Wednesday, December 26, 2012

Valuing Apple

            So much has been written about Apple’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 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.

             As of the end of the third quarter of 2012 (the last available data) Apple 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.

            The first question to ask is what would Apple 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) annual 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 December 26, 2012) is about $520 down from a high of $705.

            But we have forgotten to take account of inflation.  The foregoing calculation was based on the assumption that excess earnings remained constant in dollar terms.  It is more reasonable to assume that Apple 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 after the end of the quarter.  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 is more appropriate than the depressed third quarter number of $32.9 billion.  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 has to do is maintain its current excess earnings in real terms.  That looks to be a hurdle Apple can clear.  In actuality, inflation adjusted earnings have grown at approximately 50 percent during the last five years – right through the financial crisis.  To be pricing the stock at $520, the market must be very pessimistic regarding Apple’s future.

No comments: