I am looking at Facebook (NASDAQ:FB) today because it's less expensive than it was a while back, when it hit $72.59. I am looking at Facebook because while it is expensive, so is everything else, and investors do love Facebook. And I am looking at Facebook because perhaps, just perhaps, it is not as expensive as I think it is.

**Value**

When I look at value, I tremble at a trailing twelve-month P/E of 95.50. When I look at the several key valuation indicators set out below, I see a stock which is expensive relative to the market, its sector of operation, and its industry of operation. The one saving grace is the Price-to-Cash ratio, which is lower than the market's Price-to-Cash ratio. And that is a big comfort, because cash is important.

**Source:****Alpha Omega Mathematica**

But how expensive is the valuation, when we factor in future growth expectations? Surely, that matters too.

In the 1960s, a smart gentleman called Jim Slater realized that there is more to the math of the multiple. And he came up with the Price/Earnings Growth Ratio [PEG]. This is a lovely ratio to use, because it brings the growth differential in as an investment consideration. It is simply the P/E Ratio divided by the long-term growth rate expectation.

Facebook has a PEG Ratio of 3.04, which is higher than the market capitalization weighted average for the market, and its sector and industry of operations. Thus, on the face of it, the stock looks expensive when adjusted for growth.

But wait. Facebook achieved profitability for the first time in 2013. The trailing twelve-month fully diluted earnings for Facebook was $0.61. The P/E and PEG ratios are based on trailing twelve-month profitability. But they might be misleading, because the bulk of the profitability came during the second half of the year.

Even if we look at the trailing twelve months, the PEG ratio is quite reasonable if we consider non-GAAP earnings, which excluded non-core and non-recurring items. Non-GAAP earnings for 2013 were $0.87. The trailing twelve-month P/E based on non-GAAP diluted earnings is closer to 72, and the PEG ratio based on the non-GAAP trailing twelve-month P/E is 2.31. This does not look too bad. And the reality is better, because the first half of 2013 delivered $0.31 in adjusted earnings in comparison with $0.56 in the second half of 2013: as we move through the year, the PEG ratio will start looking prettier.

Analyst consensus earnings for 2014 are at $1.26. And based on that, we have a current year P/E Ratio of 50, and because long-term growth expectations are 31.38%, we have a current-year PEG ratio of 1.58. Now Facebook is not looking so terribly expensive when adjusted for growth expectations.

What about risk? What is missing in the PEG ratio is risk adjustment. I thought it might be worth multiplying the PEG Ratio by Beta to develop a P-RAGE ratio: that would be Price/Risk-Adjusted Growth & Earnings Ratio. This ratio would simply multiply the PEG ratio by Beta to introduce an element of risk adjustment. The problem we face for Facebook is that it is too young a company to have a reliable beta: in fact Value Line and Reuters don't report a beta for the stock. When I calculate a beta for Facebook, I get a two-year regression beta of 0.73, which I adjust for beta's tendency to converge towards 1 to 0.99. The one-year regression beta comes to 0.49, which I adjust for beta's tendency to converge towards 1 to 0.99. But these betas are not meaningful. Firstly, calculating a beta based on a regression period of less than five years is not a very good idea, though a three-year beta is better than nothing. But most importantly, Facebook's regression over two years returns a co-efficient of determination of 2.31%. This means that the movement in Facebook's stock price has little to do with movements in the S&P 500's price. Almost all of the price movement is driven by company-specific factors. Since beta is a measure of market risk, the low co-efficient of determination for Facebook suggests that beta is wholly unreliable as a measure of market risk. Facebook is not without risk, it's just that the market risk is not correlated well with the company: the standard deviation in the weekly movement of the stock price over two years has been 7.13%, compared with 1.48% for the S&P 500. That says there is risk or volatility, but the risk or volatility comes about from company-specific factors, rather than market-driven macro factors.

In such circumstances, a far higher degree of due diligence is necessary. And we need to set return expectations based on our assessment of risk. The biggest risk for Facebook is growth risk. So let us have a look at growth.

**Growth**

The key growth indicators I track show that Facebook outperforms the market, its sector and its industry of operations. Most of these key indicators are historic growth trends, and what they tell us is that the company has established a reasonable track record of well-managed and rapid growth. The most important growth key indicator is earnings growth expectations over the coming five years. And that calls for an annualized growth rate of 31.38%.

**Source:****Alpha Omega Mathematica**

How credible are growth expectations of 31.38%? In my view, this growth rate is very credible.

Earnings estimates for the March 14 quarter are at $0.24, in comparison with the December '13 quarter non-GAAP earnings of $0.31. In my view, this is a very conservative estimate, which I expect will be beaten by at least $0.03 to $0.04. Secondly, earnings estimates for 2014 are at $1.26. This is also, in my view, a conservative estimate. I will look for at least $1.29 for the year: indeed, I believe a rise in expectations to $1.49 as the year progresses will not surprise me. Conservative estimation in the immediately foreseeable period suggests that 31.38% might not be a hugely aggressive estimate. **For the purpose of valuation, I will use consensus estimates of $1.26 for 2014 as an estimate of sustainable earnings.**

ZenithOptimedia's analysis of advertising spends expected in the coming years is a must-read: you can download the report here.

