Ursula Burns calls less than 30 minutes after the markets close on the most tumultuous trading day in Xerox (XRX) history, and she sounds, well, energized. Not quite 100 days into the CEO job, on Monday she launched the biggest acquisition bid in the company’s history and survived a 15% drop in its stock price on record volume. And she’s still standing.

“I was positively surprised that it wasn’t as bad as it could be,” she says, adding that she’s ready to continue explaining the deal to Wall Street. “Exciting times.”

Investors are understandably less sanguine than Burns. Her $5.7 billion cash and stock offer for outsourcing giant Affiliated Computer Services (ACS) would put $3 billion in debt onto the books, and more than double Xerox’s employee headcount from 54,00 to 128,000. This, when investors had been expecting nice, safe stock buybacks.

Burns, a plainspoken New York native known for her engineering savvy and her operational discipline, isn’t interested in playing it safe. In her move to grab ACS, she is embracing the same forces that drove Hewlett-Packard (HPQ) to purchase EDS for $13.9 billion last year, and Dell (DELL) to offer $3.9 billion for Perot Systems (PER) just last week.

In a maturing enterprise technology market, customers increasingly want to outsource the purchase and management of complicated systems, and to offload administrative tasks. By purchasing ACS, Xerox can offer to handle more tasks for its customers, and earn profits while putting its products to work. It helps that ACS has 10% profit margins, and grew revenue at about 6% this past year. The deal is expected to close in early 2010.

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From copiers to services

Though investors aren’t yet buying it – Burns will have to convince them – this move probably makes sense for Xerox. ACS would transform the company from a seller of printing equipment and print services with $16 billion in revenues into a $22 billion specialist in gathering, analyzing and sharing information. Without a bold services move, Xerox faces stagnating revenue in its core product business as it matures.

Dallas-based ACS specializes in business process outsourcing, the paper-intensive, back-office work like payroll and benefits, auto and mortgage loan processing and Medicaid claims. Burns believes that with ACS in the Xerox portfolio, her sales team could expand its business to Europe, where Xerox’s brand is strong and ACS has almost no presence today. And Xerox could boost ACS margins by offering its technology to eliminate paper and automate more processes.

“ACS has got a services portfolio in state and local government that, at this point in the maturity scheme of things, cannot be replicated,” says Jefferies & Co. analyst Joseph Vafi, who covers ACS. “At this valuation, the deal is a success for Xerox even without much synergy. Obviously Xerox needs to sell the deal a little more to their investor base, which wasn’t looking for a big acquisition.”

Though it blindsided Wall Street, this deal arguably looks downright sweet for Xerox – compared, say, to Dell’s plan to buy Perot Systems. Dell is paying 29 times estimated 2010 earnings for Perot, while Xerox would get ACS for about 14 times its estimated 2010 earnings. Plus, many of the information analysis problems ACS tackles every day are precisely the ones Xerox scientists are trying to solve. For example, ACS, which runs the E-ZPass electronic toll collection system in some areas on the East Coast, could use Xerox character recognition technology to digitally read the license plates of toll lane violators and issue them tickets.

A deal too rich for investors?

In fact, the deal might be a little too sweet. Even before Xerox shares took their beating on Monday, Burns was offering a relatively modest 33.6% premium over ACS’s Friday closing price. Some analysts suggested to Fortune that she might have to raise the bid to make up for the stock shrinkage and satisfy ACS shareholders.

Then again, flamboyant ACS founder and Chairman Darwin Deason, who holds super-voting class B shares in the company, may have the only opinion that ultimately matters. Xerox plans to pay him $300 million in convertible preferred stock for those class B ACS shares, on top of the even bigger payout he would get for his stake on the company. He, not surprisingly, supports the deal.

Burns says she isn’t too worried about other companies swooping in to snatch ACS from Xerox. “We have a fair price on the table. ACS has been in and out of deals over the past couple of years – if somebody wanted to come in, I think they would have come in already.”

Now her challenge will be convincing a skeptical Wall Street that this deal is good for everyone. Day one didn’t go so well – she had to rush the news out to keep it from breaking in the press, and short sellers and arbs jumped into the fray, a combination that drove Xerox trading volumes to more than 25 times the normal level.

Over the next days and weeks, her message to investors will be to take a deep breath and take a fresh look at ACS. “If you asked us to stay in the print and copy infrastructure business, you would sell us only because we’d have very little future,” she says. “We’re actually scaling our services business and scaling our BPO in a very effective way to respond to changes in the marketplace.”

Related:

See Ursula Burns on Fortune’s 50 Most Powerful Women list.

Why Xerox CEO Burns is buying big