GOODRICH B F CO
S-3/A, 1999-04-07
GUIDED MISSILES & SPACE VEHICLES & PARTS
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<PAGE>   1
 
   
     AS FILED WITH THE SECURITIES AND EXCHANGE COMMISSION ON APRIL 7, 1999
    
   
                                                      REGISTRATION NO. 333-74987
    
- --------------------------------------------------------------------------------
- --------------------------------------------------------------------------------
 
                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549
                           -------------------------
   
                                AMENDMENT NO. 1
    
                                       TO
 
                                    FORM S-3
                           -------------------------
                             REGISTRATION STATEMENT
                                     UNDER
                           THE SECURITIES ACT OF 1933
                           -------------------------
 
                            THE B.F.GOODRICH COMPANY
             (EXACT NAME OF REGISTRANT AS SPECIFIED IN ITS CHARTER)
 
<TABLE>
<S>                                      <C>                                      <C>
                NEW YORK                        4020 KINROSS LAKES PARKWAY                       34-0252680
    (STATE OR OTHER JURISDICTION OF             RICHFIELD, OHIO 44286-9368                    (I.R.S. EMPLOYER
     INCORPORATION OR ORGANIZATION)                   (330) 659-7600                       IDENTIFICATION NUMBER)
</TABLE>
 
         (ADDRESS, INCLUDING ZIP CODE, AND TELEPHONE NUMBER, INCLUDING
            AREA CODE, OF REGISTRANT'S PRINCIPAL EXECUTIVE OFFICES)
                           -------------------------
 
                               NICHOLAS J. CALISE
                                   SECRETARY
                            THE B.F.GOODRICH COMPANY
                           4020 KINROSS LAKES PARKWAY
                           RICHFIELD, OHIO 44286-9368
                                 (330) 659-7600
 (NAME, ADDRESS, INCLUDING ZIP CODE, AND TELEPHONE NUMBER, INCLUDING AREA CODE,
                             OF AGENT FOR SERVICE)
                           -------------------------
                                   COPIES TO:
 
                             DYNDA A. THOMAS, ESQ.
                        SQUIRE, SANDERS & DEMPSEY L.L.P.
                                 4900 KEY TOWER
                               127 PUBLIC SQUARE
                           CLEVELAND, OHIO 44114-1304
                                 (216) 479-8500
                           -------------------------
        APPROXIMATE DATE OF COMMENCEMENT OF PROPOSED SALE TO THE PUBLIC:
     From time to time after this registration statement becomes effective.
 
     If the only securities being registered on this form are being offered
pursuant to dividend or interest reinvestment plans, please check the following
box. [ ]
 
     If any of the securities being registered on this form are to be offered on
a delayed or continuous basis pursuant to Rule 415 under the Securities Act of
1933, other than securities offered only in connection with dividend or interest
reinvestment plans, check the following box. [X]
 
     If this form is filed to register additional securities for an offering
pursuant to Rule 462(b) under the Securities Act, please check the following box
and list the Securities Act registration statement number of the earlier
effective registration statement for the same offering. [ ]
 
     If this form is a post-effective amendment filed pursuant to Rule 462(c)
under the Securities Act, check the following box and list the Securities Act
registration statement number of the earlier effective registration statement
for the same offering. [ ]
 
     If delivery of the prospectus is expected to be made pursuant to Rule 434,
please check the following box. [ ]
                           -------------------------
     THE REGISTRANT HEREBY AMENDS THIS REGISTRATION STATEMENT ON SUCH DATE OR
DATES AS MAY BE NECESSARY TO DELAY ITS EFFECTIVE DATE UNTIL THE REGISTRANT SHALL
FILE A FURTHER AMENDMENT WHICH SPECIFICALLY STATES THAT THIS REGISTRATION
STATEMENT SHALL THEREAFTER BECOME EFFECTIVE IN ACCORDANCE WITH SECTION 8(a) OF
THE SECURITIES ACT OF 1933 OR UNTIL THE REGISTRATION STATEMENT SHALL BECOME
EFFECTIVE ON SUCH DATE AS THE COMMISSION, ACTING PURSUANT TO SAID SECTION 8(a),
MAY DETERMINE.
- --------------------------------------------------------------------------------
- --------------------------------------------------------------------------------
<PAGE>   2
 
                             ADDITIONAL INFORMATION
 
     This registration statement incorporates important business and financial
information about BFGoodrich that is not included in or delivered with this
document. This information is available without charge to shareholders upon
written or oral request. Shareholders may obtain information about BFGoodrich by
request to the following address or telephone number:
 
                         Nicholas J. Calise, Secretary
                            The B.F.Goodrich Company
                           4020 Kinross Lakes Parkway
                           Richfield, Ohio 44286-9368
                                 (330) 659-7600
 
     See "Where You Can Find More Information" on page 15.
<PAGE>   3
 
                             SUBJECT TO COMPLETION
 
   
                  PRELIMINARY PROSPECTUS, DATED APRIL 7, 1999
    
 
                            THE B.F.GOODRICH COMPANY
 
                    COMMON STOCK TO BE ISSUED ON CONVERSION
                     OF CONVERTIBLE PREFERRED SECURITIES OF
                              COLTEC CAPITAL TRUST
 
                            GUARANTEE OF OBLIGATIONS
              RELATING TO 5 1/4% CONVERTIBLE PREFERRED SECURITIES
   
             TERM INCOME DEFERRABLE EQUITY SECURITIES (TIDES)(SM*)
    
                            OF COLTEC CAPITAL TRUST
 
   
     On November 22, 1998, we and Coltec Industries agreed to merge Coltec
Industries with a subsidiary of BFGoodrich. When the merger is completed, Coltec
Industries will be a direct wholly owned subsidiary of BFGoodrich, and Coltec
Capital Trust will be an indirect wholly owned subsidiary of BFGoodrich. If we
complete our merger with Coltec Industries, then, starting on the date of the
merger:
    
 
   
     - you will have the right to convert your convertible preferred securities
       into BFGoodrich common stock instead of Coltec Industries common stock;
       and
    
 
   
     - you will have the benefit of BFGoodrich's guarantee of obligations
       relating to your convertible preferred securities.
    
 
   
We have described these rights and benefits in this prospectus. HOWEVER, UNLESS
AND UNTIL WE COMPLETE OUR MERGER WITH COLTEC INDUSTRIES, YOU WILL NOT HAVE THE
RIGHT TO CONVERT YOUR CONVERTIBLE PREFERRED SECURITIES INTO BFGOODRICH COMMON
STOCK, AND YOU WILL NOT HAVE THE BENEFIT OF OUR GUARANTEE.
    
 
   
     This prospectus relates to shares of BFGoodrich common stock that we will
issue from time to time to you, as holders of convertible preferred securities
that Coltec Capital Trust issued on April 8, 1998, if you convert your
convertible preferred securities after we complete our merger. The proper name
for those convertible preferred securities is 5 1/4% Convertible Preferred
Securities, Term Income Deferrable Equity Securities (TIDES)(SM). They have a
liquidation amount of $50 per convertible preferred security. Coltec Capital
Trust is a wholly owned subsidiary of Coltec Industries Inc. As a holder of
convertible preferred securities, your securities are currently convertible into
shares of common stock of Coltec Industries. After we complete our merger with
Coltec Industries, Coltec Industries will be our wholly owned subsidiary, and
your convertible preferred securities will be convertible into BFGoodrich common
stock. We have described our merger with Coltec Industries beginning on page 5
of this prospectus.
    
 
     This prospectus also relates to our guarantee of the obligations of Coltec
Capital Trust and Coltec Industries relating to your convertible preferred
securities. As we describe in more detail beginning on page 7 of this
prospectus, after we complete our merger with Coltec Industries, we will fully
and unconditionally agree to pay, to the extent not paid by Coltec Capital
Trust:
 
     - distributions on your convertible preferred securities to the extent that
       Coltec Capital Trust has funds available;
 
     - the amount payable upon the redemption of your convertible preferred
       securities to the extent that Coltec Capital Trust has funds available;
       and
 
     - amounts due upon a termination, dissolution or liquidation of Coltec
       Capital Trust to the extent that Coltec Capital Trust has funds
       available.
 
- ---------------
 
    * The terms Term Income Deferrable Equity Securities (TIDES)(SM) and
      TIDES(SM) are registered servicemarks of Credit Suisse First Boston
      Corporation.
<PAGE>   4
 
In addition, we will agree to pay or perform Coltec Industries' obligations
under:
 
   
     - Coltec's Industries' existing guarantee relating to your convertible
       preferred securities to the extent not paid or performed by Coltec
       Industries;
    
 
   
     - the indenture governing Coltec Industries' convertible junior
       subordinated debentures to the extent not paid or performed by Coltec
       Industries;
    
 
   
     - the convertible junior subordinated debentures; and
    
 
   
     - the declaration of trust pursuant to which Coltec Capital Trust is
       organized.
    
 
Our obligations under our guarantee will be subordinated to our senior debt that
is currently outstanding or that we may incur in the future.
 
     On May 19, 1998, Coltec Industries and Coltec Capital Trust filed a
registration statement on Form S-3 to register resales of your convertible
preferred securities and the related Coltec Industries guarantee. Coltec
Industries has also filed prospectus supplements to provide information about
selling holders of the convertible preferred securities.
 
     You may, from time to time, decide to sell your convertible preferred
securities. If you sell your convertible preferred securities, you will also
sell your rights under the related guarantees by Coltec Industries and
BFGoodrich as well as the right to convert your convertible preferred securities
into shares of common stock of BFGoodrich. Therefore, to sell your convertible
preferred securities, you will need to use:
 
     - a current prospectus supplement and prospectus relating to your
       convertible preferred securities; and
 
     - this prospectus, which relates to our guarantee and the BFGoodrich common
       stock into which you may convert your convertible preferred securities.
 
If you transfer your convertible preferred securities without using these
documents, the purchaser must use a current prospectus supplement and prospectus
of Coltec Industries and Coltec Capital Trust and this prospectus and a current
prospectus supplement of BFGoodrich to sell their convertible preferred
securities.
 
     After the merger, you will have the right to convert each convertible
preferred security you own into 0.955248 of a share of BFGoodrich common stock.
However, that conversion ratio could change. We have described the possible
adjustment to the conversion ratio in "Impact of the Merger on Your Convertible
Preferred Securities -- Conversion of Your Convertible Preferred Securities Into
Our Common Stock" beginning on page 6 of this prospectus.
 
     You can choose to convert your convertible preferred securities into shares
of BFGoodrich common stock at any time after we complete our merger with Coltec
Industries. We are offering the shares of BFGoodrich common stock from time to
time as permitted by Rule 415 under the Securities Act of 1933 while the
registration statement relating to this prospectus is effective.
 
     You will receive all of the proceeds from the sale of your convertible
preferred securities, and you will pay all underwriting discounts and selling
commissions, if any, that relate to your sale of your convertible preferred
securities. Coltec Industries will pay all other expenses that relate to the
offer and sale of your convertible preferred securities.
 
   
     BFGoodrich common stock is traded on the New York Stock Exchange under the
symbol "GR." On April 6, 1999, the closing price of BFGoodrich common stock, as
reported on the New York Stock Exchange, was $34.25 per share.
    
 
     INVESTING IN OUR SHARES OF COMMON STOCK INVOLVES RISKS SUCH AS THOSE
DESCRIBED UNDER "RISK FACTORS" BEGINNING ON PAGE 1 OF THIS PROSPECTUS.
 
     NEITHER THE SECURITIES AND EXCHANGE COMMISSION NOR ANY STATE SECURITIES
COMMISSION HAS APPROVED OR DISAPPROVED OF THESE SECURITIES OR DETERMINED IF THIS
PROSPECTUS IS TRUTHFUL OR COMPLETE. ANYONE WHO MAKES ANY REPRESENTATION TO THE
CONTRARY COMMITS A CRIMINAL OFFENSE.
 
                 The date of this prospectus is April   , 1999.
<PAGE>   5
 
THE INFORMATION IN THIS PROSPECTUS IS NOT COMPLETE AND MAY BE CHANGED. WE MAY
NOT SELL THESE SECURITIES UNTIL THE REGISTRATION STATEMENT FILED WITH THE
SECURITIES AND EXCHANGE COMMISSION IS EFFECTIVE. THIS PROSPECTUS IS NOT AN OFFER
TO SELL THESE SECURITIES AND IT IS NOT SOLICITING AN OFFER TO BUY THESE
SECURITIES IN ANY STATE WHERE THE OFFER OR SALE IS NOT PERMITTED.
<PAGE>   6
 
                                  RISK FACTORS
 
     Investing in shares of BFGoodrich common stock involves risks. Because you
could lose the entire value of your investment, you should carefully consider
the following risks before deciding to convert your convertible preferred
securities of Coltec Capital Trust into BFGoodrich common stock.
 
WE MAY NOT BE ABLE TO ACHIEVE THE EXPECTED INTEGRATION AND COST SAVINGS FROM THE
MERGER AND THAT FAILURE COULD ADVERSELY AFFECT OUR EARNINGS AND FINANCIAL
CONDITION.
 
