To Beat the Law of Large Numbers, Apple Must Expand Its Product Line

The New York Times today addressed Apple's record growth in both revenue and stock price in the context of the "law of large numbers".

Apple is so big, it’s running up against the law of large numbers.

Also known as the golden theorem, with a proof attributed to the 17th-century Swiss mathematician Jacob Bernoulli, the law states that a variable will revert to a mean over a large sample of results. In the case of the largest companies, it suggests that high earnings growth and a rapid rise in share price will slow as those companies grow ever larger.

If Apple’s share price grew even 20 percent a year for the next decade, which is far below its current blistering pace, its $500 billion market capitalization would be more than $3 trillion by 2022. That is bigger than the 2011 gross domestic product of France or Brazil.

Put another way, to increase its revenue by 20 percent, Apple has to generate additional sales of more than $9 billion in its next fourth quarter. A company with only $1 billion in sales has to come up with just another $200 million.

Apple has posted annual revenue growth of 16%, 56%, and 69% over the past three years respectively, with sales rising from $39 to $61 to $103 billion. Staggering growth for a company this large, but Apple seems to be continuing the trend for fiscal 2012. Apple reported more than $46 billion in revenue for the first quarter, and provided guidance of $32.5 billion in revenue for the second quarter.

This $78 billion in revenue for the first half of fiscal 2012 (which will likely be higher, as Apple traditionally underestimates on guidance) represents yet another massive increase in revenue from the year-previous quarters. The Q1 2012 number is a rise of more than 73% over the prior year, and the Q2 guidance would represent a 32% increase growth.


The enormous growth Apple has shown in recent years is largely on the backs of two products: the iPhone and the iPad.

The iPhone, as a product category, has grown from a mere $630 million in sales in 2007, to more than $47 billion in fiscal 2011. The iPad, for its part, tallied more than $20 billion of Apple's revenue last year. Between the two of them, Apple's main iOS devices account for more than 65% of Apple's total sales. Remove those two and Apple is a much different company.

It's all a bit of a theoretical exercise, of course. The iPhone and iPad halo effects are real, and have had a beneficial impact on other parts of Apple's businesses -- but the point remains: Apple's astounding growth is the direct result of the company's move into new product categories.


As the above chart shows, Apple's overall year-over-year revenue growth is impressive, but if the iPhone or iPad is backed out, the revenue growth is much less awe-inspiring. Without the iOS devices, Apple only showed 12% and 8% revenue, versus 56% and 69% otherwise.

To continue doubling its total revenue every two years, there are two main possibilities:

Apple would need to show extraordinary -- perhaps impossible -- growth in its iPad and iPhone divisions. Massive sales growth from the iPhone (which has grown more than 90% each of the past three years) and iPad can drive Apple's revenue growth for quite a while, but not forever.

If the iPhone were to continue its 90% annual growth for two more years (which would count 5 consecutive years of near 90% annual sales increases), in 2013 Apple would have nearly $170 billion in revenue coming just from the iPhone. The iPad, which grew an astounding 330% from 2010 to 2011, would report $78 billion in sales that same year -- $248 billion between the two.

Impressive (hypothetical) growth, and given Apple's astounding first quarter numbers, perhaps doable. But follow those numbers out to 2015 and the numbers begin to grow to improbable sizes.

The more likely prospect is for Apple to launch into yet another product category, in addition to the growth of its existing businesses. The possibilities are endless, but there is one new product that seems to be getting more attention than the others.

One thing is for sure: whatever is coming out of Apple's Cupertino R&D labs next is key to the company's continued explosive growth.

Top Rated Comments

(View all)
Avatar
113 months ago
I don't think you need the golden theorem to explain the point, the writer got a little overzealous
Score: 19 Votes (Like | Disagree)
Avatar
113 months ago
Hopefully they’ll focus first on having a passion for making great things--things that meet a need really well--rather than following the dictates of a mathematical model! The latter may be necessary to sustain maximum growth, but it’s not sufficient—and could even harm the philosophy that has caused all of Apple’s growth to date!

“The charts say we need to be in some new areas... what product lines can we add?” sounds like an approach worthy of many of Apple’s failed competitors...

Of course, as a user and not a stock owner, I don’t care whether Apple’s bottom line grows on the same curve forever. I just want them to keep making good stuff that’s so simple it seems obvious, yet can’t be duplicated!
Score: 18 Votes (Like | Disagree)
Avatar
113 months ago
APPL doomers have been around for years, maybe some year they will be right, but it's not going to be in 2012.
Score: 15 Votes (Like | Disagree)
Avatar
113 months ago
"Also known as the golden theorem, with a proof attributed to the 17th-century Swiss mathematician Jacob Bernoulli, the law states that a variable will revert to a mean over a large sample of results. In the case of the largest companies, it suggests that high earnings growth and a rapid rise in share price will slow as those companies grow ever larger."

Ugh. So wrong. So so wrong. It suggests nothing of the sort. In fact, it suggests nothing at all about Apple. He even has a paragraph about Bernoulli. Painful.
Score: 13 Votes (Like | Disagree)
Avatar
113 months ago

Apple is so big, it's running up against the law of large numbers.

Also known as the golden theorem, with a proof attributed to the 17th-century Swiss mathematician Jacob Bernoulli, the law states that a variable will revert to a mean over a large sample of results. In the case of the largest companies, it suggests that high earnings growth and a rapid rise in share price will slow as those companies grow ever larger.


