My colleague Tom's article on valuing the QQQQ drew several comments about his target prices, particularly on Apple (NASDAQ:AAPL), a favorite momentum play for traders of late. One of the more polite comments asked how a $131 fair value price for AAPL was obtained. The simple answer is "through discounted cash flow (DCF) valuation," but what does that really mean?

DCF valuation is my preferred way to value a business because the underlying principle is that a company (or stock) is worth the present value of future cash flows that can be taken out from it. There are a few parts that I'll walk through in great detail to show how the AAPL price was arrived at - free cash flow, discount rate, future growth projections, and terminal/exit multiple.

For Apple, the initial (t=0) free cash flow is $4.15 billion, which is simply the company's free cash flow in the last four quarters. No non-recurring items are readily apparent, so that figure is simply taken as-is. The next question that needs answering is "how fast will Apple grow FCF?"

There are two ways to do this: create your own estimate of Apple's cash flow growth, or do a reverse engineering of the current price to see what the implied growth rate is and make a determination of its probability of being accurate. I prefer the latter because it gives a target to adjust growth numbers to, so while it isn't the most academic exercise it is nonetheless more practical. Apple's current market cap is $141 billion, or $162 per share. So I'll fit the growth curve to that, which means taking into account analyst estimates for 34% growth in the current quarter (I'll put that as my full year-one growth even though growth estimates for the next quarter are 18.5%), and for years two through five I'll use 22.6%, which is the consensus five-year annualized growth forecast. I realize that I'm overshooting here, but this will be my "aggressive" assumption. Coming off that five year period, I should ratchet down expectations; a "bridge year" where the company transitions into a slower-growing company is appropriate, and I'll assume 15% growth for that year (year six, for those scoring at home). Keep in mind, this entire time the net growth figures are being discounted back to present, but we'll get to that later. Now we have Apple, the "maturing firm," as we move into the second half of 2013. For the next two years, let's say Apple grows at 10% per year, with 9% the year after that and 8% in the following year - solid, but not phenomenal, rates. There are two issues left: the proper discount rate, as well as the terminal (or exit) multiple, which is the inverse of the discount rate.

For the discount rate here, I'll use the Capital Asset Pricing Model (CAPM), which - let me hack a rather elegant theory apart here - basically states that the expected return of an asset is equal to the risk-free rate of return, plus some additional return that equals the risk premium multiplied by the risk of the asset. The average yield of the 1– and 3-month Treasury Bills is about 4%, and I get an expected market return of about 6.6% using the S&P 500 earnings yield and dividend. With AAPL's beta of 2.21, the CAPM gives an expected return of 9.49%. Take it for what you will, that is what I'm using for the time. Every year's cash flow is discounted at the appropriately compounded multiple of 9.49%, and the last year's cash flow is multiplied by 1/9.49% to give a terminal multiple of 10.53, which (as the name implies) is multiplied by the out-year cash flow and discounted back to present, along with the net current assets Apple has (carried on the books right now at $10.5 billion).

All of that nets out a value of $166 billion for the firm, about 18% above the current market cap for a value of $191.09/share. I consider this an aggressive set of assumptions because:

1. Growth estimates seem high, namely in the intermediate years

2. I think 9.49% is a very low discount rate to use for a stock like AAPL; and while discount rates are very subjective I think it is safe to say most people aren't in AAPL for a 9.5% annual gain.

The latter issue is strictly my view and has much to do with the difficulty of measuring "risk" in financial circles - I don't think that beta is close to perfect, but it has to suffice for the above example. On the former, however…

I realize Apple has a great growth story right now; I merely think the extent of the story is greatly over-hyped. Yes, the iPod is a nifty device from everything I hear, but that is Apple's only real successful product launch in their twenty-five years in business. The iPhone hadn't been out three months when they had to cut the price to move units - it is far too early to call the iPhone a success, but I digress… focus on the quantitative side of things. If Apple maintains the same FCF margins it does right now throughout this scenario (a big assumption, as margins usually come down), Apple will need to have 5x the sales next decade compared to right now. Sales in the last four quarters amounted to $22.6 billion, giving a target of $112 billion in sales. How impressive would it be for Apple to accomplish that feat? In the last ten years, Hewlett-Packard (NYSE:HPQ) has gone from $42.9 billion in sales to $100.5 billion in sales; starting with nearly twice the base amount to work with compared to Apple, Hewlett-Packard fell short of the amount Apple needs to get to. Very few people realize what an immense and impressive feat $100 billion in sales would be; there are 21 publicly traded companies with that amount or greater. And yet, the implied assumption for people who think AAPL has moderate upside is that Apple will quintuple sales to break that mark in slightly under a decade.

So, what does one buy stocks for? Generally, I think the answer would be along the lines of what Charlie Munger has said: "All intelligent investing is value investing - to acquire more than you are paying for." In the case of AAPL, I don't believe you are acquiring more than you are paying for unless one uses extremely aggressive assumptions, and what is the point of purchasing something on the most optimistic of forecasts?

As for the arrival of the $131 fair value; such a valuation uses a 12% discount rate, 34% front-year earnings growth followed by 19% annually through the fifth year, a bridge year growth rate of 15%, followed by 10% annualized growth for the next four years. I now see that in the initial estimate I did a bit of rounding, so this valuation scenario works out to a value of $130.33, or 20% less than Apple's last closing price. Given that one wants to buy a stock at a discount of somewhere between 30-40%, I'd very much like to see how others are arriving at the conclusion that AAPL is a great value right now.