Let the road show begin.

Aramark, one of the world's leading purveyors of hot dogs and hospital gowns (among many other things), last week began pitching itself to potential investors.

The Philadelphia company has undertaken its third IPO with a goal of raising at least $561 million after expenses to go toward paying off portions of its $5.8 billion debt.

The first step in the sale is the so-called road show, in which company representatives make presentations to analysts, fund managers, and potential investors in hopes of boosting interest.

Aramark is offering 28 million shares of Aramark Holding Co. An additional 8.25 million shares are being offered by current shareholders of the privately held company. The company will benefit only from the sale of the 28 million shares, which are expected to bring between $20 and $23 apiece (up to $644 million in gross proceeds).

The sale represents a little more than 10 percent of the company's 229.8 million shares. If the IPO attracts $23 a share, Aramark would be valued at about $11 billion ($5.28 billion market cap plus $5.8 billion in debt.) Aramark generated $13.9 billion in sales in fiscal 2013.

That is quite a rise from Aramark's $37 million revenue in 1960, the year it first went public as a company focused on putting vending machines in factories.

From that humble beginning, Aramark has grown to a behemoth that boasts being "a leader in professional services, providing award-winning food services, facilities management, and uniform and career apparel to health care institutions, universities and school districts, stadiums and arenas, and businesses around the world." It employs 272,000 in 22 countries.

The chief architect of that growth was Joseph Neubauer, 72, who served as chief executive officer for 29 years before stepping down last year. Neubauer holds 20.5 million shares - about 10 percent - and is offering to sell 1.3 million.

As CEO, Neubauer took the company private in 1984 to avoid a hostile takeover. After a second IPO in 2001, Neubauer again took the company private in 2007, selling 85 percent of its shares to a collection of equity funds, including Goldman Sachs Group Inc., JPMorgan Chase & Co., Thomas H. Lee Partners, and Warburg Pincus.

That buyout left Aramark with much of the debt it now carries.

According to the IPO prospectus, the sale will enable the company to repay approximately $411.9 million in term loans due July 26, 2016, and $150.0 million in revolving credit debt.

That will still leave the company heavily leveraged.

Given the size of the debt, some analysts are unimpressed.

"We have expected Aramark to raise much more, potentially as much as $3 billion," wrote Vicki Bryan, of Gimme Credit. Still, Bryan was bullish.

"Aramark still offers reasonable upside nevertheless via steady operating improvement over the next year. Maintain 'outperform.' "