United Rentals Inc. agreed to be bought by Cerberus Capital Management LP for $4 billion, the third sale of an American construction equipment-rental company in the past year.

Cerberus will pay $34.50 in cash for each share, Greenwich, Conn.-based United Rentals said yesterday in a statement. That is about 25% more than the price on April 9, the day before the company said it was considering a sale. Cerberus, a New York-based buyout firm, will assume about $2.6 billion of debt, the statement said.

United Rentals, the biggest American construction-gear rental company, said in April it might sell because its shares were undervalued. The stock dropped 22% in the 12 months before that announcement as the housing industry weakened. The deal follows the purchases last year of competitors NationsRent Cos., the second-largest equipment renter, for $600 million and No. 3 Rental Service Corp. for $4.1 billion.

“I was hoping they would have gotten more, but this is the price I figured they would get,” an analyst with CIBC World Markets in New York, Scott Schneeberger, said. He rates the shares “sector perform” and doesn’t own any. “It’s a good company that’s made incredible strides from a couple of years ago.”

The purchase comes as the subprime mortgage rout is spreading to the credit markets that fund such private-equity purchases. Chrysler, the car-maker being sold by DaimlerChrysler AG, last week boosted interest on $12 billion of loans to fund its buyout by Cerberus, and at least 20 bond and loan deals worldwide have been disrupted in the past month.

Cerberus has announced 12 deals since former U.S. Treasury Secretary John Snow joined as chairman in October. Terms were disclosed for eight of the transactions with a total value of $27.7 billion.

United rents equipment from almost 700 locations in America, Canada, and Mexico, supplying builders, utilities and homeowners in a $33 billion market.

“We started in 1997 with about $35 million in start-up equity, and today we signed an agreement for about 200 times that initial investment,” the chairman of United Rentals, Bradley Jacobs, said in an interview. “It’s not every day we see that kind of success story.” Shares of United Rentals rose 61 cents, or 1.9%, to $32.98 at 4 p.m. in New York Stock Exchange composite trading.

The board of United Rentals has approved the agreement. Completion of the transaction is subject to approval by the company’s stockholders and regulatory review.

Holders of the company’s preferred stock, including Apollo Management L.P., which represent shares with 18% of the voting power, have agreed to support the purchase.

United Rentals may continue to solicit proposals for alternative deals from other parties for a period of 30 business days through August 31.

Bank of America Corp., Credit Suisse Group, Morgan Stanley, and Lehman Brothers Holdings Inc. will provide financing.

Leatherhead, England-based Ashtead Group Plc agreed in July 2006 to buy Florida-based NationsRent to compete with United.

Atlas Copco AB, the world’s largest maker of air compressors and rock drills, sold its North American equipment-rental division, called Rental Service, to buyout firms Ripplewood Holdings LLC and Oak Hill Capital Management in October for $4.1 billion to concentrate on mining machinery. The North American company is No. 3 in the American market.

United was advised by UBS AG, with Simpson Thacher & Bartlett LLP acting as legal adviser. Lowenstein Sandler PC and Schulte, Roth & Zabel provided legal advice to Cerberus.