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So much has been written about Apple Inc. (NASDAQ:AAPL)’s valuation in general and the recent price drop in particular that it is worth putting the whole debate in the context of modern valuation theory. That theory teaches that the value of a company’s stock is composed of two parts: 1) the company’s book value, which can be thought of as the value contributed by investors, and 2) the value created by the company. With a little math it can be proven that this second part equals the present value of the company’s excess earnings, discounted at the cost of equity. If this seems a little confusing, don’t worry, we will get to the numbers in a minute and that should clarify things. It is important, however, to understand that excess earnings equal the rate of return the company earns on its book value over and above the cost of capital. If a company fails to earn in excess of its cost of capital, its share price will not rise no matter how rapidly it is growing. To make all of this more concrete, let’s turn to Apple.

As of the end of the third quarter of 2012 (the last available data ) Apple Inc. (NASDAQ:AAPL) had a book value of $118.2 billion. Application of the capital asset pricing model, a well-known tool in modern finance, suggests that Apple’s cost of equity capital is on the order of 9.0 percent. Finally, in the third quarter of 2012 Apple’s net income was $8.22 billion. Multiplying by four produces an annualized estimate of earnings of $32.9 billion, which along with a cost of equity of 9 percent and a book value of $118.2 billion, means that Apple’s annualized excess earnings were $22.3 billion during the third quarter of 2012.

Given this background, the first question to ask is what would Apple Inc. (NASDAQ:AAPL) be worth if its excess earnings were stuck at the level of the third quarter of 2012 forever – Apple’s growth engine just stopped. The answer is that the shares would be worth the book value of $126 per share, plus the present value of the (assumed fixed) excess earnings which comes to $263 per share, for a total value of $389 per share. In comparison, Apple’s current stock price (as of November 12, 2012) is about $550. Even after the drop from $702, Apple looks expensive by this measure.

But we have forgotten to take inflation into account. The foregoing calculation was based on the assumption that excess earnings remained constant in dollar terms. It seems more reasonable to assume that Apple Inc. (NASDAQ:AAPL) can at least keep up with inflation. If that is so, then excess earnings should grow at the rate of inflation in the future. By comparing the yield on long-term government bonds indexed to inflation with government bonds that are not indexed, it is found that the market is expecting long-run inflation to be about 2.5 expecting long-run inflation to be about 2.5 percent, so let’s use that number. If Apple’s excess earnings are assumed to grow at 2.5 percent, the estimated value of the stock rises to $490.

However, the estimate of $490 was arrived at by annualizing third quarter earnings. This ignores not only the fact that the fourth quarter is traditionally Apple’s biggest, but that the third quarter of 2012 was penalized by the expected release of a host of new products. Currently analysts are predicting earnings for the fourth quarter at an annualized rate of $50 billion or more. In light of this, an average annualized rate of at least $40 billion seems far more appropriate the depressed rate based on the third quarter of 2012. Putting annualized earnings of $40 billion into the model produces a value of $607 per share.

Now remember, the $607 valuation still assumes no inflation adjusted growth. All Apple Inc. (NASDAQ:AAPL) has to do is maintain its current excess earnings. That looks to be a hurdle Apple can clear without too much difficulty. In actuality, inflation just earnings have grown at approximately 50 percent during the last five years – right through the financial crisis. This makes $550 look like a very attractive price.

By Brad Cornell, Professor of Finance at Caltech

What Is Eating Apple Inc. (AAPL) Stock?

November 15, 2012, By Sheeraz Raza

In recent weeks we have seen myriad of issues that have led to Apple Inc. (NASDAQ:AAPL)’s under-performance (-23% since Sep-19 vs. S&P -6%). According to RBC Capital Markets’ research report, there are five consistent concerns:

1) What’s the next product launch

2) Long-term gross-margin declines

3) Supply-chain constraints

4) 2013 Tax Increases

5) Management Changes.

The research firm believe fundamentals at Apple Inc. (NASDAQ:AAPL) remain strong and the stock should outperform over the next 6-12 months driven by

· Strong Dec-qtr results given impressive product line-up for holidays,

· Gross-margins begin to improve in Dec-qtr and beyond,

· Potential ramp with China-Mobile and iTV launch in 2013.

Concerns

What’s Next? There is concern that innovation is slowing at Apple Inc. (NASDAQ:AAPL) as recent products are evolutionary in nature. Apple Inc. (NASDAQ:AAPL) historically has announced a new product line on a 3-year basis, suggesting that a new product could be launched in 2013 (June potentially). In RBC’s view, the next product could be an “iTV”, which redefines the living room experience.

Gross-Margins Structurally Lower?

This concern gained momentum post LQ’s guide for Gross-margins to decline by 400bps to 36%. The fear is Apple Inc. (NASDAQ:AAPL) now has to sacrifice gross-margins to defend market positioning. RBC, believe Apple Inc. (NASDAQ:AAPL)’s gross-margin guide is more reflective of their conservative stance and transitory ramp headwinds vs. structural challenges. Its analysis suggests that iPad mini while below corporate GM’s will end-up having better margins than iPad4. The research firm estimate iPad margins should sustain at the high 20’s range, while iPhone’s will carry a “low 50%”. Challenges With Supply-Chain: Apple Inc. (NASDAQ:AAPL)’s challenges with supplychain may diminish the magnitude of upside. With the 2-3 week wait time for the iPhone 5 and 2 week wait time for iPad mini, the research firm – RBC Capital Markets, believe Apple Inc. (NASDAQ:AAPL) is seeing a 2.5 week impact from supply constraints for the iPhone and ~2M unit impact from iPad Mini. However, its recent analysis shows that constraints for iPhone 5 are starting to ease-up.

Tax Selling:

Investors may be locking in long-term gains before the expiration of the Bush Tax-Cuts. Notably, top tax-rate on capital gains is expected to increase by 15% in 2013.

Management Changes:

Investors are rattled by recent management changes and are taking a wait-and-see approach into Dec-qtr earnings-call. RBC maintain its Outperform rating and price target of $750. Its price target is based on 15x FTM EPS (ex $121B in cash). The research firm believe Apple Inc. (NASDAQ:AAPL) deserves to trade at a slight premium to the S&P 500 as it continues to grow at rapid rates on both the top and bottom lines.

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