     We expect to achieve cost savings from our merger with Coltec Industries.
By the year 2001, we believe the cost savings could be $60 million per year.
Difficulties may arise, however, in the integration of the business and
operation of the combined entity. As a result, we may not be able to achieve the
cost savings and synergies that we expect will result from the merger. Achieving
cost savings is dependent on consolidating our corporate and aerospace staffs
with Coltec Industries' corporate staff in Charlotte, North Carolina and
achieving other synergies in combining our two organizations. Additional
operational savings are dependent upon the integration of our aerospace business
and Coltec Industries' aerospace business and the elimination of duplicate
facilities and excess capacity. Actual savings in 1999 may be materially less
than expected if the merger is delayed beyond April 30, 1999, if the
reorganization of both companies' staffs is delayed beyond what we anticipate or
if the reductions in personnel are less than we currently envision. We expect
material cost savings from the reduction in personnel.
 
WE MAY HAVE LIABILITIES RELATED TO ASBESTOS LITIGATION WHICH COULD ADVERSELY
AFFECT OUR EARNINGS AND FINANCIAL CONDITION.
 
     The historical business operations of Coltec Industries have resulted in a
substantial volume of asbestos litigation. Plaintiffs in these matters have
alleged personal injury or death as a result of exposure to asbestos contained
in some products that were manufactured or distributed by two of Coltec
Industries' subsidiaries. We believe that the funding agreements with our
insurance carriers will provide resources sufficient to meet the vast majority
of the currently anticipated costs and expenses associated with known and
pending litigation. It is difficult to predict the number of asbestos lawsuits
that Coltec Industries' subsidiaries will be parties to in the future. These
future claims and insurance and other related costs may result in future
liabilities that are significant and may be material. For additional information
regarding Coltec Industries' involvement in asbestos litigation, you should read
Coltec Industries' December 31, 1998 financial statements which are incorporated
by reference into this prospectus.
 
WE MAY HAVE LIABILITIES RELATED TO ENVIRONMENTAL LAWS AND REGULATIONS WHICH
COULD ADVERSELY AFFECT OUR EARNINGS AND FINANCIAL CONDITION.
 
     We and Coltec Industries are generators of both hazardous and non-hazardous
wastes. The treatment, storage, transportation and disposal of these hazardous
and non-hazardous wastes are governed by various environmental laws and
regulations. We have been notified that we and Coltec Industries have been
designated as potentially responsible parties by the U.S. Environmental
Protection Agency for the costs of investigating and, in some cases, remediating
contamination by hazardous materials at several sites, most of which related to
businesses previously discontinued. Liability for these costs may be imposed on
present and former owners or operators of the properties or on parties who
generated the wastes that contributed to the contamination. For additional
information regarding potential environmental liability for both us and Coltec
Industries, you should read BFGoodrich's December 31, 1998 financial statements
<PAGE>   7
 
and Coltec Industries' December 31, 1998 financial statements which are
incorporated by reference into this prospectus.
 
OUR MARKET SEGMENTS HAD WEAK STOCK MARKET PERFORMANCE IN 1998.
 
     In 1998, we operated in two business segments -- aerospace and performance
materials. During 1998, total return to shareholders in these segments was less
than broad based stock market indices. For example, the Standard & Poor's 500
index had a total return to shareholders in 1998 of 28.58% while the Standard &
Poor's aerospace/defense index had a return of negative 23.34% and the Standard
& Poor's specialty chemical index had a return of negative 14.84%. We had a
return of negative 11.06% during 1998. Total return to shareholders consists of
change in stock price and assumes dividends are reinvested in additional shares
of stock of the company paying the dividend.
 
THE MARKET PRICE OF BFGOODRICH COMMON STOCK IS VOLATILE AND THE VALUE OF
BFGOODRICH COMMON STOCK COULD DECREASE.
 
     The market price of BFGoodrich common stock has fluctuated widely over the
past twelve months and may continue to do so. Many factors could cause the
market price of our common stock to rise and fall. Some of these factors are:
 
     - variations in our quarterly operating results;
 
     - announcements of technological innovations;
 
     - introduction of new products or new pricing policies by us or our
       competitors;
 
     - trends in the aerospace industry;
 
     - acquisitions or strategic alliances by us or others in the aerospace
       industry;
 
     - the hiring or departure of key personnel;
 
     - changes in accounting principles;
 
     - changes in estimates of our performance or recommendations by financial
       analysts; and
 
     - market conditions in the industry and economy as a whole.
 
     In addition, the stock market has recently experienced extreme price and
volume fluctuations. These fluctuations have particularly affected the market
prices of the securities of many aerospace companies. These broad market
fluctuations could adversely affect the market price of BFGoodrich common stock.
If the market price of BFGoodrich's common stock decreases, the value of the
BFGoodrich common stock you convert into would decrease and the value of your
convertible preferred securities may decrease.
 
THE CYCLICAL NATURE OF OUR BUSINESS COULD ADVERSELY AFFECT OUR EARNINGS AND
FINANCIAL CONDITION.
 
     The business sectors to which we sell our product are, to varying degrees,
cyclical and have historically experienced periodic downturns. These downturns
have often had a negative effect on demand for our products resulting in lower
net sales, gross margin and net income. Any future material weakness in demand
in any of these business sectors could have a material adverse effect on our
earnings and financial condition. In addition, some of our competitors have
greater financial resources than we do and may be better able to withstand the
effects of those periodic downturns.
 
                                        2
<PAGE>   8
 
THE DOWNTURN IN ASIA COULD CONTINUE TO ADVERSELY AFFECT OUR EARNINGS AND
FINANCIAL CONDITION.
 
     The current economic downturn in some Asian countries has adversely
affected and could continue to adversely affect the worldwide aerospace
industry. According to industry analysts, as a result of the recession in Japan,
as well as currency fluctuations and other problems in other Asian countries,
Asian airlines have slowed purchases of new aircraft. The reduction in demand
for new aircraft has led and could continue to lead aircraft manufacturers to
build fewer aircraft than they might otherwise have built. As a result, we have
experienced and could continue to experience delays or cancellations of orders
for our products for aircraft. Those delays or cancellations could seriously
harm our earnings and financial condition.
 
OUR DEPENDENCE UPON CURRENT CONDITIONS IN THE AIRLINE INDUSTRY COULD ADVERSELY
AFFECT OUR EARNINGS AND FINANCIAL CONDITION.
 
     The airline industry is undergoing a process of consolidation and
significantly increased competition. This consolidation could result in a
reduction of future aircraft orders as overlapping routes are eliminated and
airlines seek greater economies through higher aircraft utilization. Increased
airline competition may also result in airlines seeking to reduce costs by
promoting greater price competition from aerospace suppliers, which could
adversely affect our earnings and financial condition.
 
THE FINANCIAL RESULTS OF THE PERFORMANCE MATERIALS SEGMENT COULD BE ADVERSELY
AFFECTED IF GROWTH IN DEMAND FOR PERFORMANCE MATERIALS DOES NOT OCCUR OR COST
REDUCTIONS ARE NOT ACHIEVED AS WE EXPECT.
 
     Our financial results could be adversely affected if the expected growth in
volume demand for performance materials does not occur as we expect. Recent
turmoil in the financial markets in the Far East and Latin America could
adversely impact sales increases in those regions. Our financial results could
also be adversely affected if we do not achieve cost reduction benefits as we
integrate recent acquisitions and continue the realignment activities of
BFGoodrich and Coltec Industries.
 
COMPUTER SYSTEM FAILURES OR MISCALCULATIONS RESULTING FROM AN INABILITY TO
INTERPRET DATES BEYOND 1999 COULD MATERIALLY AND ADVERSELY AFFECT OUR
OPERATIONS.
 
     Any computer equipment that uses two digits instead of four to specify the
year will be unable to interpret dates beyond the year 1999. This "year 2000"
issue could result in system failures or miscalculations causing disruptions of
operations. The three major areas that could be affected critically are
financial and operating systems, manufacturing systems and equipment, and
third-party relationships with suppliers and customers. We have developed plans
to address this exposure.
 
                                        3
<PAGE>   9
 
     The three critical areas affected and our accomplishments to date are shown
below:
 
<TABLE>
<CAPTION>
                AREA                             ACCOMPLISHED TO DATE
                ----                             --------------------
<S>                                      <C>
Financial and operating systems          - Systems assessed
                                         - Detailed plans have been or
                                           continue to be developed
                                         - Conversion commenced
Manufacturing systems and equipment      - Systems assessed
                                         - Detailed plans have been or
                                           continue to be developed
                                         - Conversion commenced
Third-party relationship with            - Communicating with critical
  suppliers and customers                  suppliers and customers to
                                           ascertain whether they are
                                           addressing potential year 2000
                                           issues
</TABLE>
 
     Although we cannot give you any assurance, we believe that our internal
systems will be year 2000 compliant. The failure of major suppliers and
customers to achieve year 2000 compliance could materially and adversely affect
our results of operations.
 
OUR OBLIGATIONS UNDER THE GUARANTEE WILL BE SUBORDINATE TO ALL OUR SENIOR DEBT.
 
     Our obligations under the guarantee will be general unsecured obligations
which will be subordinated to our senior debt that is currently outstanding or
that we may incur in the future. Neither the terms of Coltec Industries'
convertible junior subordinated debentures, Coltec Industries' existing
guarantee, nor our guarantee will limit the amount of senior debt we may incur.
 
YOU MAY HAVE TO PAY TAXES WHEN YOU CONVERT YOUR CONVERTIBLE PREFERRED SECURITIES
INTO BFGOODRICH COMMON STOCK.
 
     If you convert your convertible preferred securities for shares of
BFGoodrich common stock, you may be required to pay tax on any gain you have
under the laws of the U.S. We strongly urge you to consult with your tax advisor
with respect to the tax consequences of the conversion of your convertible
preferred securities for shares of BFGoodrich's common stock. See "U.S. Income
Tax Considerations" on page 12 of this prospectus. Your tax consequences can
vary depending on:
 
     - where you are a resident for tax purposes; and
 
     - how long you have held your convertible preferred securities.
 
CAUTIONARY STATEMENT CONCERNING FORWARD-LOOKING STATEMENTS
 
     This document, and the documents that have been incorporated by reference,
includes statements that reflect projections or expectations of future financial
condition, results of operations and business of each of BFGoodrich and Coltec
Industries that are subject to risk and uncertainty. We believe those statements
to be "forward-looking" statements within the meaning of Section 27A of the
Securities Act of 1933 and Section 21E of the Securities Exchange Act of 1934.
 
     We cannot guarantee that actual results or events will not differ
materially from those projected, estimated, assigned or anticipated in any of
the forward-looking statements contained in this prospectus or in the documents
incorporated by reference. In addition to those factors
 
                                        4
<PAGE>   10
 
specifically noted in the forward-looking statements, other important factors
that could result in those differences include:
 
     - general economic conditions in the applicable markets, including
       inflation, recession, interest rates and other economic factors;
 
     - casualty to or other disruption of our facilities and operations; and
 
     - other factors that generally affect the business of aerospace and other
       industrial companies.
 
     We caution our shareholders not to place undue reliance on these
statements, which speak only as of the date of this prospectus or, in the case
of any document incorporated by reference, the date of that document.
 
     Whenever you read or hear any subsequent written or oral forward-looking
statements attributable to us or any person acting on our behalf, you should
keep in mind the cautionary statements contained or referred to in this section.
We do not undertake any obligation to release publicly any revisions to these
forward-looking statements to reflect events or circumstances after the date of
this prospectus or to reflect the occurrence of unanticipated events.
 
                  MERGER OF COLTEC INDUSTRIES WITH BFGOODRICH
 
     On November 22, 1998, we and Coltec Industries agreed to merge Coltec
Industries with Runway Acquisition Corporation, our wholly owned subsidiary.
When we complete the merger, Coltec Industries will be a direct wholly owned
subsidiary of BFGoodrich, and Coltec Capital Trust will be an indirect wholly
owned subsidiary of BFGoodrich. We expect that the merger will be accounted for
as a pooling of interests, which means that we will treat BFGoodrich and Coltec
Industries as if they had always been one company for accounting and financial
reporting purposes.
 
ABOUT BFGOODRICH
 
     We manufacture and supply a wide variety of systems and component parts for
the aerospace industry and provide maintenance, repair and overhaul services on
commercial, regional, business and general aviation aircraft. We also
manufacture specialty plastics and specialty additives products for a variety of
end-user applications. In 1998, we had sales of $4.0 billion. We are organized
into two principal business segments: aerospace and performance materials. We
maintain patent and technical assistance agreements, licenses and trademarks on
our products, process technologies and expertise in most of the countries in
which we operate. In 1998, we conducted our business through numerous divisions
and 98 wholly- and majority-owned subsidiaries worldwide.
 
     Our principal executive offices are located at 4020 Kinross Lakes Parkway,
Richfield, Ohio 44286-9368. Our telephone number is (330) 659-7600.
 
ABOUT COLTEC INDUSTRIES
 
     Coltec Industries manufactures and sells a diversified range of highly
engineered aerospace and industrial products, primarily in the U.S., Canada and
Europe. In 1998, Coltec Industries had sales of $1.5 billion. Coltec Industries
conducts its operations through its two principal segments: aerospace and
industrial. Through its aerospace segment, Coltec Industries manufactures
landing gear systems, engine fuel controls, flight attendant and cockpit seats,
turbine blades, fuel injectors, nozzles and related components for commercial
and military aircraft. Through its industrial segment, Coltec Industries
manufactures industrial seals, gaskets, packing



                                        5
<PAGE>   11
 
products, self-lubricating bearings and oil seals and hubodometers for trucks
and trailers and produces technologically advanced spray nozzles for
agricultural, home heating and industrial applications. Coltec Industries also
produces high-horsepower diesel engines for naval ships and diesel, gas and
dual-fuel engines for electric power plants and produces air compressors and
tooling for industrial applications.
 
