Ford Motor Co., in an effort to shore up its balance sheet, is attempting to eliminate some $10.4 billion in debt by offering cash and stock to debt holders.

Under terms of the plan, which was filed yesterday with the U.S. Securities and Exchange Commission, Ford will offer a cash premium to induce debt holders to exchange up to $4.9 billion in convertible notes issued in 2006.

To facilitate the plan, Ford and its captive finance arm, Ford Motor Credit Co., will put up $2.2 billion in cash, as well as 500 million shares.

The move has the potential to eliminate up to one-third of Ford’s outstanding debt and place it on even footing with cross-town rivals General Motors Corp. and Chrysler LLC, which are attempting to swap debt for equity under the conditions of their government-backed loans.