Gideon Yu is flying back from Dubai today, we hear. His coworkers at Facebook are surely anxious to know what gifts he's bringing back — and we don't mean the duty-free kind. TechCrunch reports he was there on a fundraising mission. The Persian Gulf's sovereign wealth funds are swollen with petrodollars. But Yu's assignment was tough. Maintaining the $15 billion valuation Facebook obtained from Microsoft and Hong Kong investor Li Ka-Shing in the face of a declining advertising market will require a lot of Yu's demonstrated slickness. But if Yu can squeeze cash out of Bill Gates, surely he can navigate a Middle Eastern bazaar.The bad news: The company needs the cash. TechCrunch editor Michael Arrington has a detailed estimate of Facebook's expenses:

The company is likely spending well over a $1 million per month on electricity alone, say experts we’ve spoken with. Bandwidth is likely another $500,000 or more per month on top of that. The company has earmarked $100 million to buy 50,000 servers this year and next.... we’ve heard estimates that they may have spent as much as $30 million this year alone with [storage systems company NetApp]. And the icing on the cake — earmark another $15 million per year in office and datacenter rent payments. And don’t forget those human assets. With 750 employees and growing, Facebook is spending at least another $10 million per month on payroll. It costs a couple of hundred million dollars a year just to keep the lights on at Facebook. But the real problem is keeping up with growth, particularly storage needs. Add another $100 million or more per year for capital expenditures, and you’ve got a company that’s doing exactly the opposite of printing money.

This estimate, I freely admit, is much better than my back-of-the-envelope math. Arrington may overstate the direness of Facebook's cash position; a $100 million computer-lease deal Yu negotiated has preserved some of its capital, though that will need to be paid off down the road. The company's rosy projections for advertising, certainly, must need to be revised downward. If Yu has come back from Dubai empty-handed, then Facebook will soon be cutting costs just like the rest of the Valley.