That's not what the law of large numbers suggests. Kind of sad that the New York Times is so badly misusing that term.

Apple's numbers are amazing.
Score: 13 Votes (Like | Disagree)
Avatar
113 months ago

I don't think you need the golden theorem to explain the point, the writer got a little overzealous


Seriously. The law of large numbers is not a law about anything that involves large numbers.

This just in: "Apple needs to spend its cash reserves if it's to beat the Heisenberg Uncertainty Principal."
Score: 12 Votes (Like | Disagree)

Top Stories

iPhone 12 Pro in Graphite and iPhone 12 in Blue Shown Off in Unboxing Videos

Monday October 19, 2020 8:20 am PDT by
While the iPhone 12 Pro does not launch until Friday, we now have an early unboxing video of the device courtesy of Twitter account DuanRui, providing a closer look at the shiny new flat-edge design and sleek Graphite color option. Ben Geskin re-uploaded the unboxing video to YouTube, which we've embedded below: Geskin has also uploaded an unboxing video of the iPhone 12 in Blue: ...

Kuo: iPhone 12 Pro Demand Higher Than Expected

Sunday October 18, 2020 10:39 pm PDT by
TF International Securities analyst Ming-Chi Kuo released a research note this morning detailing what he's seen with the volume of iPhone 12 and iPhone 12 Pro pre-orders in the first weekend of sales. Kuo had previously indicated that Apple's estimated shipment allocations for the new iPhone models placed the iPhone 12 at the top with 40-45% of inventory allocation (up from 15-20%). However, ...

Apple's New MagSafe Charger and Cases Begin Arriving to Customers

Saturday October 17, 2020 10:10 am PDT by
Apple's new MagSafe charger and cases have begun arriving to some customers earlier than expected, and images of the accessories have started to surface on Twitter. The photos provide a first look at the products in real-world use. As of writing, some MagSafe cases are also available for pickup at select Apple Stores in countries like the United States, Canada, and Germany. Filip...

HomePod Mini Cable is Non-Detachable, Ends With USB-C Connector for Use With Included 20W Power Adapter

Friday October 16, 2020 12:45 pm PDT by
While not detailed in the tech specs, MacRumors can confirm that Apple's new HomePod mini features a non-detachable power cable that ends with a USB-C connector for use with the 20W power adapter included in the box. With the switch to USB-C, the HomePod mini could potentially be powered by a wider range of devices and peripherals, ranging from MacBooks to USB-C battery packs with enough...

Samsung Mocks Apple for Ditching Power Adapters With iPhone 12 Lineup

Thursday October 15, 2020 11:51 am PDT by
Samsung on its social channels is mocking Apple for removing the power adapter from the iPhone 12 lineup and other iPhone models, pointing out the fact that the Samsung Galaxy smartphones continue to ship with a power adapter. "Included with your Galaxy," reads a Samsung Facebook post that features a picture of a power adapter. Apple notably is no longer providing power adapters or...

New Google App Feature Lets You Hum a Song to Search for It

Saturday October 17, 2020 4:05 am PDT by
Google has added a new feature to its Search app that allows you to hum a song that's stuck in your head, and then use the company's machine learning algorithm to try and identify it. In the Google app or using the Google Search widget, tap the mic icon and say "what's this song?" or click the "Search a song" button. Then start humming the tune for 10-15 seconds. When you're done, the...

Brazilian Certifications Suggest iPhone 12 Mini Features 2,227mAh Battery and iPhone 12 Has 2,815mAh Battery

Friday October 16, 2020 1:08 pm PDT by
Apple's iPhone mini has the shortest battery life out of all the iPhones in the iPhone 12 lineup due to its small size, but Apple has not provided public information about the battery's capacity. A regulatory filing from Brazil, however, suggests the iPhone 12 mini has a battery capacity of 2,227mAh. The same regulatory information says the iPhone 12 features a 2,815mAh battery, which is...

iPhone 12 Pro Pre-Orders Already Selling Out With Delivery Times Pushing Into November

Friday October 16, 2020 6:35 am PDT by
Apple today opened pre-orders for the 6.1-inch models of the iPhone 12 and iPhone 12 Pro through its website and the Apple Store app, and estimated delivery times are already slipping into November for select configurations in the United States. Customers ordering a SIM-free/Pacific Blue/128GB version of the iPhone 12 Pro, for example, are already facing an estimated delivery window of...

Hands-On With Apple's MagSafe Charger for iPhone 12

Monday October 19, 2020 11:54 am PDT by
Alongside the new iPhone 12 models, Apple introduced a MagSafe charger that attaches to the back of the iPhones using magnets embedded both in the charger and in the iPhone. It allows for speedier charging and paves the way for a portless iPhone in the future. MagSafe chargers are shipping out and are in some Apple retail locations now, and we picked one up to check it out. Subscribe to the ...

Apple Offering Free AirPods With iPhone 11 Purchase in India as Part of Diwali Celebration

Friday October 16, 2020 12:35 pm PDT by
Apple today launched a new Diwali promotion in India that will see the company providing customers with a set of AirPods with the purchase of any iPhone 11 model. The new iPhone 12 models are not part of the promotion. Apple is offering the standard AirPods With Charging Case free with purchase, but customers can choose to upgrade to the AirPods with Wireless Charging Case or the AirPods Pro....