November 2013
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Day November 6, 2013

How many years does Apple have?

The graph below shows the Revenue and Operating Income for a select group of companies. The large numbers represent the share price to earnings (trailing twelve months) ratio (P/E or PE ratio).

Screen Shot 2013-11-06 at 11-6-2.56.25 PM

Of course the P/E ratio hides a lot of subtlety. It mostly fails to account for the fact that earnings are largely a matter of opinion. A company can defer income (as Apple and Microsoft do), it can invest earnings (as Amazon does) and can otherwise avoid declaring it since it’s taxable.

The diffusion of iPhones as a learning process

All theoretical and empirical diffusion studies agree that an innovation diffuses along a S-shaped trajectory. Indeed, the S-shaped pattern of diffusion appears to be a basic anthropologic phenomenon.

This observation dates as far back as 1895 when the French sociologist Gabriel Tarde first described the process of social change by an imitative “group-think” mechanism and a S-shaped pattern.[1] In 1983 Everett Rogers, developed a more complete four stage model of the innovation decision process consisting of: (1) knowledge, (2) persuasion, (3) decision and implementation, and (4) confirmation.

Consequently, Rogers divided the population of potential adopters according to their adoption date and categorized them in terms of their standard deviation from the mean adoption date. He presented extensive empirical evidence to suggest a symmetric bell shaped curve for the distribution of adopters over time. This curve matches in shape the first derivative of the logistic growth and substitution curve as shown below. Screen Shot 2013-11-06 at 11-6-1.51.57 PM

In the graph above I applied the Rogers adopter characterization to the data we have on the adoption of smartphones in the US. The latest data covering September is included.

  1. Tarde was probably influenced by mathematician Pierre François Verhulst who first published the logistic function in 1845 []