When Chris Coughlin stepped into the CFO role at Tyco International in March 2005, the conglomerate had already put its scandal-scarred history under former CEO Dennis Kozlowski behind it. The new CEO, Ed Breen, had orchestrated the departure of the entire board of directors, replacing them with new members eager to turn things around. Indeed, the company was in the midst of a rebound, with solid earnings, moderate growth, a strong capital structure, and a share price hovering just under $30—up from a low of $8.25 during the crisis several years earlier.

Investors were reassured, but Coughlin was joining a management team pondering the best way to deliver growth to the company’s widely diverse businesses over the longer term. Their conclusion, announced in January 2006, was as bold as it was unexpected: spin off Tyco’s health care business, now called Covidien, the world’s second-biggest maker of disposable-medical products (behind Johnson & Johnson), as well as Tyco Electronics, the world’s largest manufacturer of electronic connectors. Over the following 18 months, Breen and Coughlin extricated overlapping functions, contracts, and procurement agreements, appointed two new senior-management teams, addressed securities regulations, and recruited new boards of directors. The result: parent Tyco International is today...