Yahoo has been trading up all day, with a current market cap of approximately $21.5 billion. But that isn’t what the company would be worth in an LBO.

First, Yahoo would likely sell its 39% stake in Alibaba.com. The Chinese Internet company offered to buy back the position last month for around $11 billion (Yahoo said no), so let’s keep that as the value. Some people have placed it a bit higher, but Yahoo would now become a motivated seller. That puts the value of Yahoo at $10.5 billion.

Now subtract the market cap of AOL (AOL), which reportedly could be the acquiring entity (via a reverse merger). That brings us down to around $8 billion.

Next, we add a premium. Private equity firms almost never buy public companies at cost, so we tack on 25 percent. That takes us back up to $10 billion.

Finally, we need to figure out how much of that $10 billion would actually come from the private equity firms. The most recent data from S&P Leveraged Commentary & Data shows that “large-market” buyouts averaged 38% of equity in Q2 (the rest is debt). This was down from 50% in Q1.

Using that figure as a baseline, we learn that PE firms would need to contribute $3.8 billion to fund a Yahoo buyout.

As of today, there is not a buyout firm on the planet that could write that check alone. Not because they don’t have the money in aggregate, but because fund agreements typically preclude more than 10% of a fund’s capital from being invested in any one deal (doing so can cause big problems — just ask Teddy Forstmann).

Instead, let’s assume that four firms partnered up. There have been larger PE consortiums on tech deals before — SunGard comes to mind, with seven firms writing $500 million checks — but four is a reasonable number without the guarantee of a viable IPO market (i.e., you want some potential buyers on the outside looking in).

There currently are 15 private equity firms with active funds of $10 billion or more. That makes it sound possible, particularly given that most of those firms have done tech deals in the past (albeit not Internet-specific tech deals).

But then we get to whittling down the list: Oaktree Capital is out, since it  focuses on distressed opportunities (perhaps some Carol Bartz critics would keep Oaktree on the list). I’d also dump Advent International, since it almost never gets involved in such large transactions (and has a fairly small tech practice).

KKR has been one of the private equity space’s most active tech investors (NXP, First Data, etc.), and theoretically could get involved. The tough part here is that KKR is preparing for a very tough fund-raising drive next year, and burning through $1 billion on one deal might back it into an uncomfortable corner. Providence Equity Partners also needs new money, although it’s ride should be a bit smoother.

Other firms on the list include Apollo Management, BC Partners, The Carlyle Group, Providence and Warburg Pincus.

So, yes, private equity could afford Yahoo. No, it would not be easy.

At least four firms would need to play nice with one another, and commit huge pieces of their funds to an industry in which few of them have invested (Providence is a notable exception, with portfolio companies like Hulu). Makes sense that there have been preliminary talks, but there is an awfully long way until those could turn into an actual bid.