After reading Alyce's bullish arguments, I'm further convinced that Electronic Arts (NYSE:ERTS) has a very bright future as the dominant game developer in a growing industry. However, before I buy a stock, I've got to see a sufficiently large margin of safety -- just in case the future isn't so bright that I have to wear shades (to paraphrase my favorite band of yesteryear, Timbuk 3). Since EA is the undisputed leader in its field, with way more positive qualitative characteristics than negative ones, let's spend some time on the numbers instead.

My first problem is figuring out how to reasonably project EA's free cash flow going forward. It's just too hard to predict the future success of Sony's (NYSE:SNE) Playstation 3 rollout and Microsoft's (NASDAQ:MSFT) Xbox 360 penetration, or whether Nintendo's Wii will help it regain its former glory. In addition, how formidable will the competition be when Activision (NASDAQ:ATVI), THQ (NASDAQ:THQI), and Take-Two Interactive (NASDAQ:TTWO) unleash their own new releases? All I know for sure is that their poor coders had better set aside a whole lot of Red Bull.

Investors can sometimes discern the future by studying the past. Unfortunately for EA, free cash flow has shrunk steadily since 2003 -- more than four straight years now. That could owe to the cyclical industry, but again, it doesn't help me figure out a reasonable number with which to run a valuation, or how EA's free cash will grow going forward.

My best guesstimate is an average of the past three years of free cash flow, which includes the higher numbers of the past as a proxy for any upside we'll see from the next generation of gaming hardware and software. In a nutshell, I took operating cash flow and subtracted out tax benefits from employee stock options, which I don't consider as part of a company's operations. (EA's option tax benefits tend to be substantial; for a technology firm, that's no surprise.)

Next, I subtracted capital expenditures, ignoring acquisition costs, to try to isolate the cash-generating capabilities of operations. I then took an average of the past three years and divided that by the current number of common shares outstanding, which got me to a hair more than $1.40 per share in free cash flow. Based on the current price of $55.90, that's a price-to-free cash flow ratio just less than 40. Its similarity to the forward P/E of 43 makes me comfortable that I'm in the right ballpark.

Now, what type of growth is baked into the stock? Based on my estimate of free cash flow, I calculate that EA will have to grow slightly more than 25% each year for the next 10 years just to justify the current share price. Major inputs include a 15% discount rate and 3% terminal growth rate. In other words, that EA will have to grow rapidly for at least the next decade -- an overly rosy assumption in my opinion.

Since investing is as much art as it is science, it's always a good idea to play with some of the inputs in a model. For instance, if I adjust the discount rate down to 10%, EA would have to grow more than 15% per year to justify its current price. However, I think a 15% discount rate is more appropriate, given that free cash flow has decreased over the past few years, and there's no telling how much upside the next industry boom will bring. In any case, 15% growth for a decade is still pretty aggressive, in my opinion.

I'm sure that's more math than you cared for, but it best illustrates why I think EA is not an overly compelling investment at these levels. Overall, I'm concluding that the growth projections are widely optimistic, leaving too little room for downside. For EA to outperform, it must grow faster than the growth implied in the stock price, which could be as high as 25% annually for the next 10 years.

Back in the late 1990s, EA was growing close to 25% per year, and while I believe it will continue to dominate the gaming software space, I doubt it will be able to expand as fast as the market is currently projecting. The industry has become more competitive, and EA is a larger firm than it used to be.

In short: good company, but not a good stock.

Think you're done with the Duel? You're not! Go back and read the other three arguments, then vote for a winner and share your opinion at Motley Fool CAPS.

Electronic Arts has been a Motley Fool Stock Advisor pick, while Microsoft is an Inside Value pick.

Fool contributor Ryan Fuhrmann has no financial interest in any company mentioned. Feel free to email him with feedback or to discuss any companies mentioned further. The Fool has an ironclad disclosure policy.