<PAGE>   1

                                                                      EXHIBIT 24

                               POWER OF ATTORNEY

     KNOW ALL MEN BY THESE PRESENTS, that each person whose signature appears
below constitutes and appoints Timothy J. Schmitt his true and lawful
attorney-in-fact and agent, with full power of substitution and revocation, in
his name and on his behalf, to do any and all acts and things and to execute any
and all instruments which he may deem necessary or advisable to enable Newmont
Gold Company to comply with the Securities Exchange Act of 1934, as amended (the
"Act"), and any rules, regulations or requirements of the Securities and
Exchange Commission in respect thereof, including power and authority to sign
his name in any and all capacities (including his capacity as a Director and/or
Officer of Newmont Gold Company) to the Annual Report on form 10-K of Newmont
Gold Company for the fiscal year ended December 31, 1996 and the undersigned
hereby ratifies and confirms all that said attorney-in-fact and agent shall
lawfully do or cause to be done by virtue hereof.

     IN WITNESS WHEREOF, the undersigned have subscribed these presents as of
the 19th day of March, 1997.

<TABLE>
<CAPTION>
                      SIGNATURE                                            TITLE
                      ---------                                            -----
<C>                                                    <S>

               /s/ RUDOLPH I. J. AGNEW                 Director
-----------------------------------------------------
                 Rudolph I. J. Agnew

                   /s/ J.P. BOLDUC                     Director
-----------------------------------------------------
                     J.P. Bolduc

                /s/ RONALD C. CAMBRE                   Chairman, President and Chief Executive
-----------------------------------------------------  Officer and Director (Principal Executive
                  Ronald C. Cambre                     Officer)

               /s/ JOSEPH P. FLANNERY                  Director
-----------------------------------------------------
                 Joseph P. Flannery

               /s/ LEO I. HIGDON, JR.                  Director
-----------------------------------------------------
                 Leo I. Higdon, Jr.

                /s/ THOMAS A. HOLMES                   Director
-----------------------------------------------------
                  Thomas A. Holmes

                /s/ ROBERT H. QUENON                   Director
-----------------------------------------------------
                  Robert H. Quenon

                /s/ MOEEN A. QURESHI                   Director
-----------------------------------------------------
                  Moeen A. Qureshi

                /s/ MICHAEL K. REILLY                  Director
-----------------------------------------------------
                  Michael K. Reilly

            /s/ WILLIAM I. M. TURNER, JR.              Director
-----------------------------------------------------
              William I. M. Turner, Jr.

                 /s/ WAYNE W. MURDY                    Executive Vice President and Chief Financial
-----------------------------------------------------  Officer (Principal Financial Officer)
                   Wayne W. Murdy

                 /s/ GARY E. FARMAR                    Vice President and Controller (Principal
-----------------------------------------------------  Accounting Officer)
                   Gary E. Farmar
</TABLE>