My key takeaway from this report is their expectation that the advertising spend in 2014 will grow 5.3% and approach $532 billion for 2014. They go on to say:

**Source:****ZenithOptimedia****Advertising Expenditure Forecasts for 2014**

The important point to take home is that internet advertising is growing at a fast rate, and is expected to continue to do so. And the fastest-growth category is display, which is driven by social media advertising, which is growing at a 28% rate. **Facebook is a market leader in social media.**

Another important point they make in their report is that they expect mobile advertising to grow at an annualized rate of 50% over the coming two years, even while they expect growth rates in desktop internet to slow to 7%. **Facebook has displayed considerable success in monetizing the mobile category. And they won't suffer from stagnation in the classified category either.**

**Source:****ZenithOptimedia****Advertising Expenditure Forecasts for 2014**

And lastly, this is how they see the composition of advertising spend. As you can see, the biggest share of advertising dollars is held by Television. By end-2013, desktop and mobile internet took a combined share of 20.6% of the market. In my view, further gains through disruptive innovation will continue. Newspapers and Magazines can be expected to lose further ground. And Television will also lose share to the internet as streaming and video audiences are built. Over the coming ten years, I expect to see Desktop and Mobile internet emerge as the largest category in global advertising spend, perhaps growing to 40%.

**Source:****ZenithOptimedia****Advertising Expenditure Forecasts for 2014**

An advertising spend of $532 billion today, growing at an annualized rate of 5.3%, would indicate a market size of $892 billion in ten years. Today, Desktop internet makes up $90.4 billion (17%) of the advertising spend market of $532 billion. If it grows at a 7% annualized growth rate, in ten years, it shall be $178 billion, or about 19.9% of the $892 billion advertising spend market. Mobile internet is small today, at $14.4 billion (2.7% of the $532 billion market). It is also the fastest-growing segment. If this segment grows at an annualized rate of 28.5% during the coming ten years, it will grow to $176 billion, or about 19.8% of the advertising market estimated at $892 billion in ten years. This would split the internet into two parts shared equally by Mobile and Desktop, together accounting for near 40% of the market. Newspapers and Magazines would continue to lose market share, but as video and streaming gain popularity on the internet, it is likely that the cannibalization of Television's share of the ad spend would commence.

On the internet, in my view, it is likely that Desktop will be dominated by search, while Mobile will be dominated by social. Thus, in my view, to expect Facebook to grow at a ten-year growth rate of 28.5%, compared with a current mobile growth rate of 50% and a social media growth rate of 28% has little risk. What I would look for is for Facebook to grow at 31.5% for the coming five years, followed by growth at 25.5% for the next five years, for a composite ten-year growth of 28.5%. After that, I will assume the disruption through technology will be largely complete, and growth will revert to 5.3%, which is broadly in line with nominal GDP growth rates in developed markets. A composite very long-term growth rate of 9.60% (28.5% for 10 years and 5.3% for the next 40 years) would be a very reasonable growth expectation for Facebook. And if I add a 1% growth risk premium to that number, I arrive at a risk-adjusted investor return expectation of 10.6% for Facebook. **For the purpose of valuation, I will use a composite very long-term growth rate of 9.60% and an investor return expectation of 10.6%.**

**Quality**

Let's have a quick look at quality. Ownership quality is sound, though to my surprise, insiders own less than 0.50% of the company, which is less than the market capitalization weighted insider ownership for the market, the technology sector and the internet information providers industry. The institutional ownership is also sound, at a level higher than the market capitalization weighted institutional ownership for the market and the technology sector. However, the institutional vote of confidence at industry level is missing: compared with Google's institutional ownership of over 85%, the commitment to Facebook, with 65.40%, is a bit disappointing. But all in all, ownership quality is sound. The return and profit quality indicators are also relatively strong, regardless of whether the key indicators are compared with market capitalization weighted key indicators for the market at large, the technology sector or the internet information providers industry. **For the purpose of valuation, I will use a return on equity expectation of 20%, a level consistent with the five-year average for the technology sector.**

**Quality**

**Source:****Alpha Omega Mathematica**

**Momentum**

And finally, a quick look at momentum. Momentum has been strong overall. And the strength over the past week is probably a beat on earnings expectations being priced. In my view, the momentum investors will get the beat they are looking for!

**Source:****Alpha Omega Mathematica**

**Valuation**

Mathematically, the worth of Facebook is estimated as [1 + Long-term Growth Rate] * Sustainable Earnings * Adjusted Payout Ratio / [Long-term Return Expectation-Long-term Growth Rate].

As noted previously in the Growth section of this article, I will use $1.26 as a reasonable estimate of sustainable earnings and a long-term growth rate of 9.60% for Facebook. Since the beta for Facebook is unreliable, I will set my investor return expectations at 10.60%, which represents a 1% premium to very long-term growth expectations. I estimate the risk-free rate for the several forward years and the equity risk premium at 4.5% and 5.75%. This indicates a market return expectation of 10.25%. Thus, for Facebook, I am looking for a slight premium to the market return. In fact, given that the markets are not presently priced to deliver a long-term return of 10.25%, the spread being asked is higher. But for the purposes of valuation, I am more interested in absolute value than the relative value, and so 10.60% is what it shall be.

As far as the adjusted payout ratio is concerned, I am looking for a return on equity of 20%. With a very long-term growth expectation of 9.60%, the company would need to reinvest 48% of profit (48% * 20% = 9.60%). The remaining 52% would be available to shareholders. This value would be returned via growth at premiums to the very long-term return expectations in the early years, followed by dividends and buybacks, net of dilution resulting from employee and other issuances in the later years.

Thus, Facebook would be a decent buy at $71.80 [109.60 % * $1.26 * 52% / (10.60% - 9.60%)] or below. With the stock trading at $63, investors have about $9 (14%) of alpha to capture, after which a long-term return of 10.60% would be satisfied. This is a good company trading at a fair price. It is not, however, a good company trading at a cheap price: it gets cheap at $48, a price at which it meets an investor return expectation of 11.10%, which provides a growth risk premium of 150 basis points.

**Disclosure: **I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours. 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.