Shire Plc made an unsolicited offer to buy Baxalta Inc., a business spun off by Baxter International Inc. last month, for about $30 billion in stock to create a biotech company focused on rare diseases.

Shire offered Baxalta shareholders 0.1687 American depositary receipts for each share held, valuing the target company’s stock at $45.23, a 36 percent premium over yesterday’s close, it said in a statement on Tuesday. Baxalta soared 25 percent to $41.35 in early U.S. trading.

Shire Chief Executive Officer Flemming Ornskov has tried to get his counterpart at Baxalta, Ludwig N. Hantson, to enter talks since early July, he said in a letter to Hantson dated Aug. 4. Weeks after receiving a written proposal, Baxalta on July 31 declined to engage in negotiations with Dublin-basedShire. The enlarged company would generate $20 billion in sales by 2020 with as many as 30 new drugs to launch over five years for diseases ranging from dry eye disease to hemophilia, Shire said.

“Your lack of engagement has been surprising,” Ornskov wrote in a letter dated Aug. 4. “As a result, you have left us with no choice but to make our proposal known to your shareholders. We believe they deserve an opportunity to consider it."

Shire said it hadn’t discussed the proposal with Baxter.

Baxalta, based in Deerfield, Illinois, would benefit from a lower tax rate by being taken over by a U.K. company. The U.S. drugmaker had projected a tax rate of 23 percent to 24 percent for the second half of this year. A combination with Shire would yield an effective tax rate of 16 percent to 17 percent, Shire said in its statement.

Together, Shire and Baxalta would be “the leading global biotech company in rare diseases,” according to Ornskov.

Rare-disease treatments have become one of the hottest properties for drugmakers because of the potential for high- priced products and incentives offered by regulators including tax breaks and seven years of market exclusivity. The FDA defines rare diseases as those that affect fewer than 200,000 people in the U.S.

Shire, which is seeking to boost growth after a proposed $52 billion sale to AbbVie Inc. collapsed last year, expanded its portfolio of rare-disease treatments in February with the purchase of NPS Pharmaceuticals Inc., gaining medicines for short bowel syndrome. Baxalta derives about about half of its sales from hemophilia, a rare bleeding disorder.

“From a rare disease point of view, it does seem to make sense,” said Klara Fernandes, an analyst at Berenberg Bank in London.

Evercore Partners Inc. and Morgan Stanley are advising Shire and Ropes & Gray LLP along with Slaughter & May are acting as legal counsel.

Shire shares fell as much as 7.9 percent before trading down 3.1 percent to 5,550 pence as of 1:33 p.m. in London. The stock had climbed 17 percent in the past year.

The company is registered in Jersey, in the Channel Islands, and based for tax purposes in Ireland. Its primary stock listing is in the U.K., while Ornskov and most other top executives are based in Lexington, Massachusetts.

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