                     YOUR CONVERTIBLE PREFERRED SECURITIES
 
     The following description of your convertible preferred securities is a
summary and should not be viewed as a substitute for the prospectus relating to
those securities that Coltec Capital Trust issued. Coltec Capital Trust and
Coltec Industries filed the registration statement that included that prospectus
with the Securities and Exchange Commission. We are incorporating by reference
that registration statement and its exhibits for purposes of this prospectus and
for purposes of the registration statement to which this prospectus relates.
 
     Your convertible preferred securities represent preferred ownership
interests in the assets of Coltec Capital Trust, a statutory business trust
formed under the laws of the State of Delaware. Coltec Industries owns all of
the common securities of Coltec Capital Trust. Coltec Capital Trust exists only
for purposes of issuing common and convertible preferred securities, and using
the proceeds from those issuances to purchase from Coltec Industries its 5 1/4%
convertible subordinated deferrable interest debentures due 2028. As a holder of
convertible preferred securities, you are entitled to receive quarterly cash
distributions from Coltec Capital Trust at an annual rate of 5 1/4% of the
liquidation preference of $50 per convertible preferred security. Those
distributions accrue from April 14, 1998 and are payable on January 15, April
15, July 15 and October 15 of each year until they are paid in full. Coltec
Capital Trust can elect to defer those quarterly distributions but must continue
to accumulate them and accrue interest on those cumulated distributions.
 
     When Coltec Capital Trust issued your convertible preferred securities,
Coltec Industries agreed fully and unconditionally to pay, to the extent not
paid by Coltec Capital Trust:
 
          - distributions on your convertible preferred securities to the extent
            that Coltec Capital Trust has funds available;
 
          - the amounts payable upon redemption of your convertible preferred
            securities to the extent that Coltec Capital Trust has funds
            available; and
 
          - amounts due upon a termination, dissolution or liquidation of Coltec
            Capital Trust to the extent that Coltec Capital Trust has funds
            available.
 
     Coltec Industries' obligations under the guarantee are unsecured and
subordinate to all senior debt of Coltec Industries that is currently
outstanding or that Coltec Industries may incur in the future. The terms of
Coltec Industries' guarantee are more fully described in the registration
statement on Form S-3 that Coltec Capital Trust and Coltec Industries filed with
the Securities and Exchange Commission.
 
                          IMPACT OF THE MERGER ON YOUR
                        CONVERTIBLE PREFERRED SECURITIES
 
CONVERSION OF YOUR CONVERTIBLE PREFERRED SECURITIES INTO BFGOODRICH COMMON STOCK
 
     The registration statement on Form S-3 that Coltec Capital Trust and Coltec
Industries filed with the Securities and Exchange Commission describes the terms
of your convertible preferred
 
                                        6
<PAGE>   12
 
securities and the related Coltec Industries guarantee. It also describes the
conditions under which you may convert your convertible preferred securities
into common stock. The terms and conditions of your convertible preferred
securities are unchanged except as described in this prospectus. You should
refer to the prospectus relating to your convertible preferred securities for
information on the terms and conditions that govern the conversion of your
convertible preferred securities. We are incorporating by reference the
registration statement that included that prospectus and its exhibits for
purposes of this prospectus and for purposes of the registration statement to
which this prospectus relates.
 
     Section 13.04 of the indenture relating to your convertible preferred
securities provides that if Coltec Industries merges with any other person and
Coltec Industries' common stock is converted into the right to receive other
securities, then you will have the right to convert your convertible preferred
securities into the same number of securities that you would have received had
you converted your convertible preferred securities immediately before that
transaction.
 
     In our merger with Coltec Industries, each outstanding share of Coltec
Industries common stock will be converted into 0.56 of a share of BFGoodrich
common stock. After the merger, you will have the right to convert each
convertible preferred security you own into 0.955248 of a share of BFGoodrich
common stock. We determined this conversion ratio by multiplying 1.7058 by 0.56.
The number 1.7058 is the number of shares of Coltec Industries common stock into
which each convertible preferred security is currently convertible under the
indenture relating to your convertible preferred securities. However, if we take
any action that reduces the value of your convertible preferred securities
relative to our other equity securities, then that conversion ratio will be
adjusted according to the terms of the indenture relating to your convertible
preferred securities.
 
BFGOODRICH GUARANTEE
 
     When Coltec Capital Trust issued your convertible preferred securities,
Coltec Industries provided a guarantee of Coltec Capital Trust's obligations
relating to your convertible preferred securities. We describe that Coltec
Industries guarantee in "Your Convertible Preferred Securities" beginning on
page 6 of this prospectus.
 
     When we complete the merger with Coltec Industries, we will sign a
guarantee agreement. With that guarantee agreement, we will fully and
unconditionally agree to pay, to the extent not paid by Coltec Capital Trust:
 
     - distributions on your convertible preferred securities to the extent that
       Coltec Capital Trust has funds available;
 
     - the amount payable upon the redemption of your convertible preferred
       securities to the extent that Coltec Capital Trust has funds available;
       and
 
     - amounts due upon a termination, dissolution or liquidation of Coltec
       Capital Trust to the extent that Coltec Capital Trust has funds
       available.
 
In addition, BFGoodrich will agree to pay or perform Coltec Industries'
obligations under:
 
   
     - Coltec Industries' existing guarantee relating to your convertible
       preferred securities to the extent not paid or performed by Coltec
       Industries;
    
 
   
     - the indenture governing Coltec Industries' convertible junior
       subordinated debentures to the extent not paid or performed by Coltec
       Industries;
    
 
   
     - the convertible junior subordinated debentures; and
    
 
   
     - the declaration of trust pursuant to which Coltec Capital Trust is
       organized.
    
 
                                        7
<PAGE>   13
 
     Our obligation under our guarantee will be subordinated to our senior debt
that is currently outstanding or that we may incur in the future. Our guarantee
does not guarantee payment of distributions or amounts payable on redemption or
liquidation of your convertible preferred securities if Coltec Capital Trust
does not have funds to make those payments.
 
     We have filed a form of our guarantee as an exhibit to the registration
statement of which this prospectus is a part. We have not and will not receive
any consideration for our guarantee. The Coltec Industries' existing guarantee
described beginning on page 6 of this prospectus will not be affected by the
merger and will remain in place.
 
     If Coltec Industries does not make interest payments on its convertible
junior subordinated debentures, Coltec Capital Trust will not have sufficient
funds to pay distributions on your convertible preferred securities. Our
guarantee, like the Coltec Industries guarantee, will not cover Coltec Capital
Trust's payment of distributions if Coltec Capital Trust does not have
sufficient funds to pay those distributions. In that event, your remedy would be
to require the property trustee to enforce its rights under the indenture
relating to the convertible junior subordinated debentures.
 
     Our obligations under our guarantee will be subordinated in right of
payment to all our senior debt that is currently outstanding or that we may
incur in the future. As of December 31, 1998, our aggregate outstanding senior
debt was approximately $1.07 billion, and as of February 26, 1999, our aggregate
outstanding senior debt was approximately $1.10 billion. Neither the terms of
the convertible junior subordinated debentures, Coltec Industries' guarantee,
nor our guarantee will limit the amount of senior debt that we may incur.
 
     Our obligations under the guarantee of the obligations of Coltec Capital
Trust and Coltec Industries will rank equal in right of payment to our
obligations to pay under agreements we made when one of our subsidiaries issued
preferred securities similar to your convertible preferred securities.
 
SUPPLEMENTAL INDENTURE
 
     As soon as we complete our merger with Coltec Industries, Coltec Industries
will enter into a supplement to the indenture relating to Coltec Industries'
convertible junior subordinated debentures to indicate specifically that the
Coltec Industries' convertible junior subordinated debentures will thereafter be
convertible into shares of BFGoodrich common stock instead of shares of Coltec
Industries' common stock. The terms of the indenture relating to Coltec
Industries' convertible junior subordinated debentures permit Coltec Industries
to enter into that supplemental indenture without the consent of the holders of
those debentures.
 
                                USE OF PROCEEDS
 
     Coltec Capital Trust received approximately $145.9 million in net proceeds
when it issued your convertible preferred securities. We will issue the shares
of BFGoodrich common stock offered by this prospectus when you convert your
convertible preferred securities. We will not receive any net cash proceeds when
we issue these shares of BFGoodrich common stock.
 
                        OUR TRANSFER AGENT AND REGISTRAR
 
     The transfer agent and registrar for BFGoodrich common stock is The Bank of
New York.
 
                                        8
<PAGE>   14
 
                YOUR ABILITY TO SELL YOUR CONVERTIBLE PREFERRED
                   SECURITIES OR THE BFGOODRICH COMMON STOCK
 
     As used in this prospectus, we intend the words you and your to apply to:
 
     - the record holders of your convertible preferred securities listed in
       this prospectus;
 
     - the beneficial owners of convertible preferred securities;
 
     - each of your transferees, pledgees, donees or other successors; and
 
     - the transferees, pledgees, donees or other successors of the beneficial
       owners.
 
     On April 14, 1998, Coltec Capital Trust issued your convertible preferred
securities to Credit Suisse First Boston Corporation, Lehman Brothers Inc. and
CIBC Oppenheimer Corp. Immediately after that, those original purchasers sold
your convertible preferred securities in a transaction that was exempt from the
registration requirements of the Securities Act of 1933. Those original
purchasers sold your convertible preferred securities to persons they reasonably
believed were either:
 
     - qualified institutional buyers, as that term is defined in Rule 144A
       under the Securities Act of 1933; or
 
     - institutional accredited investors, as that term is defined in Rule
       501(a)(1), (2), (3) or (7) under the Securities Act of 1933.
 
On May 19, 1998, Coltec Industries and Coltec Capital Trust filed a registration
statement on Form S-3 to register resales of your convertible preferred
securities and the related Coltec Industries guarantee.
 
     You may, from time to time, decide to sell your convertible preferred
securities. If you sell your convertible preferred securities, you will also
sell your rights under the related guarantees by Coltec Industries and
BFGoodrich as well as the right to convert your convertible preferred securities
into shares of common stock of BFGoodrich. Therefore, to sell your convertible
preferred securities, you will need to use:
 
     - a current prospectus supplement and prospectus relating to your
       convertible preferred securities; and
 
     - this prospectus, which relates to our guarantee and the BFGoodrich common
       stock into which you may convert your convertible preferred securities.
 
If you transfer your convertible preferred securities without using these
documents, the purchaser must use a current prospectus supplement and prospectus
of Coltec Industries and Coltec Capital Trust and this prospectus and a current
prospectus supplement of BFGoodrich to sell their convertible preferred
securities.
 
     The following table identifies the holders of the convertible preferred
securities that have elected to include their convertible preferred securities
in the registration statement on Form S-3 filed by Coltec Industries and Coltec
Capital Trust, as well as the number of convertible preferred securities they
owned as of January 8, 1999. These selling holders and The Bank of New York, as
property trustee, have provided Coltec Industries with this information.
 
<TABLE>
<CAPTION>
                                                                     NUMBER OF
                                                                    CONVERTIBLE
         HOLDERS WHO MAY SELL USING THIS PROSPECTUS             PREFERRED SECURITIES
         ------------------------------------------             --------------------
<S>                                                             <C>
Lipper Convertibles, L.P....................................           291,500
Credit Suisse First Boston Corporation......................           155,000
</TABLE>
 
                                        9
<PAGE>   15
 
<TABLE>
<CAPTION>
                                                                     NUMBER OF
                                                                    CONVERTIBLE
         HOLDERS WHO MAY SELL USING THIS PROSPECTUS             PREFERRED SECURITIES
         ------------------------------------------             --------------------
<S>                                                             <C>
Lord Abbett Bond Debenture Fund, Inc........................           150,000
Oppenheimer Convertible Securities Fund.....................           120,000
J.P. Morgan & Co. Inc.......................................           120,000
Deutsche Bank A.G. London...................................           100,000
The Northwestern Mutual Life Insurance Company..............            80,000
Van Kampen American Capital Harbor Fund.....................            76,900
Shriner's Hospitals for Children............................            60,000
KA Management Ltd...........................................            52,500
Lehman Brothers Inc.........................................            50,000
President & Fellows of Harvard College......................            50,000
Teachers Insurance and Annuity Association of America.......            50,000
Smith Barney Convertible Fund...............................            50,000
State of Oregon/SAIF Corporation............................            30,000
PRIM Board..................................................            29,000
The Concordia Retirement Plan of the Lutheran
  Church -- Missouri Synod..................................            28,000
The Class IC Company, Ltd...................................            22,500
Arkansas PERS...............................................            22,250
Castle Convertible Fund, Inc................................            22,000
Security Insurance Company of Hartford......................            20,000
Hatchbeam & Co..............................................            18,500
Carrigaholt Capital (Bermuda) L.P...........................            17,500
State of Delaware PERS......................................            15,500
Oxford Fund.................................................            15,000
Combined Insurance Company of America.......................            12,000
The Gabelli Convertible Securities Fund, Inc................            11,000
Capitol American Life Insurance Co. -- Convertible..........            10,500
American Travellers Life Insurance Co. -- Convertible.......            10,500
KA Trading LP...............................................            10,500
Associated Electric & Gas Insurance Services Limited........            10,000
Great American Reserve Insurance Co. -- Convertible.........            10,000
The Northern Trust Company..................................            10,000
Van Kampen American Capital Convertible Securities Fund.....             8,100
Cova Bond Debenture.........................................             7,000
ICI American Holdings Trust.................................             6,750
Zeneca Holdings Trust.......................................             6,750
Beneficial Standard Life Insurance Co. -- Convertible.......             6,000
Third Avenue High Yield Fund................................             5,000
</TABLE>
 
