Apple, Inc. (NASDAQ:AAPL) currently sports a trailing twelvemonth P/E of 10X. Based upon the discounted cash flow principles underpinning the concept of the Price/Earnings multiple, this makes little sense unless one believes the company no longer has an ability to generate incremental earnings and cash.
This article will explore the thesis in four parts:
 How the P/E ratio relates to Discounted Cash Flow methodology
 What P/E multiple relates to a "no growth" stock versus a growing enterprise
 How the Apple stock P/E has decoupled itself from past and projected earnings metrics
 A summary and concluding thoughts as to what's going on
The P/E Ratio Represents Simplified DCF Methodology
The P/E multiple concept is grounded in Discounted Cash Flow (DCF) analysis, more specifically determining the Present Value (PV) of a future series of cash flows. The DCF process discounts these future cash flow back to a single present value number.
The following formula represents this situation:
PV = E * (1 + g)/(r  g) where
PV = The present value stock price
E = Earnings for the stock
g = growth rate
r = required rate of return or discount rate
Assuming the cash flows are nogrowth constant sums, the g variable drops out and the simplified formula becomes:
PV = E / r
If we now rearrange the formula to isolate the r variable, and rename the PV variable P for Price, we obtain the following:
r = E / P
Starting to look familiar? If we invert E / P, we get P / E, as in P/E ratio.
Therefore, the P/E multiple of a stock is the inverse of r, or the assigned discount rate.
P / E = 1 / r
Let's proceed.
What P/E Multiple Corresponds to a NoGrowth Company?
We still haven't solved the formula. So now it's time to plug in some numbers. First, let's make some assumptions in order to solve the r variable, or the expected rate of return for equities in general.
Historically, investors have required equity returns that compensate them for the risk taken in lieu of investing in riskfree assets. The following formula captures this:
r = RFR + B (Rm  RFR)
RFR = RiskFree Return; often benchmarked by the 10year U.S. Treasury note. These notes have historically been pegged at approximately 5 percent.
B = Beta, defined as a measure of the volatility, or systematic risk, of a security in comparison to the market as a whole. To keep our work simple, we will assume the Beta is 1.0. For the record, it just so happens that Apple stock has a Beta of 1.0, too.
Rm = Historical market return. Let's recognize that all DCF work requires assumptions. In this case, we will assume that over the long term, equities have returned a nominal 11 percent to the investor.
Solving for r, we get
r = 0.05 + 1.0 (0.11  0.05)
= 0.11 or 11 percent
Here's a simplified explanation of the foregoing: over time investors have generally required the "risk premium" for stocks to be about six percentage points above a corresponding "no risk" investment. The tenyear Tnote has traditionally been benchmarked as such an investment. The average yield on a tenyear Tnote has been five percent. Therefore, a reasonable discount rate for equities is about 11 percent.
Now if we go back to the original equation, we can plug in the value of r and find that the P / E multiple for a nogrowth stock should be
P / E = 1 / 0.11 or 9.1
Therefore, a P/E of 9X approximates the expected multiple for a stock with a constant return, but no growth, when discounted at 11 percent.
What About a Company that Grows Earnings?
The P / E multiple is designed to give the investor a rough guide to estimate the value of a stock given its earnings growth rate. It's not an exact science. However, the concept is sure: the Price / Earnings ratio should relate to an expected Earnings growth rate.
Therefore, the better a company's growth prospects are, the higher P / E can be afforded to it.
Let's avoid a great deal of math and theory. We will cut right to the Graham valuation formula. This shorthand equation provides a practical application for handling a relatively complex DCF problem.
Benjamin Graham, the father of value investing, was known for his thorough financial analysis of companies, but he also offered followers simple rules of thumb to evaluate stocks. Here is a valuation formula adapted from "The Intelligent Investor:"
P / E = 8.5 + 2G
P / E = a fair P/E ratio for a given stock
G = earnings growth rate
Note that if the growth rate is zero, the fair P/E becomes 8.5X. That's not too far removed from our calculated zerogrowth equity formula earlier.
However, since Graham proposed his formula back in 1949, it has shown a tendency to provide fair P/E multiples that are a bit too high. Therefore, I suggest we modify the formula to make it more conservative. The following formula tends to work very well.
P / E = 9 + 0.5 G
The details outlining the rationale around this modified Graham formula can be found on this web link.
