The largest merger of two public non-oil companies began with a single phone call to discuss another matter.

Allied Corp. Chairman Edward L. Hennessy Jr. was considering making a bid to acquire Hughes Aircraft early this year when he called Michael D. Dingman, president of The Signal Companies Inc., to find out whether Signal would be interested in submitting a joint bid for the giant aerospace company. After several telephone conversations about the joint bid, the two executives agreed to hold a secret meeting in Arizona that also included Signal Chairman Forrest N. Shumway.

"Within about 10 minutes after we got together, it was very evident that it would not be in the best interest of Allied or Signal to joint-venture for Hughes because it was impossible to divide Hughes," Hennessy said recently in an interview at Allied's Washington office. "It soon became apparent as we were discussing this that we had a lot of businesses that fit well together."

In a period where the threat of hostile takeovers has driven many companies to seek friendly merger partners, the pending $5 billion merger of Allied and Signal is unusual. If the deal is approved by stockholders of the companies next month, it will join two of the nation's largest industrial companies, neither of which was threatened by a takeover, and both of which have strong leaders and strong balance sheets.

In separate interviews recently, Allied's Hennessy and Signal's Shumway asserted that the merger makes sense for the companies because they have operations that are complementary. Both said the ultimate success or failure of the combination will depend on how well the companies' personnel and complex operations are integrated.

Last week, stockholders of the companies received a lengthy proxy statement describing the deal. The proxy offered a profile of a combined Allied-Signal with annual sales in excess of $14 billion and assets in excess of $13 billion, large enough to place it among the top 20 companies on the Fortune 500 list. The combined annual budget for research, development and engineering will exceed $1 billion, the proxy said. Hennessy, who will be chairman and chief executive officer, said the research budget will rank third, behind International Business Machines Corp. and General Electric Co.

The giant being acquired by Allied is Signal, a La Jolla, Calif.-based corporation that describes itself as a multibillion-dollar high-technology and engineering and construction company with 54,000 employes. It has aerospace, electronics, energy and automotive operations, along with extensive research and development activities. The company is a leading worldwide supplier of turboprop and propjet engines for military and civilian aircraft. Its crown jewel is Garrett Corp., a giant aerospace subsidiary.

Signal has grown through acquisitions and internal development from $3.2 billion in sales in 1980 to more than $6 billion last year. The company has a very strong balance sheet, with a debt-to-total-capital ratio below 20 percent.

Allied, the suitor, barely resembles the troubled Allied Chemical of the mid-1970s that was fined for illegally discharging Kepone and other chemical wastes into the James River at Hopewell, Va. While the company still has aerospace, automotive, chemical and energy operations, it has tried to move into high-technology areas that are driven by electronics.

The acquisition of Signal would move Allied further in the direction of its highly publicized 1983 acquisition of Bendix Corp. by expanding its aerospace and automobile operations.

"Ever since Hennessy took over, Allied has been trying to get away from commodities and get into value-added manufacturing. This is a giant step forward," said Dean Witter analyst Catherine Stults.

"There will be a lot of choices to be made to hone down the product line, and I would look for some major divestitures. Superficially, the merger dilutes earnings and is extremely dilutive to cash flow. It all depends on how well they put it together. If Allied does as well integrating Signal as it did with Bendix, there is good reason to think it will work out nicely."

"We'll be on everything that flies," Hennessy said, describing the combined aerospace operations of Allied and Signal. "More of our aerospace business is in military, and they have been doing well in general and commerical aviation. That was the first good fit, and it puts us up in the $5 billion range and gives us a critical mass which we feel we must have."

Hennessy said the next complementary aspect of the merger is in the automotive area. He said Signal's Garrett subsidiary has strong production capabilities, while Allied has strong automotive marketing.

"They don't have the distribution system that we do through Bendix-Allied automotive," Hennessy said. "We see some great pluses putting these two things together."

Hennessy said Signal is strong in manufacturing catalytic converters. He is hopeful that, as Europe moves in the direction of requiring stricter automobile emission standards, the combined companies will be positioned to capture the dominant share of that market.