                                       10
<PAGE>   16
 
<TABLE>
<CAPTION>
                                                                     NUMBER OF
                                                                    CONVERTIBLE
         HOLDERS WHO MAY SELL USING THIS PROSPECTUS             PREFERRED SECURITIES
         ------------------------------------------             --------------------
<S>                                                             <C>
ELF Aquitaine...............................................             3,000
The Connecticut Hospice, Inc................................             2,000
National Pen & Associates Profit Sharing Plan...............             2,000
Echlin Inc. Convertible.....................................             2,000
Eagle Asset Management......................................             1,500
D.S.U. Charitable Trust.....................................             1,400
Forest Alternative Strategies Fund II LP Series A-5I........             1,200
Children's Surgical Associates Inc Pen......................             1,000
Children's Surgical Associates PSP..........................             1,000
LLT Limited.................................................               900
Forest Alternative Strategies Fund II LP Series A-5M........               600
Ursuline Provincialate Eastern Province.....................               400
Marian Residence Fund.......................................               200
MFS Series Trust I -- MFS Convertible Securities Fund.......               100
                                                                     ---------
          Total.............................................         1,787,550
                                                                     =========
</TABLE>
 
     None of the persons listed above currently has, and within the past three
years none of them has had, any position, office or other material relationship
with BFGoodrich, Coltec Industries or any predecessors or affiliates of
BFGoodrich or Coltec Industries that would make them affiliates of those
companies. Because you may use this prospectus to offer all or some portion of
your convertible preferred securities, the convertible junior subordinated
debentures or the BFGoodrich common stock that BFGoodrich will issue if you
convert your convertible preferred securities, we cannot estimate the amount of
the convertible preferred securities, the convertible junior subordinated
debentures or the BFGoodrich common stock that you will own when the sales using
this prospectus are completed. In addition, the persons listed above may have
sold, transferred or otherwise disposed of all or a portion of their convertible
preferred securities since the date on which they provided the information about
their convertible preferred securities, in transactions exempt from the
registration requirements of the Securities Act.
 
     BFGoodrich filed the registration statement of which this prospectus is a
part as permitted by Rule 415 under the Securities Act of 1933 to give you the
opportunity to sell your convertible preferred securities or the BFGoodrich
common stock we issued to you when you convert your convertible preferred
securities in public transactions rather than in transactions that are exempt
from the registration and prospectus delivery requirements of the Securities Act
of 1933.
 
     To take advantage of this opportunity to sell your convertible preferred
securities, if you are not listed in the table above, you must notify BFGoodrich
of your intention to sell your convertible preferred securities or your
BFGoodrich common stock. You must also provide other information concerning
yourself and the securities you intend to sell. The Securities Act of 1933 and
the rules and regulations thereunder tell what other information you must
provide. You are already required to give that notice and other information to
Coltec Industries to be permitted to sell your convertible preferred securities.
Your notification to Coltec Industries will be sufficient to notify us. You may
not make any offer or sale using this prospectus until two things occur. First,
you must give Coltec Industries notice that you intend to sell and provide
 
                                       11
<PAGE>   17
 
the required information to Coltec Industries. Second, we must file a supplement
to this prospectus or an amendment to the registration statement of which this
prospectus is a part, and that prospectus supplement or amendment to the
registration statement must become effective. That process could take several
days to complete.
 
     We will from time to time supplement or amend the prospectus or the
registration statement to add additional information concerning holders who may
sell their convertible preferred securities or their BFGoodrich common stock
using this prospectus. Each supplement to this prospectus will also disclose
whether any holder who is selling using that supplement has, during the last
three years before the date of that supplement:
 
     - held any position or office with us or any of our affiliates;
 
     - been employed by us or any of our affiliates; or
 
     - had any other material relationship with us or any of our affiliates.
 
     If that information is included in any previous supplement, it does not
need to be repeated.
 
                              PLAN OF DISTRIBUTION
 
     We have filed a registration statement on Form S-3 with the Securities and
Exchange Commission with respect to the shares of BFGoodrich common stock that
we will issue to you if you convert your convertible preferred securities. The
registration statement also relates to our guarantee, as we have described in
this prospectus, of amounts owed by Coltec Capital Trust and of the performance
of Coltec Industries' obligations relating to your convertible preferred
securities. This prospectus forms a part of that registration statement. We will
use our reasonable best efforts to keep the registration statement effective
until you may sell your convertible preferred securities without restriction. We
have not engaged a broker, dealer or underwriter in connection with the offering
of the BFGoodrich common stock described in this prospectus.
 
     You should consult your own tax advisors with respect to the U.S. and other
tax consequences of converting your convertible preferred securities for shares
of BFGoodrich common stock as described below. For more information, see "U.S.
Income Tax Considerations" below.
 
                         U.S. INCOME TAX CONSIDERATIONS
 
     You should consider the following discussion of U.S. federal income taxes
before you acquire convertible preferred securities or convert your convertible
preferred securities for BFGoodrich common stock. The following discussion
accurately summarizes the material U.S. federal income tax considerations that
usually apply to you as a holder of convertible preferred securities. This
discussion does not address all the federal income tax considerations that may
be relevant to you. In addition, this discussion does not address the tax
consequences of transactions in which you acquire your convertible preferred
securities. Furthermore, this discussion does not address any foreign, state, or
local tax considerations.
 
     WE STRONGLY URGE YOU TO CONSULT YOUR OWN TAX ADVISORS REGARDING THE
SPECIFIC TAX CONSIDERATIONS THAT APPLY TO YOU.
 
     The laws, regulations, court decisions, and Internal Revenue Service
rulings and regulations effective on the date of this prospectus form the basis
of this discussion. This discussion is for general information only. No law,
court decision, ruling or regulation directly addresses the tax
 
                                       12
<PAGE>   18
 
consequences of the ownership of instruments and rights similar to the
convertible preferred securities and the rights attached to those securities.
 
     For purposes of this discussion, a U.S. holder means a beneficial owner of
convertible preferred securities or common stock that is, for purposes of U.S.
federal income tax:
 
     - a citizen or resident of the U.S.;
 
     - a corporation, partnership, or other entity created or organized in or
       under the laws of the U.S. or of any political subdivision of the U.S.;
 
     - an estate the income of which is subject to U.S. federal income taxation
       regardless of its source; or
 
     - a trust if a court within the U.S. is able to exercise primary
       jurisdiction over its administration and at least one U.S. person has the
       authority to control all substantial decisions of the trust.
 
     We have neither sought nor obtained any advance income tax ruling regarding
the tax consequences of any of the transactions we describe.
 
TAX CONSIDERATIONS THAT APPLY TO U.S. HOLDERS
 
     If you are a "U.S. holder" for income tax purposes and you hold your
convertible preferred securities as capital assets, the following tax
considerations will generally apply to you.
 
CONVERSION OF CONVERTIBLE PREFERRED SECURITIES INTO COMMON STOCK
 
     If you convert your convertible preferred securities into shares of
BFGoodrich common stock, you will usually recognize a taxable gain or loss at
that time. Your gain or loss will be equal to the difference between the fair
market value of the shares of common stock you receive in the conversion and
your basis in the convertible preferred securities that you convert. The gain or
loss will usually be a capital gain or loss, except that you may recognize
ordinary income with respect to any declared but unpaid dividends on the
convertible preferred securities. A capital gain or loss will be a long-term
capital gain or loss under current law if your holding period for the
convertible preferred securities is more than one year at the time of the
conversion. In the case of a shareholder who is an individual, the maximum
marginal U.S. federal income tax rate applicable to that long-term capital gain
will be lower than the maximum marginal U.S. federal income tax rate applicable
to ordinary income.
 
OWNERSHIP OF COMMON STOCK
 
Payment of Dividends on Common Stock
 
     Distributions you receive on the BFGoodrich common stock, other than some
distributions of additional shares of common stock or rights to acquire
additional shares of common stock, will be treated as ordinary dividend income
to you to the extent that those distributions are considered to be paid to you
out of our current or accumulated earnings and profits, as determined under U.S.
federal income tax principles. Corporate shareholders may be entitled to a
"dividends-received deduction" with respect to those dividends.
 
     To the extent that any such distribution exceeds our earnings and profits
for a taxable year, that distribution will be treated, first, as a tax-free
return of capital to you to the extent of your adjusted tax basis in BFGoodrich
common stock. Thereafter, it will be treated as capital gain.
 
     Distributions of additional shares of BFGoodrich common stock, or rights to
acquire additional shares of BFGoodrich common stock, that you receive as part
of a pro rata
 
                                       13
<PAGE>   19
 
distribution of those shares, or rights to acquire those shares, to all of our
shareholders usually are not subject to U.S. federal income tax. The tax basis
of those new shares or rights is usually determined by allocating your adjusted
tax basis in the "old" shares of common stock between those "old" shares and the
new shares or rights you receive based upon their relative fair market value on
the date of the distribution.
 
Sale, Exchange or Retirement of Common Stock
 
     You will usually recognize gain or loss on a sale or other taxable
disposition of the BFGoodrich common stock equal to the difference between the
amount you realize on that sale or disposition and your adjusted tax basis in
that common stock. That gain or loss will usually be capital gain or loss and
will usually be considered long-term capital gain or loss if you have held that
stock for more than one year immediately before that sale or disposition. If you
are an individual, the maximum marginal U.S. federal income tax rate applicable
to that gain will be lower than the maximum marginal U.S. federal income tax
rate applicable to ordinary income if your holding period for that stock exceeds
one year.
 
TAX CONSIDERATIONS THAT APPLY TO NON-U.S. HOLDERS
 
Conversion of Convertible Preferred Securities into Common Stock
 
     If you are a non-U.S. holder, any gain you realize on the conversion of
your convertible preferred securities into BFGoodrich common stock usually will
not be subject to a U.S. federal income or withholding tax unless:
 
     - that gain is connected with a trade or business you carried on within the
       U.S.; or if you are an individual, you are present in the U.S. for 183
       days or more during the taxable year
 
     - in which you convert your convertible preferred securities and that gain
       is not otherwise offset by capital losses.
 
Payment of Dividends on Common Stock
 
     If you are a non-U.S. holder and you receive a dividend distribution with
respect to the BFGoodrich common stock that you own, the gross amount of that
dividend will be subject to U.S. federal withholding tax at a 30% or lower
treaty rate.
 
Sale, Exchange or Retirement of Common Stock
 
     If you are a non-U.S. holder, any gain you realize on the sale or other
taxable disposition of BFGoodrich common stock usually will not be subject to
U.S. federal income or withholding tax unless:
 
     - that gain is effectively connected with a trade or business carried on
       within the U.S. by that holder; or
 
     - in the case of a non-U.S. holder who is an individual, that individual is
       present in the U.S. for 183 days or more during the taxable year in which
       that sale or disposition occurs and that gain is not otherwise offset by
       capital losses.
 
                                       14
<PAGE>   20
 
                                 LEGAL MATTERS
 
   
     The validity of the shares of BFGoodrich common stock to be issued from the
conversion of your convertible preferred securities and the enforceability of
our guarantee and the supplemental indenture are being passed upon by Nicholas
J. Calise, Esquire, vice president, associate general counsel and secretary of
BFGoodrich. As of April 6, 1999, Mr. Calise owned 13,617 shares of BFGoodrich
common stock; had deferred receipt of 6,079 shares of BFGoodrich common stock
under the BFGoodrich 1995-1997 Long Term Incentive Plan; had contingently
credited to his account 2,671 phantom shares under the BFGoodrich 1998-2000 Long
Term Incentive Plan, all of which may be forfeited; held options to purchase
87,100 shares of our common stock; and had credited to his account in BFGoodrich
retirement plus savings plan approximately 5,855 shares of BFGoodrich common
stock. In addition, Mr. Calise's wife owns 1,000 shares, although Mr. Calise
disclaims beneficial ownership of these shares.
    
 
                                    EXPERTS
 
     Ernst & Young LLP, independent auditors, have audited our consolidated
financial statements included in our Annual Report on Form 10-K for the year
ended December 31, 1998 as set forth in their report, which as to 1996 is based
in part on the report of Deloitte & Touche LLP, independent auditors, and which
is incorporated by reference in this prospectus and elsewhere in the
registration statement. Our consolidated financial statements are incorporated
by reference in reliance on their reports, given on their authority as experts
in accounting and auditing.
 
     Arthur Andersen LLP, independent auditors, have audited Coltec Industries'
consolidated financial statements and schedules included in its Annual Report on
Form 10-K for the year ended December 31, 1998, as set forth in their report
which is incorporated in this prospectus by reference. Coltec Industries'
consolidated financial statements are incorporated by reference in reliance on
their report, given on their authority as experts in accounting and auditing.
 
                      WHERE YOU CAN FIND MORE INFORMATION
 
     We have filed a registration statement on Form S-3 with the Securities and
Exchange Commission to register:
 
     - the shares of the BFGoodrich common stock that we will issue to you if
       you convert your convertible preferred securities; and
 
     - our guarantee, as described in this prospectus, of amounts owed by Coltec
       Capital Trust and of the performance of Coltec Industries' obligations
       relating to your convertible preferred securities.
 
This prospectus forms a part of that registration statement. The registration
statement and the related exhibits contain additional relevant information. As
allowed by Securities and Exchange Commission rules, this prospectus does not
contain all the information contained in the registration statement or in those
exhibits.
 
