The recent drop of Apple (NASDAQ:AAPL) stock to $450 has left many investors scratching their heads: is AAPL's price still too expensive at this level? Or is it a great value and a screaming buy? Warren Buffett said that price is what you pay and value is what you get. We may never know exactly the market's sentiment on a particular stock at any given moment, but at least we can estimate the fair value of a stock based on its fundamentals. So we go back to the basics and ask ourselves: what is the fair value for AAPL? Only then can we make a rational investment decision on the stock. Our analysis suggests that AAPL at $450 is a significant discount from its fair value, even under conservative estimates of slow revenue growth and contractions of profit margins. Our analysis of the stock using the Free Cash Flow (NYSE:FCF) valuation model to derive AAPL's fair values under different scenarios is below.

The FCF model is based on the principle that a company's equity or firm value can be derived from the present value of its future free cash flows. The key assumptions used for the FCF valuation model for an analysis of AAPL are the following:

1. Revenue growth rate: Although AAPL has had an impressive annualized revenue growth rate of 40% over the last 5 years, we have to be realistic that the growth rate may plateau once Apple becomes a mature company. With 2012 revenues at $156.5B, it would be unrealistic to assume that the company can continue at a 20-40% rate of growth. Instead, in our model, we use two modest growth rate ranges, 6-8% and 3-5% for the next 5 years and assume a gradual decline to a nominal long-term growth rate of 3.5% going forward.

2. Net profit margin (NYSE:NPM): Apple's net profit margin over the last two years was 24%. However, we assume that Apple will begin to see gross profit margin compression due to competition in the smartphone and tablet markets. As a result, its net profit margin will decline accordingly. We lay out two scenarios with net profit margin decline from the current 24% to either 12-16% or 16-18% ranges over the next 5 years and determined how the margin compression affects AAPL's valuation.

3. Free cash flow to equity: To derive free cash flow for each year, we add back non-cash charges to estimated earnings (or net income) and subtract capital expenditures. Apple's non-cash charges were slightly higher than its capital expenditure for the past three years, resulting in a FCF __higher__ than its net income. However, to be on the conservative side, we assumed that capital expenditures would exceed non-cash charges by just 1.5% of net revenue. Therefore, our estimated FCF numbers are __lower__ than the estimated earnings.

4. Discount rate (NYSE:R): We used a 30-year Treasury yield (3%), AAPL's beta (1.1), and an equity risk premium of 4.5% to derive a discount rate (or required rate of return) of 8% for AAPL.

5. Apple had $137B in cash and cash equivalents as of December 2012. Among those, 70% were held in foreign subsidiaries, which are subject to 35% income tax on repatriation if the company brings them back to the U.S. So, we estimate their actual cash value as $100B in our calculations.

6. We also factored in the possibility that AAPL may repurchase 2% of its outstanding shares on an annual basis. However, it is important to note that share repurchase percentage only affects earnings per share (NYSEARCA:EPS) value. It does not affect fair value calculation. Management may consider using shares repurchases to maintain a steady increasing rather than a declining trend of EPS. This strategy has been adopted by many mature companies to manage EPS growth, because EPS is an important measure for price/earnings (P/E) multiples.

Table 1 shows an example of our analysis with a revenue growth rate of 7% and NPM decline at a medium rate (from 24% to 14%) over the next 5 years.

*(click to enlarge)*Table 2 summarizes the per share fair values under revenue growth rates at 6-8% range with NPM rates declined to 12-16% in 5 years. These analyses demonstrate that even if AAPL's revenue growth is 6% and with a NPM declining at a fast pace to 12% in 5 years, its fair value is $620. In the most promising case with an 8% revenue growth rate and a slow decline of NPM to 16%, its fair value is $863. Somewhere in between, with a 7% revenue growth rate and a modest decline of NPM to 14%, its fair value is $735.

*(click to enlarge)*

Table 3 summarizes the per share fair values under revenue growth rates at 3-5% range with NPM rates declined to 14-18% in 5 years. These analyses demonstrate that even if AAPL's revenue growth is 3% and with a NPM declining at a fast pace to 14% in 5 years, its fair value is $608. In the most promising case with a 5% revenue growth rate and a slow decline of NPM to 18%, its fair value is $820. Somewhere in between, with a 4% revenue growth rate and a modest decline of NPM to 16%, its fair value is $709.

**Conclusion:**

Apple has enjoyed impressive revenue and earnings growth over the past decade, owing to its revolutionary innovations such as the iPhone, iPad, and others. However, given its huge market cap and revenues, investors need to be realistic that APPL, at some point, will transition from a growth company to a more mature one. The recent stock moves remind us that the turning point may have arrived and that investors need to adjust their expectations on what AAPL can deliver going forward and what kind of price they are willing to pay for the stock.

Our valuation models are based on conservative assumptions that AAPL's earnings growth and net profit margin will start declining from the current 24% to 12-18% rate over 5 years. The rate is lower than the 20% net profit margins of some of the mature technology companies like Microsoft (NASDAQ:MSFT), Intel (NASDAQ:INTC), or Google (NASDAQ:GOOG). If the revenue growth rates maintain within 6-8% rates in the next 5 years, the fair value is at $620-$863 range. If the revenue growth rates maintain within 3-5% rates in the next 5 years, the fair value is at $608-$820 range. In either scenario, AAPL's fair value is 37% above the current $450 price level.

**Disclosure: **I am long AAPL, GOOG. 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.