The New York City Metropolitan Transit Authority yesterday announced it has taken advantage of the Reagan tax-cut bill to save more than $15 million on the purchase of $102 million worth of subway cars and buses by selling the depreciation rights to a private company. Washington Metro officials expect to emulate the deal.

The MTA entered into a "lease"--in fact the sale of a tax shelter--with Metromedia Inc., in which the private company will pay the transit authority $15.52 million. In return, Metromedia, the owner of seven television stations, including WTTG TV (Channel 5) here, will be able to use the capital depreciation tax breaks on the equipment.

Richard S. Page, general manager of the Washington Metropolitan Area Transit Authority (Metro), said he is exploring the possibility of working out a similar deal to save money "because we are buying 294 new rail cars from Italy, and over the next five years we are going to be buying or rehabilitating many buses."

Page said he has received inquiries about the possibility of going into a leasing deal, but Metro is not under any immediate pressure because the local authority has not put any new vehicles into service this year. Another Metro official declared flatly: "We're going to do it."

The new form of leasing permitted under the 1981 tax bill--actually paper transactions involving the sale of corporate tax breaks--was designed to allow companies with little or no profits to receive some of the benefits from the business tax cuts in the legislation. Another purpose is to prevent a wave of tax-motivated corporate takeovers as profitable companies would buy up firms sitting on unusable tax breaks.

During the last-minute negotiations over the bill, however, key New York legislators were able to slip into the measure provisions allowing public-transit authorities to "lease" depreciation tax breaks on buses and subway cars so long as the purchases are made entirely with money raised from bonds issued by the authorities.

Mortimer L. Downey, assistant executive director of the New York MTA, said the lease deal with Metromedia is just the start of a major effort to capitalize on the obscure tax break.

Over the next five years, the New York transit authority plans to buy a total of $2.5 billion in subway cars and buses, and use the leasing provision to save about $500 million, he said. If these savings work out, Downey claimed they will almost, but not quite, equal the cuts in capital grants made by the Reagan administration. They will not make up for cuts in operating costs.

Downey said the agreement with Metromedia was negotiated on behalf of the MTA by Citibank of New York. Citibank received a fee of about $1.25 million, he said, adding that in the future the MTA expects to pay smaller commission fees.

Downey pointed out that a problem facing other transit authorities is a requirement that the entire purchase of the cars and buses be with bond money, and no federal money.

Page said this requirement may cause some difficulties for the Washington Metro system.