     We and Coltec Industries file annual reports, quarterly and special
reports, proxy statements and other information with the Securities and Exchange
Commission. You may read and copy
 
                                       15
<PAGE>   21
 
those reports, statements or other information at the Securities and Exchange
Commission's public reference rooms at the following locations:
 
   
<TABLE>
<S>                        <C>                        <C>
Public Reference Room      New York Regional Office   Chicago Regional Office
450 Fifth Street, N.W.     7 World Trade Center       Citicorp Center
Room 1024                  Suite 1300                 500 West Madison Street
Washington, D.C. 20549     New York, NY 10048         Suite 1400
                                                      Chicago, IL 60661-2511
</TABLE>
    
 
     Please call the Securities and Exchange Commission at 1-800-SEC-0330 for
further information on the operation of the public reference rooms. Securities
and Exchange Commission filings are also available to the public from commercial
document retrieval services and at the Securities and Exchange Commission's
website at "http://www.sec.gov."
 
     In addition, you can inspect these filings at the offices of the New York
Stock Exchange, 20 Broad Street, New York, New York 10005.
 
     The Securities and Exchange Commission allows us to "incorporate by
reference" information from other Securities and Exchange Commission filings
with this prospectus. This means that we can disclose information to you by
referring you to those other filings, and the information incorporated by
reference is considered to be part of this prospectus, except for any
information superseded by information in this prospectus. We are incorporating
by reference the information contained in the following Securities and Exchange
Commission filings:
 
<TABLE>
<CAPTION>
 BFGOODRICH SECURITIES AND EXCHANGE
 COMMISSION FILINGS (FILE NO. 1-892)   PERIOD OR DATE FILED
 -----------------------------------   --------------------
<S>                                    <C>                    <C>
Annual Report on Form 10-K             Year ended:            - December 31, 1998
Current Reports on Form 8-K            Filed on:              - February 19, 1999; and
                                                              - February 25, 1999
Registration Statement on Form 8-A     Filed on:              - July 27, 1987
  (description of BFGoodrich common
  stock), including any amendment or
  report filed for the purpose of
  updating that description
</TABLE>
 
   
<TABLE>
<CAPTION>
COLTEC INDUSTRIES SECURITIES AND EXCHANGE
  COMMISSION FILINGS (FILE NO. 1-7568)     PERIOD OR DATE FILED
- -----------------------------------------  --------------------
<S>                                        <C>                    <C>
Annual Report on Form 10-K                 Year ended:            - December 31, 1998
Current Reports on Form 8-K                Filed on:              - January 25, 1999;
                                                                  - March 1, 1999;
                                                                  - March 4, 1999;
                                                                  - March 16, 1999;
                                                                  - March 26, 1999; and
                                                                  - March 29, 1999
Amendment No. 4 to Registration Statement  Filed on:              - August 17, 1998
  on Form S-3
(File No 333-52975)
(description of TIDES(SM))
</TABLE>
    
 
     We are also incorporating by reference additional documents that we and
Coltec Industries file with the Securities and Exchange Commission before the
termination of this offering. These documents include periodic reports, such as
Annual Reports on Form 10-K, Quarterly Reports on Form 10-Q and Current Reports
on Form 8-K, as well as proxy statements.
 
                                       16
<PAGE>   22
 
     You can request a free copy of any or all of these documents, other than
the exhibits to those documents, unless those exhibits are specifically
incorporated by reference into these documents, by writing to or calling the
following address or telephone number:
 
                               Nicholas J. Calise
                            The B.F.Goodrich Company
                           4020 Kinross Lakes Parkway
                           Richfield, Ohio 44286-9368
                           Telephone: (330) 659-7600
 
     YOU SHOULD RELY ONLY ON THE INFORMATION CONTAINED OR INCORPORATED BY
REFERENCE IN THIS PROSPECTUS BEFORE DECIDING TO CONVERT YOUR CONVERTIBLE
PREFERRED SECURITIES OF COLTEC CAPITAL TRUST INTO BFGOODRICH COMMON STOCK. WE
HAVE NOT AUTHORIZED ANYONE TO PROVIDE YOU WITH INFORMATION THAT IS DIFFERENT
FROM OR IN ADDITION TO WHAT IS CONTAINED IN THIS PROSPECTUS. THEREFORE, IF
ANYONE DOES GIVE YOU INFORMATION OF THIS SORT, YOU SHOULD NOT RELY ON IT. IF YOU
ARE IN A JURISDICTION WHERE IT IS UNLAWFUL TO OFFER TO CONVERT OR SELL OR TO ASK
FOR OFFERS TO CONVERT OR BUY THE SECURITIES OFFERED BY THIS PROSPECTUS, OR IF
YOU ARE A PERSON TO WHOM IT IS UNLAWFUL TO DIRECT THOSE ACTIVITIES, THEN THE
OFFER PRESENTED IN THIS PROSPECTUS DOES NOT EXTEND TO YOU. THE INFORMATION
CONTAINED IN THIS PROSPECTUS SPEAKS ONLY AS OF ITS DATE UNLESS THE INFORMATION
SPECIFICALLY INDICATES THAT ANOTHER DATE APPLIES.
 
                                       17
<PAGE>   23
 
          UNAUDITED PRO FORMA CONDENSED COMBINED FINANCIAL STATEMENTS
 
     The following unaudited pro forma condensed combined statements of income
for each of the three years ended December 31, 1996, 1997 and 1998 give effect
to the merger with Coltec Industries, accounted for as a "pooling of interests."
The unaudited pro forma condensed combined statements of income and the
unaudited pro forma condensed combined balance sheet at December 31, 1998 give
effect to the merger as though Coltec Industries had always been a part of
BFGoodrich.
 
     The pro forma information is based on the historical consolidated financial
statements of BFGoodrich and of Coltec Industries, under the assumptions and
adjustments set forth in the accompanying notes to the unaudited pro forma
condensed combined financial statements.
 
     You should read the information shown below in conjunction with the
consolidated historical financial statements of BFGoodrich and of Coltec
Industries, including the respective notes to those financial statements, which
are incorporated by reference in this prospectus. We have presented the pro
forma data for comparative purposes only. They are not necessarily indicative of
the results of operations or of the financial position that would have occurred
had the merger been completed during the periods or as of the date for which the
pro forma data are presented, and they are not necessarily indicative of
BFGoodrich's future results of operations or financial position.
 
     Pro forma per share amounts for the combined BFGoodrich and Coltec
Industries entity are based on the exchange ratio of 0.56 of a share of
BFGoodrich common stock for each share of Coltec Industries common stock.
 
                                       F-1
<PAGE>   24
 
              UNAUDITED PRO FORMA CONDENSED COMBINED BALANCE SHEET
                               DECEMBER 31, 1998
                             (DOLLARS IN MILLIONS)
 
     The following unaudited pro forma condensed combined balance sheet as of
December 31, 1998 is presented to show the impact of the proposed merger on
BFGoodrich's historical financial condition. The merger has been reflected under
the "pooling of interests" method of accounting.
 
<TABLE>
<CAPTION>
                                                COLTEC       PRO FORMA               PRO FORMA
                                BFGOODRICH    INDUSTRIES    ADJUSTMENTS              COMBINED
                                ----------    ----------    -----------              ---------
<S>                             <C>           <C>           <C>           <C>        <C>
ASSETS
Current Assets
  Cash and cash equivalents...   $   31.7      $   21.8       $                      $   53.5
  Accounts and notes
     receivable, net..........      629.0         148.2                                 777.2
  Inventories.................      772.5         236.0                               1,008.5
  Deferred income taxes.......      142.1          20.5                                 162.6
  Prepaid expenses and other
     assets...................       39.2          15.6                                  54.8
                                 --------      --------       -------                --------
          Total current
            assets............    1,614.5         442.1            --                 2,056.6
                                 --------      --------       -------                --------
Property......................    1,255.9         306.6            --                 1,562.5
Deferred income taxes.........       39.7            --            --                    39.7
Prepaid pensions..............      148.0            --          45.3     4(c)          193.3
Goodwill......................      771.0         214.6                                 985.6
Identifiable intangible
  assets......................      112.4            --                                 112.4
Other assets..................      251.1          92.3                                 343.4
                                 --------      --------       -------                --------
                                 $4,192.6      $1,055.6       $  45.3                $5,293.5
                                 ========      ========       =======                ========
</TABLE>
 
See notes to unaudited pro forma condensed combined financial statements
beginning on page F-7.
 
                                       F-2
<PAGE>   25
 
              UNAUDITED PRO FORMA CONDENSED COMBINED BALANCE SHEET
                               DECEMBER 31, 1998
                             (DOLLARS IN MILLIONS)
                                  (CONTINUED)
 
<TABLE>
<CAPTION>
                                                COLTEC       PRO FORMA               PRO FORMA
                                BFGOODRICH    INDUSTRIES    ADJUSTMENTS              COMBINED
                                ----------    ----------    -----------              ---------
<S>                             <C>           <C>           <C>           <C>        <C>
LIABILITIES AND SHAREHOLDERS'
  EQUITY
Current Liabilities
  Short-term bank debt........   $  144.1      $     --       $                      $  144.1
  Accounts payable............      364.4          96.6                                 461.0
  Accrued expenses............      420.1         171.1                                 591.2
  Income taxes payable........       59.4            --                                  59.4
  Current maturities of
     long-term debt and
     capital lease
     obligations..............        2.8           5.1                                   7.9
                                 --------      --------                              --------
          Total current
            liabilities.......      990.8         272.8            --                 1,263.6
                                 --------      --------       -------                --------
Long-term debt and capital
  lease obligations...........      995.2         577.5                               1,572.7
Pension obligations...........       43.6            --          33.0     4(c)           76.6
Postretirement benefits other
  than pensions...............      338.1           5.9                                 344.0
Other non-current
  liabilities.................      101.7         214.5          12.3     4(c)          328.5
Deferred income taxes.........         --         139.9                                 139.9
Mandatorily redeemable
  preferred securities of
  trusts......................      123.6         145.3                                 268.9
Shareholders' Equity
  Common stock................      381.1           0.7         175.9     4(a)          557.7
  Additional capital..........      543.7         643.6        (303.8)    4(a)(b)       883.5
  Income retained in the
     business.................      736.8        (795.3)                                (58.5)
  Accumulated other
     comprehensive income.....        3.6         (18.7)                                (15.1)
  Common stock held in
     treasury, at cost........      (65.6)       (127.9)        127.9     4(b)          (65.6)
  Unearned compensation.......         --          (2.7)                                 (2.7)
                                 --------      --------       -------                --------
          Total Shareholders'
            Equity............    1,599.6        (300.3)           --                 1,299.3
                                 --------      --------       -------                --------
                                 $4,192.6      $1,055.6       $  45.3                $5,293.5
                                 ========      ========       =======                ========
</TABLE>
 
See notes to unaudited pro forma condensed combined financial statements
beginning on page F-7.
 
                                       F-3
<PAGE>   26
 
          UNAUDITED PRO FORMA CONDENSED COMBINED STATEMENTS OF INCOME
                      FOR THE YEAR ENDED DECEMBER 31, 1998
                (DOLLARS IN MILLIONS, EXCEPT PER SHARE AMOUNTS)
 
     The following unaudited pro forma condensed combined statements of income
are presented to show the impact of the proposed merger on BFGoodrich's
historical results of operations. These statements assume that the companies had
been combined for each period presented.
 
<TABLE>
<CAPTION>
                                                      COLTEC       PRO FORMA     PRO FORMA
                                      BFGOODRICH    INDUSTRIES    ADJUSTMENTS    COMBINED
                                      ----------    ----------    -----------    ---------
<S>                                   <C>           <C>           <C>            <C>
Sales...............................   $3,950.8      $1,504.1      $     --      $5,454.9
Operating costs and expenses:
  Cost of sales.....................    2,853.1       1,080.8                     3,933.9
  Selling and administrative
     costs..........................      610.4         235.2            --         845.6
  Restructuring costs and asset
     impairment.....................       10.5            --            --          10.5
                                       --------      --------      --------      --------
                                        3,474.0       1,316.0            --       4,790.0
                                       --------      --------      --------      --------
Operating income....................      476.8         188.1            --         664.9
Interest expense....................      (79.0)        (54.3)           --        (133.3)
Interest income.....................        5.2           0.9            --           6.1
Other income (expense) -- net.......      (18.1)         56.2            --          38.1
                                       --------      --------      --------      --------
Income from continuing operations
  before income taxes and trust
  distributions.....................      384.9         190.9            --         575.8
Income tax expense..................     (146.3)        (64.9)           --        (211.2)
Distributions on trust preferred
  securities........................      (10.5)         (3.7)           --         (14.2)
                                       --------      --------      --------      --------
Income from continuing operations...      228.1         122.3            --         350.4
Income (loss) from discontinued
  operations -- net of taxes........       (1.6)           --            --          (1.6)
                                       --------      --------      --------      --------
Income before extraordinary item....      226.5         122.3            --         348.8
Extraordinary item -- net of tax....         --          (4.3)           --          (4.3)
                                       --------      --------      --------      --------
Net income..........................   $  226.5      $  118.0      $     --      $  344.5
                                       ========      ========      ========      ========
Basic earnings per share:
  Continuing operations.............   $   3.09      $   1.88      $     --      $   3.18
  Discontinued operations...........      (0.02)           --            --         (0.01)
  Extraordinary item................         --         (0.07)           --         (0.04)
                                       --------      --------      --------      --------
  Net income........................   $   3.07      $   1.81      $     --      $   3.13
                                       ========      ========      ========      ========
Diluted earnings per share:
  Continuing operations.............   $   3.04      $   1.81      $     --      $   3.08
  Discontinued operations...........      (0.02)           --            --         (0.01)
  Extraordinary item................         --         (0.06)           --         (0.04)
                                       --------      --------      --------      --------
  Net income........................   $   3.02      $   1.75      $     --      $   3.03
                                       ========      ========      ========      ========
Weighted average number of common
  and common equivalent shares
  outstanding -- in millions
     Basic..........................       73.7          65.1            --         110.2
     Diluted........................       75.0          69.4            --         113.9
</TABLE>
 
See notes to unaudited pro forma condensed combined financial statements
beginning on page F-7.
 
