Alexandria Cablevision Co. said yesterday it plans to sell its two-year-old city franchise to a subsidiary of The Chicago Tribune for $16 million, a sale that should give the cable company's local stockholders a five-fold return on their initial investment.

The sale, if approved by the Alexandria City Council, is expected to give the firm's 48 investors, a cross-section of Northern Virginia's powerbrokers, about $50 for each share of company stock that they purchased for $10 or $11.

Among those shareholders who stand to gain from the proposed sale are Rep. Stanford Parris, the district's Republican member of Congress, former Federal Communicaions Commission chairman Frederick W. Ford, former Virginia House majority leader James M. Thomson, and former White House aide Harry S. Flemming.

The civic stature and political muscle of its shareholders were key factors in the council's 1979 decision to choose Alexandria Cablevisiion over two other local companies that bid for the franchise, one with the financial backing of the giant General Electric Co.

The sale of the Alexandria system, which now has 10,000 customers, reflects a trend in what cable analysts call an "overheated" cable industry. Local governments, hoping for maximum accountability, the analysts say, award franchises to local companies, only to see the locals sell out to a national cable operator a few years later.

While cable TV is thought to be enormously lucrative, most cable ventures require large initial injections of capital. As a result, few systems return a profit during their first 10 years. During that time, small companies, which frequently underestimate their construction costs, find themselves in over their heads and without the financial resources to see the franchise through the early lean years.

According to Alexandria Cablevision shareholders, that's exactly what happened to their firm. As one of them put it: "The payoff kept moving further and further and further back," as costs -- and bank loans -- mounted.

Alexandria Cablevision currently has about $9 million in outstanding debts, a sum that will be paid off with the $16 million selling price. What's left after that will be disbursed to the stockholders. Cablevision Chairman Charles Henry Smith said that should yield about $50 a share for the stockholders.

"No one's going to be a millionaire overnight on this deal," Smith said. "You have to remember, this was a very high-risk investment. Our initial investors put money in blindfolded. It was very high risk. The day after we were awarded the franchise, we were deluged with offers from shareholders, but when we started, we were begging people for money."

The firm's decision to sell, announced at a City Council meeting two weeks ago, took Alexandria officials by surprise. It followed by several months financial troubles reported by another local firm that had won Arlington's cable franchise, the only other large franchise yet awarded in the Washington area.

Smith, who owns 7,954 shares of the company, told the council then that high interest rates were the main factor in the company's decision. "Inflation in the cable industry has caused our costs to skyrocket," Smith said then.

In addition to interest rates, Smith cited the high costs of laying underground cable, and management and personnel problems that plague a small, independent firm. "The terrible expense of today makes it very hard for local folks alone to compete with the outside world," he said.

Cable analysts said yesterday that the sale price is about average for a franchise of Alexandria's size and technological sophistication, the range being anywhere from $14 million to $18 million. The decision to sell should not affect the system's service and Smith said may result in an earlier than expected completion of the system. The franchise agreement calls for completion of the system by 1983.

The choice of Tribune Company Cable Inc., a New Jersey subsidiary of the Chicago newspaper firm, capped a spirited bidding war for the Northern Virginia franchise that has involved as many as 11 major cable companies. The Tribune Company Cable already operates the Gaithersburg cable franchise and 39 others around the country. It is currently bidding with a Canadian firm for the Montgomery County franchise and it may also seek the adjoining Fairfax franchise.

A Tribune Company Cable official yesterday described the Alexandria franchise as "an attractive system we want to bring into the fold."

The Tribune bid was not the largest the company received, Smith said yesterday. "I had one bid in hand for $700,000 more than that, but we felt we wanted to go with a company that would have the best interests of the city in mind."