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During Apple's (NASDAQ:AAPL) Q2 earnings call the company announced the largest share buyback program in history. They also mentioned some IDC estimates for growth in the tablet and smartphone industries. Using the information provided plus some educated guesses on other key metrics, we can generate a prediction for future EPS that can be used to value the company going forward and determine if now is a good time to purchase the stock.

Let's first take a look at the record $100 billion Apple plans to return to shareholders by 2015.

Shareholder Return Plan

Year

2013

2014

2015

2016

Total Dollars Returned

$33,000,000,000

$30,000,000,000

$30,000,000,000

Estimated Share Price

$400

$500

$600

Quarterly Dividend

$3.05

$3.36

$3.69

Annual Distributions

$11.80

$13.42

$14.76

Total Shares Outstanding

939,000,000

889,200,500

858,066,641

834,177,941

Total Dividend Payments

$11,080,200,000

$11,933,070,710

$12,666,779,761

Amount left for buybacks

$21,919,800,000

$18,066,929,290

$17,333,220,239

Share Dilution

5,000,000

5,000,000

5,000,000

Apple made two quarterly dividend payments of 2.65 in 2012 plus bought back 4,077,774 shares at an average share price of $478.20 for a total of approximately $7 billion returned to shareholders, leaving $93 billion of the $100 billion Apple plans to return to shareholders by 2015. In order to arrive at the total shares outstanding in 2016 I made the following assumptions:

· Share price increasing by $100/year between now and 2016.

· Annual dividend increase of 10%.

· Annual share dilution of 5,000,000 shares.

If these assumptions are accurate, Apple will have approximately 835 million shares outstanding going into 2016.

Now that we have an estimate for shares outstanding, we need to determine revenue and margins before coming to an estimate on 2016 EPS. The IDC estimates that the smartphone and tablet markets will grow to 1.4 billion and 375 million units respectively by 2016 (market size estimates come from Apple's 2Q conference call). Assuming a 20% market share for iPhones and 40% market share for iPads, we get the following numbers for 2016 sales estimates:

Projected 2016 Smartphone and Tablet Units (in millions)

Market

Total Units

Apple Share

Apple Units

Smartphones

1,400

20%

280

Tablets

375

40%

150

I realize Apple's smartphone market share dropped below 20% in the previous quarter. I think this is a temporary drop that can be explained by the lack of a product refresh. I believe Apple's strong consumer satisfaction scores and customer loyalty ratings will allow it to capture close to 20% of the market going forward. I also think Apple can maintain a high share in the tablet market for the same reasons and the fact iOS accounted for 77% of corporate device activations (according to a Good Technologies report). As they noted in the conference call, corporate customers, once they choose to go with iOS, start developing in-house iOS applications, which makes it more likely they will remain with iOS in the future.

For average selling price, I believe we will continue to see declines from current levels, albeit at a slower pace than we have seen over the past year, with ASP flattening out by 2016 due to inflation and new products combating the competitive pressures that have been driving ASP down. Apple has a history of being able to sell its products at a premium, and I don't foresee that changing in the near future.

Average Selling Price Estimates

2012

2013

2014

2015

2016

$640

$613

$582

$553

$553

$552

$449

$427

$405

$405

Taking the projected 2016 unit sales and ASP we get the following estimates for revenue:

2016 iPhone and iPad Revenue Projection

Product

Units

ASP

Revenue

iPhone

280,000,000

$553

$ 154,905,100,000

iPad

150,000,000

$405

$ 60,783,375,000

Using the market size, market share and ASP estimates from above, we get 2016 revenue of slightly over $215 billion from the iPhone and the iPad combined.

To determine 2016 revenue estimates for all other products lines, I used a 1H 2013 YoY change as a starting point then modified slightly to determine a reasonable growth rate. I attempted to be conservative with the growth rate projections.

Revenue Estimate by Product (in millions)

Product

2012

Rate

2013

2014

2015

2016

iMac

$23,200

-2%

$22,736

$22,281

$21,836

$21,399

iTunes

$8,500

20%

$10,200

$12,240

$14,688

$17,626

Peripherals

$2,700

15%

$3,105

$3,571

$4,106

$4,722

iPod

$5,600

-30%

$3,920

$2,744

$1,921

$1,345

Other

$3,400

15%

$3,910

$4,497

$5,171

$5,947

Total

$43,400

$43,871

$45,333

$47,722

$51,038

Adding these together we get projected 2016 revenue for all other products of about $51 billion, giving us a total revenue estimate of $266 billion for 2016.

The average difference between the gross and net margins since 2011 is close to .17 (1700 basis points) in the past two years, so I will use that when determining earnings. Considering the downward trend in gross margins and the uncertainty of future margins, I will generate EPS estimates under 3 different margin scenarios, due to the high impact even a slight margin change will have on earnings.

2016 EPS (with 835 million shares outstanding)

Gross Margin

Net Margin

EPS

0.35

0.18

$57.34

0.33

0.16

$50.97

0.30

0.13

$41.41

At the 35% gross margin level, we are looking at a 2016 EPS of $57.34, which represents over 7% annual earnings growth on 2012's EPS of 44.15. This compares favorably to AB-InBev (NYSE:BUD) or Johnson & Johnson (NYSE:JNJ), as both pay dividends over 2% and are expected to grow at a similar rate. The difference is that AAPL is trading at a P/E of 10 whereas BUD and JNJ both have P/Es in the 20s.

As I mentioned before, if gross margin declines, then EPS falls sharply. If gross margins were to decline below 30%, then 2012 was probably the high-point for Apple's EPS and stock price. However if you think Apple can hold its gross margin in the mid-30s, then its shares are decidedly undervalued today. In the worst case, you at least have your 3% and growing dividend to fall back on. Another factor in Apple's favor is the "new category" Tim Cook mentioned in the last earnings call. If they are able to come up with a new blockbuster, the stock will skyrocket. The stock is currently priced as if Apple has no more tricks left up its sleeve. Any product added or other new profit potential will be pure upside for the stock.

Source: Apple's Valuation Is Not Rational

Additional disclosure: Always perform your own due diligence before purchasing any security. I make several assumptions in this article, which may or may not be accurate.