                                       F-4
<PAGE>   27
 
          UNAUDITED PRO FORMA CONDENSED COMBINED STATEMENTS OF INCOME
                      FOR THE YEAR ENDED DECEMBER 31, 1997
                (DOLLARS IN MILLIONS, EXCEPT PER SHARE AMOUNTS)
 
<TABLE>
<CAPTION>
                                                      COLTEC       PRO FORMA     PRO FORMA
                                      BFGOODRICH    INDUSTRIES    ADJUSTMENTS    COMBINED
                                      ----------    ----------    -----------    ---------
<S>                                   <C>           <C>           <C>            <C>
Sales...............................   $3,373.0      $1,314.9      $     --      $4,687.9
Operating costs and expenses:
  Cost of sales.....................    2,454.7         898.3            --       3,353.0
  Charge for MD-90 contract.........       35.2            --            --          35.2
  Selling and administrative
     costs..........................      556.0         218.8            --         774.8
  Merger-related costs..............       77.0            --            --          77.0
                                       --------      --------      --------      --------
                                        3,122.9       1,117.1            --       4,240.0
                                       --------      --------      --------      --------
Operating income....................      250.1         197.8            --         447.9
Interest expense....................      (73.0)        (54.6)           --        (127.6)
Interest income.....................       12.0            .6            --          12.6
Gain on issuance of subsidiary
  stock.............................       13.7            --            --          13.7
Other income (expense) -- net.......       15.0            --            --          15.0
                                       --------      --------      --------      --------
Income from continuing operations
  before income taxes and trust
  distributions.....................      217.8         143.8            --         361.6
Income tax expense..................      (94.1)        (48.9)           --        (143.0)
Distributions on trust preferred
  securities........................      (10.5)           --            --         (10.5)
                                       --------      --------      --------      --------
Income from continuing operations...      113.2          94.9            --         208.1
Income from discontinued
  operations -- net of taxes........       84.3            --            --          84.3
                                       --------      --------      --------      --------
Income before extraordinary item....      197.5          94.9            --         292.4
Extraordinary item -- net of tax....      (19.3)           --            --         (19.3)
                                       --------      --------      --------      --------
Net income..........................   $  178.2      $   94.9      $     --      $  273.1
                                       ========      ========      ========      ========
Basic earnings per share:
  Continuing operations.............   $   1.59      $   1.44      $     --      $   1.93
  Discontinued operations...........       1.19            --            --          0.78
  Extraordinary item................      (0.27)           --            --         (0.18)
                                       --------      --------      --------      --------
  Net income........................   $   2.51      $   1.44      $     --      $   2.53
                                       ========      ========      ========      ========
Diluted earnings per share:
  Continuing operations.............   $   1.53      $   1.42      $     --      $   1.86
  Discontinued operations...........       1.13            --            --          0.75
  Extraordinary item................      (0.25)     $     --            --         (0.17)
                                       --------      --------      --------      --------
  Net income........................   $   2.41      $   1.42      $     --      $   2.44
                                       ========      ========      ========      ========
Weighted average number of common
  and common equivalent shares
  outstanding -- in millions
     Basic..........................       71.0          65.9            --         107.9
     Diluted........................       74.6          66.9            --         112.1
</TABLE>
 
See notes to unaudited pro forma condensed combined financial statements
beginning on page F-7.
 
                                       F-5
<PAGE>   28
 
          UNAUDITED PRO FORMA CONDENSED COMBINED STATEMENTS OF INCOME
                      FOR THE YEAR ENDED DECEMBER 31, 1996
                (DOLLARS IN MILLIONS, EXCEPT PER SHARE AMOUNTS)
 
<TABLE>
<CAPTION>
                                                      COLTEC       PRO FORMA     PRO FORMA
                                      BFGOODRICH    INDUSTRIES    ADJUSTMENTS    COMBINED
                                      ----------    ----------    -----------    ---------
<S>                                   <C>           <C>           <C>            <C>
Sales...............................   $2,845.8      $1,159.7      $     --      $4,005.5
Operating costs and expenses:
  Cost of sales.....................    2,042.5         811.1            --       2,853.6
  Selling and administrative
     costs..........................      481.8         191.0            --         672.8
  Restructuring costs and asset
     impairment.....................       11.2            --            --          11.2
                                       --------      --------      --------      --------
                                        2,535.5       1,002.1            --       3,537.6
                                       --------      --------      --------      --------
Operating income....................      310.3         157.6            --         467.9
Interest expense....................      (89.3)        (76.2)           --        (165.5)
Interest income.....................        4.2           1.3            --           5.5
Other income (expense) -- net.......      (30.8)           --            --         (30.8)
                                       --------      --------      --------      --------
Income from continuing operations
  before income taxes and trust
  distributions.....................      194.4          82.7            --         277.1
Income tax expense..................      (68.4)        (28.1)           --         (96.5)
Distributions on trust preferred
  securities........................      (10.5)           --            --         (10.5)
                                       --------      --------      --------      --------
Income from continuing operations...      115.5          54.6            --         170.1
Income from discontinued
  operations -- net of taxes........       58.4          57.1            --         115.5
                                       --------      --------      --------      --------
Income before extraordinary item....      173.9         111.7            --         285.6
Extraordinary item -- net of tax....         --         (30.6)           --         (30.6)
                                       --------      --------      --------      --------
Net income..........................   $  173.9      $   81.1      $     --      $  255.0
                                       ========      ========      ========      ========
Basic earnings per share:
  Continuing operations.............   $   1.74      $   0.79      $     --      $   1.62
  Discontinued operations...........       0.87          0.83            --          1.09
  Extraordinary item................         --         (0.44)           --         (0.29)
                                       --------      --------      --------      --------
  Net income........................   $   2.61      $   1.18      $     --      $   2.42
                                       ========      ========      ========      ========
Diluted earnings per share:
  Continuing operations.............   $   1.65      $   0.79      $     --      $   1.57
  Discontinued operations...........       0.83          0.82            --          1.05
  Extraordinary item................         --         (0.44)           --         (0.28)
                                       --------      --------      --------      --------
  Net income........................   $   2.48      $   1.17      $     --      $   2.34
                                       ========      ========      ========      ========
Weighted average number of common
  and common equivalent shares
  outstanding -- in millions
     Basic..........................       66.6          69.1            --         105.3
     Diluted........................       70.9          69.4            --         109.8
</TABLE>
 
See notes to unaudited pro forma condensed combined financial statements
beginning on page F-7.
 
                                       F-6
<PAGE>   29
 
      NOTES TO UNAUDITED PRO FORMA CONDENSED COMBINED FINANCIAL STATEMENTS
 
1. BASIS OF PRESENTATION
 
     The unaudited pro forma condensed combined statements of income for each of
the three years in the period ended December 31, 1998 and the unaudited pro
forma condensed combined balance sheet at December 31, 1998 give effect to the
merger as though Coltec Industries had always been a part of BFGoodrich.
 
     We have presented the unaudited pro forma condensed combined financial
statements for comparative purposes only. They are not necessarily indicative of
the results of operations or of the financial position that would have occurred
had the merger been completed during the periods or as of the date for which the
pro forma data are presented. They are also not necessarily indicative of
BFGoodrich's future results of operations or financial position.
 
     We have included certain reclassifications in the unaudited pro forma
condensed combined balance sheet and statements of income to conform statement
presentations to those expected to be used by BFGoodrich after the merger.
 
2. CONFORMITY OF ACCOUNTING POLICIES
 
     We are still in the process of reviewing our respective accounting policies
to determine if they are consistent or if they need to be conformed. As a result
of this review, we might need to restate either Coltec Industries' or
BFGoodrich's financial statements to conform to those accounting policies that
are most appropriate. We have not included any restatements of prior periods in
the unaudited pro forma condensed combined financial statements. At this time,
we do not expect that conforming such accounting policies will have a material
impact on the unaudited pro forma condensed combined financial statements. We
will make any restatements, if appropriate, upon completion of this review
process.
 
3. MERGER-RELATED AND CONSOLIDATION EXPENSES
 
     The unaudited pro forma condensed combined financial statements do not
include any merger-related and consolidation expenses which we expect to incur
in connection with completing the merger and integrating the operations of
BFGoodrich and Coltec Industries. It is not possible to determine the actual
amount of these costs and expenses until the related operational and
transitional plans are complete. These costs and expenses relate to professional
and registration fees; employee benefit-related costs such as severance,
relocation and retention incentives; facility consolidations; and satisfaction
of contractual obligations. Most of these costs and expenses will be incurred to
eliminate duplicate facilities and excess capacity in the combined BFGoodrich
operations. We cannot determine the exact timing of these charges at this time.
They are dependent on the completion of the necessary plans.
 
     In connection with the merger, the managements of BFGoodrich and Coltec
Industries estimate that BFGoodrich will incur a one-time charge for
merger-related and consolidation expenses at the effective date of the merger
that is expected to be material. Other merger-related transaction costs include
investment banking fees, registration and listing fees, and various accounting,
legal and other related costs.
 
4. PRO FORMA ADJUSTMENTS
 
     Pro forma adjustments to reflect the effect of the merger on the unaudited
pro forma condensed combined balance sheet at December 31, 1998 are as follows:
 
                                       F-7
<PAGE>   30
 
        a. Common stock increased by $175.9 million to record the BFGoodrich
           common stock issued in the merger. That increase is calculated by
           multiplying the 63.1 million shares of Coltec Industries common stock
           outstanding by the exchange ratio of 0.56 and the par value of
           BFGoodrich common stock of $5 per share, reduced by $0.7 million to
           record the retirement of Coltec Industries common stock.
 
        b. Combined additional capital is adjusted for the effects of pro forma
           adjustment a. above, and for the retirement of Coltec Industries
           treasury shares.
 
        c. Coltec Industries' pension obligations are reclassified in accordance
           with BFGoodrich's presentation.
 
        d. For purposes of the pro forma information and references to the
           shares to be issued by BFGoodrich in the merger, we have not included
           the 14,000,000 shares of BFGoodrich common stock to be issued in the
           merger in exchange for the 25,000,000 shares of Coltec Industries
           common stock currently owned by a subsidiary of Coltec Industries.
 
                                       F-8
<PAGE>   31
 
             ------------------------------------------------------
             ------------------------------------------------------
 
             ------------------------------------------------------
             ------------------------------------------------------
             ------------------------------------------------------
             ------------------------------------------------------
 
                                THE B.F.GOODRICH
                                    COMPANY
 
                          COMMON STOCK TO BE ISSUED ON
                           CONVERSION OF CONVERTIBLE
                                   PREFERRED
                       SECURITIES OF COLTEC CAPITAL TRUST
 
                            GUARANTEE OF OBLIGATIONS
                                  RELATING TO
                          5 1/4% CONVERTIBLE PREFERRED
                                   SECURITIES
                         TERM INCOME DEFERRABLE EQUITY
                            SECURITIES (TIDES)(SM*)
                            OF COLTEC CAPITAL TRUST
                              -------------------
 
                                   PROSPECTUS
                              -------------------
 
                                 APRIL   , 1999
* The terms Term Income Deferrable Equity Securities (TIDES)(SM) and TIDES(SM)
  are registered servicemarks of Credit Suisse First Boston Corporation.
             ------------------------------------------------------
             ------------------------------------------------------
<PAGE>   32
 
                                    PART II
                     INFORMATION NOT REQUIRED IN PROSPECTUS
 
ITEM 14. OTHER EXPENSES OF ISSUANCE AND DISTRIBUTION.
 
     The following table sets forth the various expenses to be paid by
BFGoodrich in connection with the issuance and distribution of the securities
being registered. All amounts shown are estimates except for amounts of filing
and listing fees.
 
   
<TABLE>
<S>                                                           <C>
Securities and Exchange Commission registration fee.........  $ 27,835
New York Stock Exchange listing fee.........................    22,150
Trustee fees................................................     2,500
Legal fees and expenses.....................................    40,000
Accounting fees and expenses................................    10,000
Printing, EDGAR formatting and mailing expenses.............    35,000
Miscellaneous...............................................     8,000
                                                              --------
          Total.............................................  $145,485
                                                              ========
</TABLE>
    
 
ITEM 15. INDEMNIFICATION OF DIRECTORS AND OFFICERS.
 
     Under our certificate of incorporation no member of our board of directors
shall have any personal liability to BFGoodrich or its shareholders for damages
for any breach of duty in such capacity, provided that such liability shall not
be limited if a judgment or other final adjudication adverse to the director
establishes that his or her acts or omissions were in bad faith or involved
intentional misconduct or a knowing violation of law or that the director
personally gained a financial profit or other advantage to which he or she was
not legally entitled or that the director's acts violated section 719 of the New
York Business Corporation Law ("NYBCL") (generally relating to the improper
declaration of dividends, improper purchases of shares, improper distribution of
assets after dissolution, or making any improper loans to directors contrary to
specified statutory provisions). Reference is made to Article TWELFTH of our
certificate of incorporation filed as Exhibit 3(A) to our Annual Report on Form
10-K for the year ended December 31, 1988.
 
