Reaping the benefits of tax inversion isn't as straightforward as many think.

Through its $42.9 billion merger with Covidien, Medtronic will gain an Irish address, a lower overall tax rate and more overseas cash to spend in America without paying US taxes. But at least initially, the new cash flow will come only from surgical tools and hospital supplies maker Covidien, whose overseas profits have always rested outside the US tax net, Medtronic said.