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.

appleq112topchart
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.

applerevegrowth
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

jackc Avatar
138 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)
nagromme Avatar
138 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)
snowmoon Avatar
138 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)
DeltaRage Avatar
138 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)
iSee Avatar
138 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)
Capt Crunch Avatar
138 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)

Popular Stories

apple watch ultra hammer test

YouTuber Tests Apple Watch Ultra Durability With a Hammer: Table Breaks Before the Watch

Sunday September 25, 2022 2:27 pm PDT by
A YouTuber has put Apple's claims for the durability of the Apple Watch Ultra to the test by putting it up against a drop test, a jar of nails, and repeated hits with a hammer to test the sapphire crystal protecting the display. TechRax, a channel popular for testing the durability of products, first tested the Apple Watch Ultra by dropping it from around four feet high. The Apple Watch...
tim cook spring loaded event

Six Major Products to Expect From Apple in 2023

Sunday September 25, 2022 10:57 am PDT by
As we approach the end of a busy product release season for Apple with only new iPads and Macs left to be announced over the next month or so, we're also setting our sights on 2023. Apple is rumored to have several major products in the pipeline for next year, including new Macs, a new HomePod, a VR/AR headset, and so much more. Other than new iPhones and Apple Watches, which are expected...
apple watch ultra deuglify 1

Apple Watch Ultra User Mods Titanium Casing to 'Deuglify' Design

Tuesday September 27, 2022 8:05 am PDT by
An Apple Watch Ultra user has modified their new device's casing to add a brushed finish and remove the orange color of the Action Button in an effort to make it more visually appealing. The Apple Watch Ultra offers the first complete redesign of the Apple Watch since the product line's announcement in 2014, and while the design has been met with praise from many users, some have criticized...
General iOS 16 Feature Yellow

Some iOS 16 Users Continue to Face Unaddressed Bugs and Battery Drain Two Weeks After Launch

Monday September 26, 2022 7:34 am PDT by
Today marks exactly two weeks since Apple released iOS 16 to the public. Besides the personalized Lock Screen, major changes in Messages, and new features in Maps, the update has also seen its fair share of bugs, performance problems, battery drain, and more. After major iOS updates, it's normal for some users to report having issues with the new update, but such reports usually subside in...
iPhone 14 Pro Sports Scores Dynamic Island

iPhone 14 Pro Features Live Sports Scores in Dynamic Island on iOS 16.1

Monday September 26, 2022 7:52 am PDT by
Earlier this month, Apple announced that iOS 16.1 will enable a new Live Activities feature that allows iPhone users to stay on top of things that are happening in real time, such as a sports game or a food delivery order, right from the Lock Screen. On the iPhone 14 Pro and Pro Max, Live Activities also integrate with the Dynamic Island. Premier League match in Dynamic Island via Paul Bradford ...
iPhone 14 Pros in Hand Black Background Feature

Verizon iPhone 14 Pro Customers Reporting Cellular Connection Issues

Monday September 26, 2022 6:23 am PDT by
iPhone 14 Pro customers on the Verizon network in the U.S. are reporting issues with slow and unreliable 5G cellular connections and calls randomly dropping. Several threads on Reddit (1,2,3) and the MacRumors forums chronicle issues faced by Verizon customers and Apple's latest iPhone. According to user reports, signal strength on the iPhone 14 Pro is unreliable and weak, while other...
Tim Cook Apple Event

Gurman: New iPads and Macs May Be Announced Through Press Releases, No October Event

Sunday September 25, 2022 6:50 am PDT by
Apple may decide to release its remaining products for 2022, which include updated iPad Pro, Mac mini, and 14-inch and 16-inch MacBook Pro models, through press releases on its website rather than a digital event, according to Bloomberg's Mark Gurman. In his latest Power On newsletter, Gurman said that Apple is currently "likely to release its remaining 2022 products via press releases,...
Stage Manager Extension Thumb 1

New iPadOS 16.1 Beta Expands Stage Manager to Older iPad Pro Models, Delays External Display Support

Tuesday September 27, 2022 10:24 am PDT by
The most recent beta of iPadOS 16.1 expands the controversial Stage Manager feature to older iPads, allowing it to work with iPad Pro models that have an A12X or A12Z chip, according to information Apple provided to Engadget. The beta also removes the external display support from Stage Manager for the current time, with the feature set to return in a later iPadOS 16 update. Apple's...
iOS 16

Everything New in the Latest iOS 16.1 and iPadOS 16.1 Betas: Stage Manager Expansion, Wallpaper Tweaks and More

Tuesday September 27, 2022 11:36 am PDT by
Apple today released new betas of iOS 16.1 and iPadOS 16.1 to developers, tweaking some of the functionality that's been introduced in prior betas and in the case of iPadOS 16.1, adding a major new feature to Stage Manager. We've rounded up everything new in both betas below. Wallpaper Updates Apple has updated the Wallpaper section of the Settings app to allow users to swap between...
john meyer ultra

Apple Watch Ultra Praised by Watch World Tastemaker John Mayer

Monday September 26, 2022 4:42 am PDT by
Apple Watch Ultra has been endorsed by American musician and famous watch collector John Mayer, who has been showing off the new device on his Instagram account. "Been wearing the Apple Watch Ultra for a week... and it's great," writes Mayer over a photo of the watch. "The first Apple Watch that excited me as a mechanical watch collector." "It's loaded with capability and what I call...