Acquiring Signal's chemical operations would enable Allied to add more than $300 million to its specialty chemicals, something the company has been attempting to do unsuccessfully for the last few years as it has tried to move away from commodity chemicals, Hennessy said.

Because Allied is being acquired for a combination of cash and stock, the deal will not leave the combined company heavily in debt, as most of the other megamergers have. Ironically, Hennessy said the merger will leave Allied with a stronger financial base.

Signal comes "to us with a very strong balance sheet," Hennessy said. "Total debt to total capital is something less than 20 percent, while ours is running 34 to 35 percent. They have $1.2 billion in cash, and we just sold 50 percent of our oil and gas company for $1.4 billion in cash. When we merge the companies, we will still have $1 billion in cash , and with divestitures we have planned between now and year end, we will end up with close to $2 billion in cash by year end. Our total debt to total capital on the company's balance sheet will probably be in the 20 percent range."

Allied and Signal have formed a 30-person task force, made up of 15 representatives from each of the companies, that is trying to decide how to combine the operations. The new company will have its headquarters in Morristown, N.J., in Allied's current headquarters. Dingman and Hennessy will work out of New Jersey, while Shumway, who will be vice chairman of the combined company, will work out of California.

Hennessy said his goals have changed dramatically since he joined Allied as the company's chairman.

"Six years ago, it was a question of 'could Allied survive,' " he said. "We had a couple of huge legal suits: the Kepone affair and a $235 million Armco steel suit for nonperformance. Our debt was 44 percent of total capital, and we had no R&D base. . . . It is scary because the reaction from Wall Street on the deal has been so positive. Something's wrong. They were so negative then when Allied acquired Bendix and so positive now."

When asked to describe the key strategic reasons for the merger, Signal's Shumway mentioned the same basic elements as Hennessy: the benefit of combining the aerospace operations, the strength of the combined commodity and specialty chemical operations, and the joining of Allied's automotive distribution and marketing operations with Signal's production capabilities.

"The big aerospace companies are substantially larger than either Bendix or Garrett," Shumway said. "Combining them will put us in their class, particularly in the worldwide situation, where size is getting to be important because you're bucking stiff competition from the Japanese and the French."

Shumway said he believes the deal is fair for Signal shareholders, even though the premium is not that large. Signal was trading in the high 30s when the deal was announced. While about 20 percent of the company's stock already has been purchased by Allied for $45 a share in cash, the rest will be exchanged for shares in the new company. Shumway said Signal shareholders will have an 80 percent increase in their dividend, from about $1.00 a share to about $1.80. In addition, they will have the chance to participate in the company's future growth if they retain their stock, he said.

"I can't prognosticate the future, and you know this thing may come unglued," Shumway said, when asked to discuss the merger's chances for long-term success. "That's true of any deal you make. You never know. But this thing has such a good fit. . . . I've been through a lot of these mergers, and I think this is one of the better straight business fits that I've been involved in. . . ."

"In any deal like this, you run into problems you didn't foresee. You can have personnel problems that you never anticipated. You can have all kinds of internecine warfare that you didn't anticipate. But on the other hand, that's what you're paid for."

While Shumway has worked at Signal for more than 20 years, Hennessy has worked for many, many companies, including ITT Corp., Heublein Inc. and United Technologies Corp. Hennessy has a reputation as a tough boss.

While management experts will be watching to see how Hennessy, Shumway and Signal President Dingman work together at the top, Hennessy will have the ultimate responsibility for managing the giant corporation. He said that his techniques for motivating others are as straightfoward as the one he used to light a fire under Allied executives when he joined the company as chairman in 1979.

"I arrived at work early at 7:30 a.m., and if the others weren't in, I left a note asking them to call me when they got in," he said. "Instead of the parking lot being empty at 8 a.m., there was a rush to see who would get what space. [Before], they came in at 9 or 9:30, whatever they felt like. It is a different company today."