After seeing shares of its spinoff Mead Johnson Nutrition (NYSE:MJN) nearly double since its IPO in February, Bristol-Myers Squibb (NYSE:BMY) has decided now's the time to sell the 83% of the baby formula producer that it still owns.

Who's the sucker that Bristol-Myers is trying to pawn the inflated shares onto? Its own shareholders.

Investors will have an option of exchanging some or all of their Bristol-Myers shares for shares in Mead Johnson for a slight discount -- $1.00 worth of Bristol-Myers will get you $1.11 worth of Mead Johnson. The exact exchange rate will be determined by the price of the companies over three trading days next month, but so far the exchange is looking like a slightly better deal, with Bristol-Myers trading up and Mead Johnson going down since the announcement.

With Mead Johnson sporting a much higher P/E than Bristol-Myers, the exchange will benefit Bristol-Myers' earnings per share next year. Plus, the resulting lower Bristol-Myers share count will decrease the total cash Bristol-Myers currently pays out as dividends, which should make that massive 5.1% yield feel a little safer; free cash flow hasn't quite covered the dividend over the past 12 months.

A private equity firm might have been willing to buy Mead Johnson from Bristol-Myers for a premium, but that would have resulted in a capital gains tax, which would only make Uncle Sam happy. And besides, the company has a pretty decent war chest. After Mead Johnson recently paid back a $1.75 billion loan by refinancing it, Bristol-Myers expects to end the year with more than $10 billion.

It's interesting that while other drugmakers are diversifying away from being strictly drug companies -- Merck (NYSE:MRK) and Pfizer (NYSE:PFE) gained consumer health-care divisions with their recent acquisitions -- Bristol-Myers has divested its non-drug holdings, including Zimmer (NYSE:ZMH) and its medical-imaging and wound-healing businesses.

Bristol-Myers is making an all-in bet on drugs. If it can string together a few blockbusters, perhaps we'll see Bristol-Myers' stock rise 80%. Eventually.

This article represents the opinion of the writer, who may disagree with the “official” recommendation position of a Motley Fool premium advisory service. We’re motley! Questioning an investing thesis -- even one of our own -- helps us all think critically about investing and make decisions that help us become smarter, happier, and richer.