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 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