NEW YORK (TheStreet) -- Now's not the time to let go of your General Electric (GE) - Get Report stock, despite the enticing offer to swap it for discounted shares of Synchrony Financial.

Just a week after obtaining approval from the Federal Reserve, GE began Monday what's expected to be a month-long exchange of its 85% stake in Synchrony (SYF) - Get Report , valued at about $21 billion, for its own stock. The Fairfield, Conn.-based company is offering an enticing bargain: $107.50 of Synchrony shares for every $100 of GE stock.

Prior to its initial public offering last summer, Synchrony was GE's consumer credit arm, dating to the Great Depression when the company used it to provide financing for cash-strapped customers shopping for appliances. It has since grown into a $25 billion private label credit-card provider for regional retailers and businesses throughout the U.S.

GE is shedding its stake in the company as CEO Jeffrey Immelt winds down the lucrative lending business, which generated 42% of GE's profit last year, to focus on the company's manufacturing roots. The shift should enable GE to escape tighter federal regulation in the wake of the 2008 financial crisis, and overcome subsequent shareholder concern that weighed on the company's stock price.

By repurchasing and then retiring its own shares, GE expects to slash up to $21 billion of its market capitalization, or roughly 7% of its shares outstanding. The deal will end on Nov. 21.

While a steep discount on Synchrony shares may sound like a bargain, the reduction in GE's share base is a good reason to hold on to GE since the value of the remaining stock will be higher. Nick Heymann, an analyst with William Blair, estimates GE will get a boost of 8 to 9 cents of earnings per share by trimming the number of shares outstanding.

"GE likes to talk about returning capital to shareholders, but the trade will depend on whether you like Synchrony or GE's prospects," he said in a phone interview. "Our belief is that GE's stock could potentially double by 2020."

The exchange will be tax-free for investors, who are being approached through mailed prospectuses from by GE or by their brokers if they invest in managed accounts.

GE stock is also getting a boost from institutional holders and other large investors, like activist Nelson Peltz, who recently announced the acquisition of a 1% stake valued at about $2.5 billion, said William Blair's Heymann.

"As GE moves to accelerate both the pace of its portfolio transformation and the pace at which its fundamentals improve, we sense there is a groundswell building among institutional investors who are now realizing that instead of discussing what it plans to do, GE is completing its transformation much faster than expected," William Blair said in a recent report.

Immelt said on Friday's third-quarter earnings call that, with last week's $30 billion sale of three finance units to Wells Fargo, GE has surpassed its year-end targets for winding down the lending business.

"GE should be the one stock among large-capitalization diversified industrials to own for the rest of this decade," the William Blair report said. The firm maintains an "outperform," or buy, rating on GE and a $32 price target. The shares touched $28.99 on Monday, the highest price this year.

GE still trades 28% below its levels in 2001, when Immelt succeeded longtime CEO Jack Welch just days before the 9/11 attacks. GE, which provided reinsurance on both the World Trade Center and four hijacked jetliners that crashed in the attacks, received nearly $400 million in claims afterward. The stock later declined for several years, then plunged during the 2008 financial crisis.

The true beneficiaries from the exchange may be holders of Synchrony, whose shares leaped 4% Monday as uncertainty ended about what GE would do with its 85% stake in the company, according to Henry Coffee, an analyst with Sterne Agee.

"The exchange offer makes tremendous sense for the Synchrony holder because it opens the stock to a broader investor base," he said in a phone interview.

Immelt's ability so far to meet his targets in the GE overhaul makes the company one of the "best ideas in the industrial sector," according to Barbara Noverini, an analyst with Morningstar.

"Year to date, GE's aggressive unwinding of GE Capital is ahead of schedule, cementing our confidence in management's ability to swiftly execute remaining targets," she wrote in a recent report.