, the term refers to the overall market value of the company and is simply the total dollar market value of of a company’s outstanding shares. It is easily calculated by multiplying a company’s shares outstanding by the current market price of one share. So, in the case of Apple, its market cap at the end as of December 31, 2012 was $503 billion.

The table below of U.S. companies with the Top 3 market capitalization’s over the last 3 years shows that Apple, despite its swoon over the last quarter, still managed by the end of 2012 to be the most valuable U.S. company.

Top 3 Market Caps (U.S. Companies)

Top 3 Market Caps


Given Apple’s price performance over the last quarter, some are asserting that the law of large numbers is already starting to have its impact on Apple. As conviction that growth is starting to slow, they offer the following evidence:

  1. Valuation: Apple’s P/E is less than 11 based on 2013‘s earnings while the markets P/E for the year is 13. This is a low growth valuation because investors are asking how Apple can get bigger. And, indeed, Q3 and Q4 2012 earnings reflected only high single-digit year-over-year growth, down significantly from the previous 2 quarters and below the growth experienced in 2011, proof that things are slowing for Apple.
  2. Competition: On a variety of fronts. While its ecosystem is vaunted, Apple may lose its edge as computing shifts to the cloud and it faces a slew of competitors from Microsoft to Google to Amazon. On the handset front, Samsung is the market leader in unit sales. Its Galaxy S3 and Note2 devices, with bigger screens, “phablet”-type features and innovations like NFC that enable devices to interact with each other put Apple at a disadvantage and call into question Apple’s innovation strategy.
  3. Stumbles: Production snafus and the Apple Maps debacle are just two of the more recent errors, allowing competitors like Samsung and Google to gain a foothold casting further doubt on Apple’s growth trajectory.

The upshot of all of this is that the valuation of Apple stock is 20% below that of the overall market – a P/E compression brought on by the concern that Apple has confronted the Law of Large Numbers and has lost.


Others do not subscribe to the Law of Large Numbers theory for Apple and feel that the stock looks like a bargain by any measure. They offer as evidence:

  1. Market Share: Apple has low penetration in world’s biggest markets – cellphones and PCs. Given that there are over 6 billion cellphone subscribers worldwide, Apple’s market share today is in the single digits, leaving more room for expansion. Expanding to carriers like China Mobile may be one such avenue. Ditto for PCs, where Apple’s 10% share offers some upside opportunity. Admittedly, the PC market is expected to be flat to slightly down, but Apple has room to grow relative share.
  2. Rapidly Growing Markets: Even in markets where Apple’s share is significant, such as for Tablets, the size of the market is expanding at a rate where relative market share declines for Apple (given the slew of competitive devices entering the market), are still expected to result in significant unit volume increases for Apple for the foreseeable future. Apple’s Tim Cook has been quoted as saying that there will be a day when the Tablet market will be larger than the PC market.
  3. Operating Leverage: The concept of Operating Leverage is one where fixed costs can be spread over a larger production base to provide gross margin advantages. This augurs favorably as Apple continues to grow its currently modest share in cellphones and as it continues to enjoy unit volume increase in Tablets as that market expands significantly. This operating leverage provides outsized gains in margins and earnings at slower rates of revenue growth.
  4. Next Big Thing: whether it be an Apple TV, wearable computing, different iPhone form factors or something else, Apple has a tradition of introducing innovative new products that should help fuel Apple’s growth engine.
  5. Recommended: Of the 57 analysts covering Apple, 50 still rate it a buy. Proof that there is confidence that the arguments offered above can continue to fuel Apple’s earnings growth.

Opponents of the Large Numbers Law are not naive enough to believe that the Law will never affect Apple. In fact, they believe that the Law of Large numbers will only begin to affect Apple once the products they compete with achieve critical mass from a market share perspective.


Nothing can continue to grow forever. Believing that it can defies the laws of nature and the laws of business. The critical question regarding the sustainability of growth concerns the point at which growth either starts to decelerate, slow down or reverse.

Apple bears argue that slowing growth was already evident in FY Q3 and Q4 earnings and that FY Q1 guidance points to negative earnings growth. What they’re essentially saying is that the Law of Large Numbers has started to assert itself and Apple will never regain its stock price highs of 2012.

Apple bulls contend that growth may have slowed, but this is a temporary situation caused by transition quarters where Apple was renewing virtually its entire product line. This led to demand hiccups, put pressure on supply channels, created production challenges and negatively impacted margins. Bulls feel that growth will resume and continued double-digit growth will re-assert itself going forward, leading to new highs for the stock in 2013 and beyond.

2013 will be a pivotal year in determining whether Apple is yet another victim of the Law of Large Numbers. If the bears are correct, 2012‘s comparisons will prove to be too much to overcome and flat or negative growth will be the outcome. If the bulls are right, Apple will have been successful in continuing to innovate and increase market share and will be able to delay its destiny with the Law of Large Numbers. But it will merely be a deferral, because at some point in time, the inevitability of the Law of Large Numbers will catch up, even with Apple.

Disclosure: I am long AAPL. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it. I have no business relationship with any company whose stock is mentioned in this article.

Written by Bhagwan Motwani.