     Under our bylaws, any person made, or threatened to be made, a party to an
action or proceeding by reason of the fact that he, his testator or intestate is
or was a director or officer of BFGoodrich or served any other corporation in
any capacity at the request of BFGoodrich shall be indemnified by BFGoodrich to
the extent and in a manner permissible under the laws of the State of New York.
 
     In addition, our bylaws provide indemnification for directors and officers
where they are acting on behalf of BFGoodrich where the final judgment does not
establish that the director or officer acted in bad faith or was deliberately
dishonest, were material to the cause of action so adjudicated, or gained a
financial profit or other advantage to which he was not legally entitled. Our
bylaws provide that the indemnification rights shall be deemed to be "contract
rights" and continue after a person ceases to be a director or officer, or after
rescission or modification of our bylaws with respect to prior occurring events.
They also provide directors and officers with the benefit of any additional
indemnification which may be permitted by later amendment to the NYBCL. Our
bylaws further provide for advancement of expenses and specify procedures in
seeking and obtaining indemnification. Our bylaws permit BFGoodrich to maintain
insurance, at its own expense, to indemnify its directors and officers.
Reference is made to Article VI of our bylaws filed as Exhibit 3(B) to our
Quarterly Report on Form 10-Q for the quarter ended March 31, 1998.
 
                                      II-1
<PAGE>   33
 
     The company has insurance to indemnify its directors and officers, within
the limits of our insurance policies, for those liabilities in respect of which
such indemnification insurance is permitted under the laws of the State of New
York.
 
     Reference is made to Sections 721-726 of the NYBCL, which are summarized
below.
 
     Section 721 of the NYBCL provides that indemnification pursuant to the
NYBCL shall not be deemed exclusive of other indemnification rights to which a
director or officer may be entitled, provided that no indemnification may be
made if a judgment or other final adjudication adverse to the director or
officer establishes that (i) his acts were committed in bad faith or were the
result of active and deliberate dishonesty, and, in either case, were material
to the cause of action so adjudicated, or (ii) he personally gained in fact a
financial profit or other advantage to which he was not legally entitled.
 
     Section 722(a) of the NYBCL provides that a corporation may indemnify a
director or officer made, or threatened to be made, a party to any civil or
criminal action, other than a derivative action, against judgments, fines,
amounts paid in settlement and reasonable expenses actually and necessarily
incurred as a result of such action or proceeding, or any appeal therein, if
such director or officer acted in good faith, for a purpose which he reasonably
believed to be in the best interests of the corporation and, in criminal actions
or proceedings, in addition, had no reasonable cause to believe that his conduct
was unlawful. With respect to derivative actions, Section 722(c) of the NYBCL
provides that a director or officer may be indemnified only against amounts paid
in settlement and reasonable expenses, including attorneys' fees, actually and
necessarily incurred in connection with the defense or settlement of such
action, or any appeal therein, if such director or officer acted in good faith,
for a purpose which he reasonably believed to be in the best interests of the
corporation and that no indemnification shall be made in respect of (1) a
threatened action, or a pending action which is settled or otherwise disposed
of, or (2) any claim, issue or matter as to which such person shall have been
adjudged to be liable to the corporation unless and to the extent an appropriate
court determines that the person is fairly and reasonably entitled to partial or
full indemnification.
 
     Section 723 of the NYBCL specifies the manner in which payment of such
indemnification may be authorized by a corporation. It provides that
indemnification by a corporation is mandatory in any case in which the director
or officer has been successful, whether on the merits or otherwise, in defending
an action. If the director or officer has not been successful or the action is
settled, indemnification may be made by the corporation only if authorized by
any of the corporate actions set forth in such Section 723 (unless the
corporation has provided for indemnification in some other manner as otherwise
permitted by Section 721 of the NYBCL).
 
     Section 724 of the NYBCL provides that upon proper application by a
director or officer, indemnification shall be awarded by a court to the extent
authorized under Sections 722 and 723 of the NYBCL. Section 725 of the NYBCL
contains certain other miscellaneous provisions affecting the indemnification of
directors and officers, including a provision for the return of amounts paid as
indemnification if any such person is ultimately found not to be entitled
thereto.
 
     Section 725 of the NYBCL contains other miscellaneous provisions affecting
the indemnification of directors and officers, including provision for the
return of amounts paid as indemnification if any such person is ultimately found
not to be entitled thereto.
 
     Section 726 of the NYBCL authorizes the purchase and maintenance of
insurance to indemnify (1) a corporation for any obligation which it incurs as a
result of the indemnification of directors and officers under the above
sections, (2) directors and officers in instances in which they may be
indemnified by a corporation under such sections, and (3) directors and officers
in instances in which they may not otherwise be indemnified by a corporation
under such sections,
 
                                      II-2
<PAGE>   34
 
provided the contract of insurance covering such directors and officers
provides, in a manner acceptable to the New York State Superintendent of
Insurance, for a retention amount and for co-insurance.
 
     We have purchased liability insurance for our officers and directors as
permitted by the NYBCL.
 
     In the guarantee agreement, we have guaranteed Coltec Industries'
obligation to indemnify the Coltec Capital Trust trustees for, and to hold the
trustees harmless against, any loss, liability or expense incurred without
negligence or bad faith on their part, arising out of or in connection with the
acceptance or administration of the Coltec Capital Trust declaration of trust,
including the costs and expenses of defending itself against any claim or
liability in connection with the exercise or performance of any of its powers or
duties hereunder.
 
ITEM 16. EXHIBITS.
 
   
     The following is a list of exhibits included in this registration
statement. The registrant agrees to furnish supplementally a copy of any omitted
exhibit or schedule to the Securities and Exchange Commission upon request.
 
<TABLE>
<C>    <S>
 2.1   Agreement and Plan of Merger, dated as of November 22, 1998,
       among The B.F.Goodrich Company, Runway Acquisition
       Corporation and Coltec Industries Inc, is incorporated by
       reference to Exhibit 2.1 to BFGoodrich's Registration
       Statement on Form S-4, File No. 333-74067.
 3.1   Certificate of incorporation, as amended, of The
       B.F.Goodrich Company, is incorporated by reference to
       Exhibit 3(A) to the B.F.Goodrich Form 10-K for the year
       ended December 31, 1998.
 3.2   The bylaws, as amended, of The B.F.Goodrich Company are
       incorporated by reference to Exhibit 3(B) of B.F.Goodrich's
       Form 10-Q for the quarter ended March 31, 1998.
 4.1   See Exhibits 3.1 and 3.2 for provisions of the certificate
       of incorporation and bylaws of The B.F. Goodrich Company
       defining the rights of holders of common stock of The B.F.
       Goodrich Company.
 4.2   Rights Agreement dated as of June 2, 1997, between the
       Company and The Bank of New York, as Rights Agent, is
       incorporated by reference to Exhibit 1 to BFGoodrich's
       Registration Statement on Form 8-A, File No. 001-00892.
 4.3*  Form of Guarantee Agreement, dated as of April   , 1999,
       between The B.F.Goodrich Company and The Bank of New York,
       as trustee.
 4.4*  Form of Supplemental Indenture, dated as of April   , 1999,
       between The B.F.Goodrich Company and The Bank of New York,
       as trustee.
 5.1*  Opinion of Nicholas J. Calise, Esquire, vice president,
       associate general counsel and secretary of BFGoodrich, as to
       the validity of the shares and the enforceability of the
       guarantee and the supplemental indenture.
23.1+  Consent of Ernst & Young LLP.
23.2+  Consent of Deloitte & Touche LLP.
23.3+  Consent of Arthur Andersen LLP.
23.4*  Consent of Nicholas J. Calise (included in Exhibit 5.1).
</TABLE>
    
 
                                      II-3
<PAGE>   35
 
   
<TABLE>
<C>        <S>
    24.1+  Power of Attorney.
    24.2+  Power of Attorney.
     25*   Statement of Eligibility of The Bank of New York under the Trust Indenture Act of 1939, as
           amended, on Form T-1 in its capacity as Guarantee Trustee.
</TABLE>
    
 
   
* Filed herewith.
    
   
+ Previously filed.
    
 
ITEM 17. UNDERTAKINGS.
 
     (a) The undersigned registrant hereby undertakes:
 
      (1) To file, during any period in which offers or sales are being made, a
     post-effective amendment to this Registration Statement:
 
        (i) To include any prospectus required by Section 10(a)(3) of the
      Securities Act of 1933;
 
        (ii) To reflect in the prospectus any facts or events arising after the
      effective date of the Registration Statement (or the most recent
      post-effective amendment thereof) which, individually or in the aggregate,
      represent a fundamental change in the information set forth in the
      Registration Statement. Notwithstanding the foregoing, any increase or
      decrease in the volume of securities offered (if the total dollar value of
      securities offered would not exceed that which was registered) and any
      deviation from the low or high end of the estimated maximum offering range
      may be reflected in the form of a prospectus filed with the Commission
      pursuant to Rule 424(b) if, in the aggregate, the changes in volume and
      price represent no more than a 20 percent change in the maximum aggregate
      offering price set forth in the "Calculation of Registration Fee" table in
      the effective Registration Statement;
 
        (iii) To include any material information with respect to the plan of
      distribution not previously disclosed in the Registration Statement or any
      material change to such information in the Registration Statement;
 
provided, however, that paragraphs (a)(1)(i) and (a)(1)(ii) do not apply if the
information required to be included in a post-effective amendment by those
paragraphs is contained in periodic reports filed with or furnished to the
Commission by the registrant pursuant to Section 13 or 15(d) of the Securities
Exchange Act of 1934 that are incorporated by reference in this Registration
Statement.
 
      (2) That, for the purpose of determining any liability under the
     Securities Act of 1933, each such post-effective amendment shall be deemed
     to be a new registration statement relating to the securities offered
     therein, and the offering of such securities at that time shall be deemed
     to be the initial bona fide offering thereof.
 
      (3) To remove from registration, by means of a post-effective amendment,
     any of the securities being registered which remain unsold at the
     termination of the offering.
 
     (b) The undersigned registrant hereby undertakes that, for purposes of
determining any liability under the Securities Act of 1933, each filing of the
registrant's annual report pursuant to Section 13(a) or 15(d) of the Securities
Exchange Act of 1934 (and, where applicable, each filing of an employee benefit
plan's annual report pursuant to Section 15(d) of the Securities Exchange Act of
1934) that is incorporated by reference in the Registration Statement shall be
deemed to be a new registration statement relating to the securities offered
therein, and the offering of such securities at that time shall be deemed to be
the initial bona fide offering thereof.
                                      II-4
<PAGE>   36
 
     (c) Insofar as indemnification for liabilities arising under the Securities
Act of 1933 may be permitted to directors, officers and controlling persons of
the registrant pursuant to the foregoing provisions, or otherwise, the
registrant has been advised that in the opinion of the Securities and Exchange
Commission such indemnification is against public policy as expressed in the Act
and is, therefore, unenforceable. In the event that a claim for indemnification
against such liabilities (other than the payment by the registrant of expenses
incurred or paid by a director, officer or controlling person of the registrant
in the successful defense of any action, suit or proceeding) is asserted by such
director, officer or controlling person in connection with the securities being
registered, the registrant will, unless in the opinion of its counsel the matter
has been settled by controlling precedent, submit to a court of appropriate
jurisdiction the question whether such indemnification by it is against public
policy as expressed in the Act and will be governed by the final adjudication of
such issue.
 
                                      II-5
<PAGE>   37
 
                                   SIGNATURES
 
   
     Pursuant to the requirements of the Securities Act of 1933, the registrant
certifies that it has reasonable grounds to believe that it meets all of the
requirements for filing on Form S-3 and has duly caused this registration
statement to be signed on its behalf by the undersigned, thereunto duly
authorized, in the City of Richfield, Ohio on this 7th day of April, 1999.
    
 
                                       THE B.F.GOODRICH COMPANY
 
   
                                       By: /s/     NICHOLAS J. CALISE
    
   
                                           -------------------------------------
    
   
                                           Nicholas J. Calise
    
   
                                           Vice President, Associate General
                                           Counsel
    
   
                                           and Secretary
    
 
   
     Pursuant to the requirements of the Securities Act of 1933, this
registration statement has been signed by the following persons in the
capacities indicated on this 7th day of April, 1999.
    
 
   
<TABLE>
<CAPTION>
                      SIGNATURE                                        TITLE
                      ---------                                        -----
<S>                                                      <C>
 
/s/ DAVID L. BURNER*                                     Chairman, Chief Executive
- -----------------------------------------------------    Officer, President and Director
David L. Burner                                          (Principal Executive Officer)
 
/s/ LAURENCE A. CHAPMAN*                                 Senior Vice President, Chief
- -----------------------------------------------------    Financial Officer (Principal
Laurence A. Chapman                                      Financial Officer)
 
/s/ ROBERT D. KONEY, JR.*                                Vice President and Controller
- -----------------------------------------------------    (Principal Accounting Officer)
Robert D. Koney, Jr.
 
/s/ JEANNETTE GRASSELLI BROWN*                           Director
- -----------------------------------------------------
Jeannette Grasselli Brown
 
/s/ DIANE C. CREEL*                                      Director
- -----------------------------------------------------
Diane C. Creel
 
/s/ GEORGE A. DAVIDSON, JR.*                             Director
- -----------------------------------------------------
George A. Davidson, Jr.
 
