This weekend I spent a lot of time researching Apple, as it is the largest holding in my clients' portfolios. In doing so, I stumbled across the following news item on Seeking Alpha's "Market Currents" from November 15, 2013:

**Samsung extends smartphone crown**

- Samsung (OTC:SSNLF, OTC:SSNGY) widened its lead over Apple (NASDAQ:AAPL) in the smartphone market in Q3, with Gartner estimating that Samsung sold 80.36M smartphones vs. 55M a year earlier and Apple 30.33M vs. 24.62M.

- The Korean company's market share held steady at 32.1% while Apple's dropped to 12.1% from 14.3%.
- Overall, the number of smartphones sold increased to 250.2M from 171.65M.
- By operating system, Google's (NASDAQ:GOOG) Android accounted for 205M devices, or 81.9% of the market, Apple's iOS 30.33M, or 12.1%, and Microsoft's (NASDAQ:MSFT) Windows 8.9M, or 3.6%.

- The total number of cellular phones sold rose to 455.6M from 431M. Samsung was in first place with 117M units and Nokia (NYSE:NOK) second with 63M. (PR)

There is a real Clash of the Titans going on in the smartphone industry, and since I was able to track down the various financial statements for Samsung , I thought it would interesting to compare Apple with Samsung and try to discover which company came out ahead.

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

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

The "2014 Mycroft Free Cash Flow per share" estimate in the table above was generated by taking the trailing twelve months (TTM) free cash flow result for both companies and then adding my Mycroft Michaelis Growth Rate into the equation in order to generate forward looking estimates for 2014. That growth rate is generated by using my 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 has a FROIC of 30%, which means that for every $100 of invested capital, they generate $30 in free cash flow.

Samsung has a FROIC of 22%, which means that for every $100 of invested capital, they generate $22 in free cash flow.

Now my Mycroft/Michaelis Ratio takes that FROIC result for each company 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.

Therefore from this 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%.

Samsung has a reinvestment rate of 96% and went on to use 4% of its free cash flow to pay out its dividend. Thus by taking 22% (FROIC) x 96% = 21.12%. From there we add the dividend yield of 0.54% and we have a Mycroft/Michaelis growth rate of 21.12% + 0.54% = 21.66% (rounded off at 22%).

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 $560.02 and divide it by $58.85 and get a Price to Mycroft Free Cash Flow result of 9.51. 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.

Samsung's Mycroft Free Cash Flow per share of **â‚©225,134** was generated by taking its TTM free cash flow per share and multiplying it by (100% + 22% or 1.22). Once we have our result, we then take its current market price of **â‚©1,428,000** and divide it by **â‚©225,134** and get a Price to Mycroft Free Cash Flow result of 6.34. 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.

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 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. Samsung on the other has a CapFlow of 44%, which allows it to use 56% of the company's cash flow to buy back stock.

Apple earlier in the year was an extreme bargain as its stock price fell down to $390.55 on April 19, 2013 and was selling 11.5% below my buy price. Anyone who bought it then made a very smart move as my hold price or where I think Apple should be trading at is $882.75.

In conclusion, as illustrated by the chart above, an investment made in December 2011, in either of the two companies would have made you about 40%. Both companies are generating an incredible amount of free cash flow and that is why each has a very low Price to Mycroft Free Cash Flow per share, thus making each a bargain. Apple, for its part, has a CapFlow that is about half as much as Samsung's, making Apple the safer bet, even though Samsung is trading at a much lower Price to Mycroft Free Cash Flow per share. I say this because as Apple moves into China for example, on a large scale, they will grow their free cash flow at twice the rate that Samsung would, as Apple spends half as much in capital spending (CapEx) as a percentage of cash flow. Finally I believe that both companies are great bargains right now. If one decides to invest in Samsung, I recommend one purchase it on the South Korean market with ticker 005930.KS, instead of the US market, for the simple reason that Samsung trades on the OTC Grey market and over the last three months has had an average volume per day of just 6 shares a day and thus is extremely illiquid.

**Disclosure: **I am long AAPL. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.