There have been several reports this week that private equity firms Silver Lake Partners and Andreessen Horowitz may offer to buy Yahoo (YHOO), the oft-troubled Internet company that has been particularly rudderless since firing its CEO last week.

The two firms most recently teamed up to buy a majority stake in Skype from eBay (YHOO), and then quickly turned around and sold the entire thing to Microsoft (MSFT) at a heady profit (or at least agreed to do so, as that deal hasn’t yet closed). In other words, they are no strangers to either co-investments or Internet brand revivals.

But even if they want to buy Yahoo, can they afford it?

Yahoo currently has a market cap of just over $19 billion. Or that, approximately half is believed to be the value of Yahoo’s 40% stake in China’s Alibaba Group, which Silver Lake and Andreessen Horowitz would reportedly seek to sell off. So let’s assume they can get around $8 billion for the Alibaba position, a discount based on Alibaba’s previous rejection of a $9.5 billion buyback offer.

That leaves us with an $11 billion hole. But there would have to be some sort of premium, which we’re going to put at a modest 9%. So they really need $12 billion.

Last year, S&P LCD reported that the average equity portion of a $1 billion+ leveraged buyout was 39.28%. Credit markets have begun tightening up a bit, but let’s stick with that figure. It means that Silver Lake and Andreessen Horowitz would be responsible for $4.71 billion.

Now let’s presume that each firm is willing to commit a whopping 15% of their current fund to the effort. It likely would be the largest single investment each shop has ever made — and possibly require some limited partner approval, since 10% of often the limit — but clearly Yahoo would be a make-or-break sort of deal. Combined, that would be around $1.5 billion. Or, put another way, $3.2 billion short.

At this point, Silver Lake and Andreessen Horowitz need to get creative. One option is to tap existing limited partners for co-investments. Let’s say that adds another $500 million. And then another $500 million comes in from institutional co-investors, like the Canadian pension fund that helped out on Skype. You also could add another large private equity firm, although that could eat away at the LP co-invest (since many Silver Lake investors also are in Blackstone, KKR, etc… and wouldn’t want to quadruple down on Yahoo).

The solution now is to partner on the buyout with select, large holders of Yahoo stock. Maybe individuals like co-founder Jerry Yang and institutions like The Capital Group and State Street. Let them hold the remaining 11%, thus getting us to the magic number.

Yes, all of this would be pretty complicated. And perhaps a better solution is for Silver Lake and Andreessen Horowitz to simply buy a minority stake and help reorganize the company from that position (as suggested by Henry Blodget). And there always is the chance that Microsoft will finally pull the trigger, given that it has more than $50 billion of cash just lying around (a bit less once Skype closes). Or that Microsoft will somehow partner with the PE firms.

But my point is that Silver Lake could afford Yahoo. At least in theory.

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