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On Monday December 9, 2013, Seeking Alpha published my article: Apple Vs. Samsung: A Free Cash Flow Clash Of The Titans." In the comments section, I was asked the following question:

"How has Apple changed from, say jan2011 until now, in your valuation methods? It would be nice to plot these ratios over time." ~ pbanados

I thought this was a great idea and decided to run a free cash flow analysis of Apple (AAPL) from 2008 to 2014E (estimate).

Those new to this analysis can find an introduction by going here that will explain in detail how each ratio is calculated. When used together, these unique ratios generate a quantitative picture of a company's underlying fundamentals, taking into account strengths and weaknesses.

This analysis will use the following six free cash flow ratios:

• CapFlow
• FROIC
• Price to Mycroft Free Cash Flow
• Mycroft/Michaelis Growth Rate
• Free Cash Flow Payout Ratio
• Free Cash Flow Reinvestment Rate

(click to enlarge)

The "Mycroft Free Cash Flow per share" results, shown in the table above, were generated by taking the free cash flow results for Apple, for each preceding year and then adding the "Mycroft Michaelis Growth Rate" into the equation in order to generate a forward looking estimate for each coming year in the table above. In other words for 2008, I used Apple's free cash flow results for 2007 and then duplicated the same process for each year that followed. Those growth rates were generated by using the FROIC ratio (Free Cash Flow Return on Invested Capital). Basically FROIC tells us how efficient operations are as it zeros in on how much free cash flow is generated for every \$1 of total capital employed. Apple for example in 2010 had a projected FROIC of 28%, which means that for every \$100 of invested capital, the company was projected to generate \$28 in free cash flow. Now the Mycroft/Michaelis Ratio takes that 28% and multiplies it by the firm's free cash flow reinvestment rate. The reinvestment rate that I use is a free cash flow reinvestment rate instead of the standard one used by analysts that simply uses net income. It is calculated as follows:

Free Cash Flow Reinvestment Rate = 100% - (Free Cash Flow Payout Ratio).

Or;

Free Cash Flow Reinvestment Rate = 100% - (Total Dividend/Total Free Cash Flow).

By replacing net income in the payout and reinvestment ratios with free cash flow, I am thus able to make my analysis more precise by incorporating capital spending (Cap Ex) into the equation.

To demonstrate this fully we will use our estimates for 2014 in the examples below.

From the preceding calculations, we can determine that Apple has a reinvestment rate of 75% and went on to use 25% of its free cash flow to pay out its dividend. Thus by taking 30% (FROIC) x 75% = 22.5% (rounded off at 23%). From there we add the dividend yield of 2.3% (rounded off at 2%) and we have a Mycroft/Michaelis growth rate of 23% + 2% = 25%.

Apple's Mycroft Free Cash Flow per share of \$58.85 was generated by taking its TTM free cash flow per share and multiplying it by (100% + 25% or 1.25). Once we have our result, we then take its current market price of \$565.27 and divide it by \$58.85 and get a Price to Mycroft Free Cash Flow result of 9.60. I consider a Price to Mycroft Free Cash Flow per share result of less than 15 to be good for purchase, and anything under 7.5 to be excellent.

(click to enlarge)

The higher you go above 15, the more overvalued a company becomes. I use a Price to Mycroft Free Cash Flow per share result of 22.5 as my sell price, and 45 as my short price.

An appropriately priced stock should trade around a Price to Mycroft Free Cash Flow per share result of 15. This benchmark result was determined by backtesting.

Buy (opinion) = A Price to Mycroft Free Cash Flow per share result of less than 7.5 is considered excellent (50% below the initial Hold level), and anything under 15 is attractive.

The result I give as my Buy opinion in the table above uses a Price to Mycroft Free Cash Flow per share result of 7.5.

Hold (opinion) = 15 to 22.5 (I use 15 in the table).

Sell (opinion) = 22.5 or higher (50% above the initial Hold level). (I use 22.5 in the table).

Short (opinion) = 45 or greater. The Price to Mycroft Free Cash Flow per share result of 45 was determined by going back to the peak of the market (in the year 2000) and averaging the Price to Free Cash Flow per share results for the key players at that time. (I use 45 in the table).

The 2014 estimated CapFlow ratio result that you see in the first table above is an original ratio I created in order to tell me how much Capital Spending is used as a percentage of Cash Flow. A result of less than 33% is considered ideal and with Apple coming in at just 19%, means that 81% of the company's cash flow is actually free cash flow and can be used to buy back stock.

Now that I have explained how my analysis is done, let us now venture forward and analyze the results of my backtesting. We will start with the second table and show how someone investing in Apple would have done using my system vs. someone who just bought in 2008 and held until today.

All market prices listed are from the first trading day in January of each year.

On January 2, 2008, Apple closed with a market price of \$188 and was considered a strong sell on that day, according to my system, as it was selling for \$40 above my sell price opinion. It eventually hit a high of \$200.30, but then was hit hard by the "Crash of 2008-2009" and proceeded to fall to a low of \$78.20 for a percentage drop (from high to low) of -60.95%.

Had you sold at my sell price of \$148.50, you would have avoided a huge loss and would have started buying back in at \$97.70 in 2009 at my buy price opinion. From there, you would have never looked back as the stock never hit my sell price in any of the coming years. In 2013 you would have had a second opportunity to buy Apple again at a bargain price as its stock fell below my buy price of \$421.76.

Thus when all is said and done, had you bought \$100,000 worth of Apple on January 2, 2008 and held it to today you would have had a total of 530 shares and those shares at today's closing price of \$565.55 would now be worth \$299,741.50, which comes out to about a 200% gain, which is fantastic. But had you followed my system and bought at my buy price of \$97.70 in 2009, you would have bought 1023 shares that would now be worth \$578,557.65 for a gain of 478.55%. As you can see "buy and hold" is wonderful if you are in the right stock, but buying the right stock at the right price is even better. I have backtested this system using the DJIA from 1950-2009 and if you want to see the results of buying at 15 times free cash flow or less you can see the complete backtest by going here.

So how is Apple able to perform so well? The very simple answer is that it is an amazing free cash flow generator, as you can see by going to the first table above. What you see there is consistency of results on Main Street, which is paramount to a growth company. Through such things as "Economies of Scale" it is still able to grow at Mycroft/Michaelis growth rates similar to what it did in 2008, even though it has the law of large numbers working against it.

Another amazing thing about Apple is that it is able to have a consistent FROIC of 30%+ in all the years under analysis even though it currently is sitting on \$147 billion in cash reserves. The reason I continue to believe that Apple is a great bargain at today's prices, is for the simple fact that this \$147 billion is only earning about 2% interest for Apple and the company is still able to have a FROIC of 30%. Just imagine what its FROIC would be if instead Apple were to put that huge war chest to work and buy a company like Accenture (ACN) for example, which has a 63% FROIC and is a world leader in cloud computing.

Apple is the largest holding in my clients' portfolios as I believe that as it starts to dominate the Chinese smartphone market, with the help of China Mobile (CHL), that the Apple story is far from over. Steve Jobs handpicked Tim Cook to be his successor and I believe Mr. Cook to be a highly competent CEO. He is doing an amazing job running a company as complex and as large in scale as Apple is. In my opinion, Apple, with its entry into China will start a new chapter in its history that should bring it to a whole new level of performance on Main Street as well as Wall Street. If it were ever to be allowed to repatriate its \$147 billion in cash, then it very well could be the greatest investment I have ever made.