It is hard to imagine that Peter May, one of New York’s most successful entrepreneurs and investors, would be rattled by mere numbers.

His discreet smile, trim build, pleasant manner, and sartorial elegance project the sort of quiet self-confidence that’s prized in America’s boardrooms. It is easier imagining him coolly performing triage on a corporate train wreck than being shocked by the sight.

But one early spring day three years ago, Mr. May, then the newly appointed board chairman of Mount Sinai Medical Center, was stopped in his tracks.

“I didn’t know how bad it was at Mount Sinai,” he said yesterday. “The institution was in trouble – the numbers were very alarming. Nobody had known how bad it was. There was little leadership. Morale was terrible. Everybody was worried.”

The Long Island-born Mr. May was scarcely comforted by a call from the institution’s chief financial officer, who said: “We’re running out of cash.”

Out of cash? Mr. May thought. Mount Sinai? How could that be?

But that was indeed the case.

The venerable institution – founded in 1852 as the Jews Hospital to accommodate Jewish patients and physicians who were barred from New York’s mainstream medical facilities out of prejudice – had long been running in the red. With an annual budget of some $1.8 billion, Mount Sinai, which consists of a hospital and a medical school, was experiencing budgetary deficits of more than $100 million a year.

Its billings were so behind that administrators had lost count of just how much was owed by patients and insurance companies. Its doctors were being wooed away by other hospitals. Its corridors were not as clean as a hospital’s should be.

The reasons went beyond irresponsible management, although administrative ineptitude had contributed significantly to the malaise.

A seminal change in medical economics was just as responsible for Mount Sinai’s misfortunes. In the 1980s, the traditional “cost-plus” system, under which hospitals assigned price tags for specific services and accordingly billed patients and insurance companies, was replaced by a “fee for service” practice. Under the new system, the fee for services was often arbitrarily set by health providers. While that meant hospitals were forced to streamline their practices, it also resulted in bigger losses for institutions, as reimbursements were often inadequate.

Mr. May joined Mount Sinai’s 50-member board in 1989, a natural extension of his wide-ranging charitable activities that included contributing to the UJA Federation, among other nonprofits, where he’d helped raise more than $250 million for its Operation Exodus campaign. When the medical center looked for a new chairman in 2002, a board member, Robert Rubin – a former secretary of the Treasury – called Mr. May.

“I was petrified,” Mr. May said yesterday. “What if I failed?”

Failure wasn’t in his playbook. Back in his Long Island days, growing up as the only son of a successful businessman, Samuel, and a social worker, Isabel, Mr. May had excelled in school. Samuel May gave his son odd jobs in his office, and both Peter and his sister Linda found themselves in lively discussions about business at the family dining table.

It was natural, therefore, that the young Peter head toward a business degree. He obtained an MBA at the University of Chicago, and then worked for the accounting firm of Peat Marwick. In 1972, he joined Nelson Peltz in what ultimately became the Triarc Companies, where Mr. May serves as president and chief operating officer of an extremely successful firm that, among other things, invests in equities.

“The two enduring partnerships in my life have been Nelson, whom I’ve known for 34 years, and Leni, my wife and best friend for 41 years,” Mr. May said.

Both Leni May and Nelson Peltz were enthusiastic about Mount Sinai’s invitation to Mr. May to become chairman.

“I always felt that my skills were best suited to tangible objectives,” Mr. May said. “I recognized that the opportunity at Mount Sinai was both exciting and incredibly frightening. After all, Mount Sinai plays such an important role in the life of New York, in the medical world, and in the Jewish community.”

At his very first meeting as chairman, Mr. May reached into his trademark optimism and said: “I really believe that we can turn this place around. And we’ll do it in three years! We can do it!”

He set about creating a new team. It included Dr. Kenneth Davis, a Mount Sinai veteran, who was named CEO and with whom Mr. May came to establish a special professional and personal bond. Administrative and billing procedures were revamped.

Mr. May decided that, if needed, he would ask the board to tap into $180 million in unrestricted funds that were part of the institution’s $500 million endowment.

He decided against layoffs and slice-to-the bone cutbacks.

“It’s hard to cut your way out of a business problem – you need to build your way out,” Mr. May said.

That meant accelerating fund raising. It meant widening Mount Sinai’s marketing campaign. It meant recruiting talented staff members. It meant injecting greater transparency into the institution’s management. It meant making public appearances on behalf of Mount Sinai. It meant seeking out individual workers in order to bring good cheer to them.

“It meant, most of all, creating a fresh spirit of teamwork,” Mr. May said. “At the end of the day, people will judge you by the respect you accord them. As board chairman, one of the best things you can do is to roll up your sleeves and work along with other board members and colleagues.”

His longtime friend and a Triarc director, Clive Chajet – a leading branding consultant – said of Mr. May last night: “Peter May’s strength is his understanding of how to motivate executives, and he communicates ‘Job well done!’ in such a manner that the executive tries harder and harder to grow because of the compliments. It’s unusual for a trained accountant to be that sensitive to the human factor of successful organizations.”

Mr. May seems shy about such encomiums.

Why should he be reserved about this, the reporter asked? Hadn’t Mr. May met his self-enforced deadline of making Mount Sinai profitable in three years? Had he not avoided touching a penny of the $180 million of unrestricted money? Hadn’t the endowment increased to more than $700 million from $500 million, its budget to $2.1 billion, and its cash availability to $250 million?

“It’s taken sheer willpower,” Mr. May said.

As he marks the third anniversary of his chairmanship – he recently signed on for another three-year term – Mr. May often thinks of what his father once said to him.

“Always do more than what’s expected of you,” Samuel May said to his son a long time ago in their Hewlett, Long Island, home.

Yesterday, as he ended lunch, the board chairman of Mount Sinai said: “I hold myself by that, and I look to people who share that attitude.”