If one accepts this formula as a rough guide, a stock that grows at 4 percent a year, for example, should command a P/E of 11X.
So How Does this Relate to Apple Stock?
Apple stock currently trades at a ttm P/E of 10X. We have established that a stock with no growth should trade at a P/E of about 9X. Furthermore, we outlined how it is reasonable to premise that a stock with an expected two percent earnings growth rate should trade at 10X.
Yet AAPL has grown operating earnings at 33 percent a year over the past 15 years. Street analyst consensus fiveyear forward EPS growth estimate for Apple is between 15 and 18 percent depending upon the source. Wall Street believes that after a flat FY 2013, growth will resume. Here's a link to one such consensus.
Wall Street says Apple EPS will grow at a midtohigh double digit rate. Yet Mr. Market assigns Apple stock a P/E implying a 2 percent forward growth rate.
Some Additional Color on the Subject
Are Earnings the Same as Cash?
No, earnings are not the same as cash. Therefore, if Apple, Inc. is growing earnings it does not mean that it is necessarily growing cash flow. If a stock were earningsrich, but cashpoor, it could explain why a stock can deserve major P/E compression.
A review of past financial filings indicate that this is not an issue. Here's a summary of the past five years; comparing AAPL earnings versus freecashflow (FCF). FCF is operating cash less capital expenditures.
Apple Earnings per Share and Free Cash Flow (FY 2008  2012)
FY 2008 
FY 2009 
FY 2010 
FY 2011 
FY 2012 

EPS 
$6.78 
$9.08 
$15.15 
$27.68 
$44.15 
FCF per share 
$9.57 
$10.02 
$18.11 
$35.81 
$45.33 
While past performance is no guarantee of future returns, I did find the chart incredible. Indeed, Apple clearly has not had an earningstocash conversion problem. The company actually generates better FCF per share than EPS. Remarkable.
The Bottom Line
Granted, the P/E ratio is more of a blunt instrument than a surgical knife. Like any DCF or financial multiple analysis, the underlying assumptions make or break the results.
However, in the current case of Apple stock, even conservative DCF assumptions don't jibe with the Street's projected earnings and cash expectations. Hence, there is an apparent anomaly.
Wall Street forecasts a company growing earnings at high double digits, yet the market assigned a Price / Earnings ratio that implies about two percent future growth.
Please note this analysis doesn't purport to make any demands upon the market. Stocks behave as they will based upon buyers and sellers. They don't behave as we expect them to.
Nevertheless, it does seem like AAPL Street earnings growth expectations and market multiples are unusually disjointed.
So What's Going On?
There are any number of theories as to what's going on, but here's my take on a few of them:
 Market Sentiment / Negative Momentum: AAPL stock price may have separated from earnings and expected growth due to a simple lack of buyers. The stock had been touted via buyside analysts for a long, long time. At some point, the buyers are exhausted and sellers take charge. The multiyear run up in price and tax considerations at yearend 2012 may have provided a catalyst for shareholders to begin to take profits. They did. Negative momentum ensued: Selling begets more selling until equilibrium is reached again.
 Transition from Growth to Value Stock: Apple had been recognized as a tremendous growth story for years. The law of large numbers makes it nearly impossible for a stock to continue to grow so rapidly year after year after year. Large growthcompany money managers may have decided that the jig was up on the AAPL growth story. They started unloading the stock, creating a vortex of other managers to follow suit and do likewise. At some point, the value money managers will move in and begin to buy shares based upon fundamentals and the dividend. If true, the process can take awhile.
 The market is correct: Perhaps my thesis for this article is entirely wrong. It is possible that the market has properly handicapped Apple stock. It "deserves" a 10X multiple. Most analysts indicate that Apple EPS will be flat in FY 2013. If the company earnings were to stay flat to low single digit growth for an extended period of time, then a low P/E is warranted. While I find this a low probability thesis, it cannot be dismissed.
I believe that over time, undervalued stocks either demonstrate that they deserve to be priced as such (the proverbial "value trap"), or the market eventually recognizes the disconnect and bids up the shares to reach normalized valuation. It may not happen when we want it to happen, but it does.
Having bought Apple shares some years ago, I plan to hold for the time being. I do not intend to buy more, nor cut my current position. My view is that the shares are undervalued.
Disclosure: I am long AAPL. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.