Robert Allen sleeps easier at night now.

Nine months ago, the president of Chesapeake & Potomac Telephone Cos. suffered a strong bout of insomnia just after he learned that his company was about to be split from its friendly and protective parent, American Telephone & Telegraph Co.

For at least two nights after he heard the news, Allen didn't sleep, thinking about the implications of the largest divestiture in corporate history and its effect on his company's financial health, 5.2 million customers and 45,000 employes.

Today, however, Allen appears much more at ease about C&P's future and says he is confident his company will be financially strong after divestiture.

"I am perhaps more upbeat," acknowledged the 47-year-old Allen in an interview given the same day last week that U.S. District Judge Harold H. Greene signed the historic divestiture agreement between AT&T and the Justice Department.

"I've always had faith and confidence but now I know what the tasks are," which makes the corporate reshuffling much easier to contemplate, he said.

At the same time, Allen appears much more optimistic about C&P's future, largely because of recent changes that were made to the divestiture plan by Judge Greene. The changes, designed in part to give the divested local telephone companies more revenue, will permit C&P to continue offering its highly profitable Yellow Page service and will also allow C&P to sell a wide variety of telephone equipment.

In both the short- and long-term, these revisions will help keep C&P on a strong financial footing which, in turn, should help minimize rate increases for local service, Allen said.

Even so, he added, local bills will certainly continue to rise over the next several years, especially if the economy remains sluggish and continues to cut into C&P's traditionally high growth rate.

Although demand for the company's services continues to grow, the rate of expansion is currently the lowest in 20 years, Allen said. For the first seven months of the year, C&P installed about 40,000 new telephone lines.. "Last year, at this time, it was over 80,000," Allen said.

What's more, Allen noted the company has experienced only a 2 1/2 percent growth in long-distance calls for the first seven months of this year, compared to the traditional growth of 8 to 12 percent a year. "Of course not all that is related to the economy. A lot of that is related to competition," Allen admitted.

Overall, this lower growth will mean that the company will be more than $50 million shy of its estimated revenue for 1982. As a result, C&P has had to cut its construction budget by $64 million "simply to react to this lack of growth."

Additionally, in an effort to reduce costs, C&P has been trying to reduce its work force. In the past year, it has reduced its work force by about 750 through attrition and early-retirement incentives for middle and upper managers. The company is now offering similar early-retirement packages to lower level managers in hopes of reducing the number of slots in that area by 390 by the end of the year.

Yet, despite these cost-cutting measures, rate increases are inevitable, according to Allen.

"I don't like rate increases better than anybody else," Allen said. "But the fact of the matter is we are still only earning about 11 percent on equity and that's not a very competitive investment in the marketplace today. So we just have to keep working on keeping profits up particularly in view of divestiture if we are going to be standing on our own and not have the umbrella coverage of our parent company."

This month the company asked to boost most Virginia local telephone bills by 19 percent a month. That request follows applications last month for a 27 percent increase in rates for Maryland customers and a 22 percent rake hike for West Virginia residents. (C&P won a 19.6 percent rate hike for almost all District residents last April.)

Another rate request for District residents is likely next year, Allen said, adding that "we haven't finally decided about that."

But Allen indicated that, once divestiture occurs, rate increases may not have to be as high as many communications analysts had predicted. The main reason: C&P will be able to continue obtaining a good portion of its profits through Yellow Pages.

Although Yellow Pages account for only 4 to 5 percent of the company's revenues, it makes a much larger contribution to the company's profits. However, Allen would not reveal how much.

But Allen would say that the profit from Yellow Pages "contributes on a nationwide basis somewhere in the order of $1 to $1.50 a month per telephone line."

Given that the average C&P local phone bill is $10, that means that Yellow Pages profits contribute about 10 percent, Allen calculated. As a result, rates will not have to go up an extra 10 percent after divestiture to recoup the loss from Yellow Pages, he said.

Judge Greene also gave the local companies permission to sell terminal equipment.