Exhibit 10.31(a) FIRST AMENDMENT TO THE UCAR INTERNATIONAL INC. BONUS II PLAN ------------------------------------- The UCAR International Inc. Bonus II Plan (the "Plan") is hereby amended as follows: 1. A new Section 16 is hereby added to the Plan to read as follows: "16. Definition of "Bonus" for Retirement Plan. For purposes of determining ----------------------------------------- pensionable compensation under the UCAR Carbon Retirement Plan, "Bonus" shall mean an amount equal to the amount of the Award under this Plan made to a participant multiplied by the percentage by which EBITDA in the applicable Performance Year exceeded EBITDA in the immediately preceding calendar year (including 1994 for the 1995 Performance Year)." 2. This First Amendment shall be effective as of January 1, 1995. UCAR INTERNATIONAL INC. Dated: May 7, 1996 By: /s/ Peter B. Mancino ------------------------ E-4