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The Apple Conundrum

|Includes: Apple Inc. (AAPL)

With an upcoming earnings report, the facts are finally going to reveal the truth about Apple (NASDAQ:AAPL). Four times a year, every third month of the year culminates with the disclosure of financial information about the largest company in the world. A total of 45 professional analysts covering Apple estimate that the company's earnings will be $13.31 for the holiday quarter. Since Apple earned $13.87 per share last year, this would mean a 4.037% drop in earnings for the quarter year over year. This leaves an essential question to be answered: do the estimated device unit sales analysts expect project a more than 4% drop in earnings compared to last year? The only way to answer this question is to apply the expected growth in units sold to the expected average profit per unit to render a final earnings estimate. This final estimate can be compared to the average earnings expected by analysts to render an important difference; the difference between the earnings expected by analysts and our projected earnings based on analyst device sales estimates When this earnings report occurs, one of the only things that matter to investors is the difference between the actual earnings of Apple vs. the earnings estimated by analysts. Our estimates will give some insight as to what this difference will be.

To attempt to estimate Apple's earnings, the most important factor to consider is the number of iPhones sold, which accounts for approximately 60% of the total gross profit earned by Apple in quarters containing or following an iPhone release. According to Apple's website, "The Company sold 37.04 million iPhones in the quarter" for quarter ending on December 31, 2011. However, despite this predicted 4% yoy decline in earnings predicted by analysts, the consensus among analysts for the number of iPhones sold this quarter is 45 to 46 million iPhones. The analysts predicted last quarter's iPhone sales to within 2% of the actual number, so this is a safe projection to use. Because the lowest priced unsubsidized/unlocked iPhone is a $450 compared to $375 last year, raising the average price of the iPhones offered by Apple from $634 to $650, Apple has the potential to earn much more per device. The iPhone is one of the only technology products in history to steadily increase in average sales price over time after its release, as shown below.

Average Sales Price For Each iDevice From

However, we must also account for the possibility that higher manufacturing costs for the iPhone offset this increase in average revenue per unit. So for our low iPhone growth estimate we will assume no change in profit per iPhone, and for our high iPhone estimate, we will assume this estimated change in price per unit sold. This gowth can then be projected towards Apple's overall earnings, accounting for approximately 60% of Apple's total earnings growth year over year.

Low Estimate: (45.5-37.04)/37.04 = 22.8% increase

High Estimate: (650-634)/634 = 2.5% increase in revenue per device * 22.8% increase in number of devices (1.025*1.228) = 25.89% increase

As for iPads, The consensus among analysts is 23 million to 24 million for iPads sold in the holiday quarter compared to 15.43 million iPads sold last year. Contrary to the common misconception, the iPad Mini has a better gross margin than the iPad 3rd generation and the recently released iPad 4th generation due to the extremely high cost of purchasing retina displays from Samsung. According to tear-downs performed by IHS iSuppli Research, the iPad 3rd generation 16 GB wifi model has a gross margin of 36.6%, only slightly different from that of the 4th generation iPad, while the iPad Mini 16 GB wifi has a gross margin of 39.8%. However, the iPads sold during last Christmas' quarter were predominantly iPad 2's, which carry a gross margin of about 41.8%- 43.3%. So overall, iPad margins should decrease between 2% and 6.7% depending on the distribution of iPad models sold this quarter, which will be our high and low estimates for iPad growth. Note that iPad distribution between models is an unpredictable factor considering this is the first quarter that includes an iPad Mini.

Another key difference to consider for Apple's iPad sales number this quarter lies in the difference of average revenue per unit sold, which amounted to $593 last year. BGC Financial analyst Colin Gillis expects the iPad's average selling price to fall to $485 this quarter, a decrease of 18.2%. However, this could be more than made up for by the magnitude of iPad sales for the quarter. Using this summation of facts, we now can predict the expected earnings growth this quarter stemming from iPad growth.

Last Year's iPad Profit:

#iPads GM ASP

High Est : 15.43 *41.7% *593 = $3,815.54 million in profit

Low Est : 15.43 *43.3% *593 = $3,961.94 million in profit

This Year's iPad Profit:

#iPads GM ASP

High Est : 23.5 *39.8% *485 = 4,536.205 million

(4,535.54-3,816.21)/3,816.21 = increase yoy of 18.85%

Low Est. 23.5 *36.6% *485 = 4,171.485 million

(4,171.48-3,961.94)/3,961.94 = increase yoy of 5.29%

Considering that analysts expect low growth in all of the other departments where Apple derives revenue from, to get a more conservative estimate we will assume 0% growth in these areas. This will have the effect of keeping 25% of Apple's earnings flat, as 75% of profits are derived from the iPad(15%) and iPhone(60%.) Finally, we must add the separate components to see the estimated growth in earnings yoy, then extrapolate this towards Apple's earnings last year.

High Estimate:

(1.189*.15)+(1.259*.6)+(1.00*.25) = 1.1836 = 18.36% earnings growth

($13.87*1.1836) = $16.42 EPS

Low Estimate:

(1.0529*.15)+(1.228*.6)+(1.00*.25) = 1.1447, 14.47% earnings growth

($13.87*1.1447) = $15.87 EPS

In conclusion, using analysts' own expectations for number of iDevices sold this quarter, we have derived an earnings growth of 14.47-18.36%, and an EPS of $15.87-$16.42 this quarter. This disconnect from analysts' expectations of a $13.31 EPS and a 4.037% drop in earnings for the quarter year over year presents investors with a very rare opportunity: that if Apple manages to come near analysts' expectations for number of devices sold, they will blow away the earnings expected by analysts. Whether this vast disconnect is a result of inaccurate iPad gross margin projections, production ramp-up costs, or the idea that analysts have been consistently lowering their EPS estimates while negligibly changing their device estimates over the past couple of months is for the reader to decide. However, considering that Apple has already launched the iPhone 5 in 100 countries, has launched a brand new product this quarter, and recently sold 2 million iPhones in the first 3 days of sales in China, approximately equal to the estimated number of iPhones sold in the opening weekend in the US of 2-2.5 million*, we will be fully invested in Apple preceding their upcoming earnings report. Apple has bottomed in the 480s without a doubt, and is set to take off into the stratosphere

*Note: the total of 5 million devices released by Apple includes 8 other highly developed countries. This estimate is an average of the approximations of research firms.

Disclosure: I am long AAPL.