/s/ JAMES J. GLASSER*                                    Director
- -----------------------------------------------------
James J. Glasser
 
/s/ JODIE K. GLORE*                                      Director
- -----------------------------------------------------
Jodie K. Glore
 
/s/ DOUGLAS E. OLESEN*                                   Director
- -----------------------------------------------------
Douglas E. Olesen
 
/s/ RICHARD DE J. OSBORNE*                               Director
- -----------------------------------------------------
Richard de J. Osborne
</TABLE>
    
 
                                      II-6
<PAGE>   38
 
   
<TABLE>
<CAPTION>
                      SIGNATURE                                        TITLE
                      ---------                                        -----
<S>                                                      <C>
/s/ ALFRED M. RANKIN, JR.*                               Director
- -----------------------------------------------------
Alfred M. Rankin, Jr.
 
/s/ ROBERT H. RAU*                                       Director
- -----------------------------------------------------
Robert H. Rau
 
/s/ JAMES R. WILSON*                                     Director
- -----------------------------------------------------
James R. Wilson
 
/s/ A. THOMAS YOUNG*                                     Director
- -----------------------------------------------------
A. Thomas Young
</TABLE>
    
 
     * The undersigned, as attorney-in-fact, does hereby sign this registration
       statement on behalf of each of the officers and directors indicated
       above.
 
   
                                   By: /s/ NICHOLAS J. CALISE
    
                                       -----------------------------------------
   
                                       Nicholas J. Calise
    
 
                                      II-7
<PAGE>   39
 
                                 EXHIBIT INDEX
 
   
<TABLE>
<CAPTION>
EXHIBIT
  NO.                              DESCRIPTION
- -------                            -----------
<C>        <S>
  2.1      Agreement and Plan of Merger, dated as of November 22, 1998,
           among The B.F.Goodrich Company, Runway Acquisition
           Corporation and Coltec Industries Inc, is incorporated by
           reference to Exhibit 2.1 to BFGoodrich's Registration
           Statement on Form S-4, File No. 333-74067.
  3.1      Certificate of incorporation, as amended, of The
           B.F.Goodrich Company, is incorporated by reference to
           Exhibit 3(A) to the B.F.Goodrich Form 10-K for the year
           ended December 31, 1998.
  3.2      The bylaws, as amended, of The B.F.Goodrich Company are
           incorporated by reference to Exhibit 3(B) of B.F.Goodrich's
           Form 10-Q for the quarter ended March 31, 1998.
  4.1      See Exhibits 3.1 and 3.2 for provisions of the certificate
           of incorporation and Bylaws of The B.F. Goodrich Company
           defining the rights of holders of common stock of The B.F.
           Goodrich Company.
  4.2      Rights Agreement dated as of June 2, 1997, between the
           Company and The Bank of New York, as Rights Agent, is
           incorporated by reference to Exhibit 1 to BFGoodrich's
           Registration Statement, File No. 001-00892.
  4.3*     Form of Guarantee Agreement, dated as of April   , 1999,
           between The B.F.Goodrich Company and The Bank of New York,
           as trustee.
  4.4*     Form of Supplemental Indenture, dated as of April   , 1999,
           between The B.F.Goodrich Company and The Bank of New York,
           as trustee.
  5.1*     Opinion of Nicholas J. Calise, Esquire, vice president,
           associate general counsel and secretary of BFGoodrich, as to
           the validity of the shares and the enforceability of the
           guarantee and the supplemental indenture.
 23.1+     Consent of Ernst & Young LLP.
 23.2+     Consent of Deloitte & Touche LLP.
 23.3+     Consent of Arthur Andersen LLP.
 23.4*     Consent of Nicholas J. Calise (included in Exhibit 5.1)
 24.1+     Power of Attorney.
 24.2+     Power of Attorney.
 25*       Statement of Eligibility of The Bank of New York under the
           Trust Indenture Act of 1939, as amended, on Form T-1 in its
           capacity as Guarantee Trustee.
</TABLE>
    
 
- ---------------
 
   
* Filed herewith.
    
 
   
+ Previously filed.
    
 
                                      II-8

<PAGE>   1
                                                                     Exhibit 4.3

================================================================================





                               GUARANTEE AGREEMENT




                                     Between




                            THE B.F.GOODRICH COMPANY



                                       and



                              THE BANK OF NEW YORK



                         Dated as of April___, 1999










================================================================================



<PAGE>   2






                             CROSS-REFERENCE TABLE*
                             ----------------------


Section of                                                 Section of
Trust Indenture Act                                        Guarantee Agreement
of 1939, as amended                                        -------------------
- -------------------

310(a).................................................    4.01(a)
310(b).................................................    4.01(c), 2.08
310(c).................................................    4.01(a)
311(a).................................................    2.02(b)
311(b).................................................    2.02(b)
311(c).................................................    Inapplicable
312(a).................................................    2.02(a)
312(b).................................................    2.02(b)
313   .................................................    2.03
314(a).................................................    2.04
314(b).................................................    Inapplicable
314(c).................................................    2.05
314(d).................................................    Inapplicable
314(e).................................................    1.01, 2.05, 3.02
314(f).................................................    2.01, 3.02
315(a).................................................    3.01(d)
315(b).................................................    2.07
315(c).................................................    3.01
315(d).................................................    3.01(d)
316(a).................................................    1.01, 2.06, 5.04
316(b).................................................    5.03
317(a).................................................    Inapplicable
317(b).................................................    Inapplicable
318(a).................................................    2.01(b)
318(b).................................................    2.01
318(c).................................................    2.01(a)


- ----------

* This Cross-Reference Table does not constitute part of the Guarantee Agreement
and shall not affect the interpretation of any of its terms or provisions. 

                                       i

<PAGE>   3


                                TABLE OF CONTENTS
                                -----------------

                                                                            Page
                                                                            ----
<TABLE>

<S>                              <C>                                                                    <C>
          ARTICLE I

         Definitions
         -----------
 
SECTION 1.01.                    Definitions....................................................         2



         ARTICLE II

     Trust Indenture Act
     -------------------

SECTION 2.01.                    Trust Indenture Act; Application...............................         6

SECTION 2.02.                    Lists of Holders...............................................         6

SECTION 2.03.                    Reports by the Guarantee                                                6
                                   Trustee......................................................

SECTION 2.04.                    Periodic Reports to the Guarantee Trustee......................         7

SECTION 2.05.                    Evidence of Compliance with                                             7
                                   Conditions Precedent.........................................

SECTION 2.06.                    Events of Default; Waiver......................................         7

SECTION 2.07.                    Event of Default; Notice.......................................         7

SECTION 2.08.                    Conflicting Interests..........................................         7



         ARTICLE III

Powers, Duties and Rights Of The
- --------------------------------
      Guarantee Trustee
      -----------------

SECTION 3.01.                    Powers and Duties of the Guarantee Trustee.....................         8

SECTION 3.02.                    Certain Rights of Guarantee Trustee............................         9

SECTION 3.03.                    Indemnity......................................................        11

SECTION 3.04.                    Expenses.......................................................        11
</TABLE>


                                       ii

<PAGE>   4

<TABLE>

<S>                              <C>                                                               <C>
         ARTICLE IV

      Guarantee Trustee
      -----------------

SECTION 4.01.                    Guarantee Trustee;                                                
                                   Eligibility..................................................   11
                                                                                                   
SECTION 4.02.                    Appointment, Removal and
                                   Resignation of the Guarantee
                                   Trustee......................................................   12



          ARTICLE V

          Guarantee
          ---------

SECTION 5.01.                    Guarantee......................................................   12

SECTION 5.02.                    Waiver of Notice and Demand....................................   13

SECTION 5.03.                    Obligations Not Affected.......................................   13

SECTION 5.04.                    Rights of Holders..............................................   14

SECTION 5.05.                    Guarantee of Payment...........................................   14

SECTION 5.06.                    Subrogation....................................................   14

SECTION 5.07.                    Independent Obligations........................................   14



         ARTICLE VI

 Covenants and Subordination
 ---------------------------

SECTION 6.01.                    Subordination..................................................   15

SECTION 6.02.                    Pari Passu Guarantees..........................................   15



         ARTICLE VII

Consolidation, Merger, Conveyance, Transfer or Lease
- ----------------------------------------------------

SECTION 7.01.                    Company May Consolidate, Etc., Only
                                   on Certain Terms.............................................   15
</TABLE>


                                      iii


<PAGE>   5

<TABLE>

<S>                              <C>                                                              <C>
        ARTICLE VIII

         Termination
         -----------

SECTION 8.01.                    Termination....................................................   16



         ARTICLE IX

        Miscellaneous
        -------------

SECTION 9.01.                    Successors and Assigns.........................................   16

SECTION 9.02.                    Amendments.....................................................   16

SECTION 9.03.                    Notices........................................................   16

SECTION 9.04.                    Benefit........................................................   18

SECTION 9.05.                    Interpretation.................................................   18

SECTION 9.06.                    Governing Law..................................................   18
</TABLE>


                                       iv

<PAGE>   6



                  GUARANTEE AGREEMENT, dated as of April___, 1999, executed
and delivered by THE B.F.GOODRICH COMPANY, a New York corporation (the
"Guarantor"), and THE BANK OF NEW YORK, a New York banking corporation, as
trustee (the "Guarantee Trustee"), for the benefit of the Holders (as defined
herein) from time to time of the Convertible Preferred Securities (as defined
herein) of COLTEC CAPITAL TRUST, a Delaware statutory business trust (the
"Issuer").

                  WHEREAS, pursuant to an Amended and Restated Declaration of
Trust (the "Declaration"), dated as of April 14, 1998, executed by Coltec
Industries Inc, as sponsor ("Coltec Industries"), The Bank of New York
(Delaware), as Delaware Trustee, The Bank of New York, as Property Trustee, and
the Administrative Trustees named therein, the Issuer issued $150,000,000
aggregate liquidation amount of its 5 1/4% Convertible Preferred Securities,
Term Income Deferrable Equity Securities (TIDES(SM))* liquidation amount $50 per
security (the "Convertible Preferred Securities"), and $4,639,200 aggregate
liquidation amount of its Common Securities, liquidation amount $50 per security
(the "Common Securities" and, collectively with the Convertible Preferred
Securities, the "Trust Securities"), representing undivided beneficial ownership
interests in the assets of the Issuer and having the terms set forth in the
Declaration;

                  WHEREAS, the Trust Securities were issued by the Issuer and
the proceeds thereof were used to purchase the 5 1/4% Convertible Junior
Subordinated Debentures due April 15, 2028 (as defined in the Declaration) (the
"Convertible Junior Subordinated Debentures") of Coltec Industries which were
deposited with the Property Trustee under the Declaration, as trust assets;

                  WHEREAS, Coltec Industries owns all of the outstanding Common
Securities of Coltec Capital Trust and each Convertible Preferred Security is
convertible, at the option of the Holder, into 1.7058 shares of Coltec
Industries common stock, subject to certain adjustments;

                  WHEREAS, pursuant to an Agreement and Plan of Merger dated as
of November 22, 1998 among Guarantor, Runway Acquisition Corporation, a wholly
owned subsidiary of Guarantor, and Coltec Industries (the "Merger Agreement"),
Coltec Industries merged with Runway Acquisition Corporation, and Coltec
Industries became a wholly owned subsidiary of Guarantor;

                  WHEREAS, in the Merger Agreement, Guarantor agreed to take
those actions required to permit Coltec Industries to give the Holders of
Convertible Preferred Securities the right to convert each of those securities
into 0.955248 of a share of Guarantor common stock, subject to certain
adjustments; and

- ----------
* The terms Term Income Deferrable Equity Securities (TIDES)(SM) and TIDES(SM)
are registered service marks of Credit Suisse First Boston Corporation.

<PAGE>   7

                  WHEREAS, the Guarantor desires to provide certain assurances
with respect to the Trust Securities, including its agreement (i) to pay to the
Holders of the Trust Securities the Guarantee Payments (as defined herein) and
to make certain other payments on the terms and conditions set forth herein and
(ii) to otherwise guarantee the performance of the obligations of Coltec
Industries under (w) the Guarantee Agreement, dated as of April 14, 1998 (the
"Coltec Guarantee Agreement"), between Coltec Industries and The Bank of New
York, (x) the Indenture, (y) the Convertible Junior Subordinated Debentures, 
and (z) the Declaration;

                  NOW, THEREFORE, intending to be legally bound hereby, the
Guarantor executes and delivers this Guarantee Agreement for the benefit of the
Holders from time to time of the Trust Securities.


                                    ARTICLE I

                                   DEFINITIONS
                                   -----------

                  SECTION 1.01. DEFINITIONS. As used in this Guarantee
Agreement, the terms set forth below shall, unless the context otherwise
requires, have the following meanings. Capitalized or otherwise defined terms
used but not otherwise defined herein shall have the meanings assigned to such
terms in the Declaration as in effect on the date hereof.

                  "Affiliate" of any specified Person means any other Person
directly or indirectly controlling or controlled by or under direct or indirect
common control with such specified Person; PROVIDED, HOWEVER, that the Issuer
shall be deemed not to be an Affiliate of the Guarantor. For the purposes of
this definition, "control" when used with respect to any specified Person means
the power to direct the management and policies of such Person, directly or
indirectly, whether through the ownership of voting securities, by contract or
otherwise; the terms "controlling" and "controlled" have meanings correlative to
the foregoing.

                  "Coltec Guarantee Agreement" has the meaning specified in the
sixth recital to this Guarantee Agreement.

                  "Coltec Industries" has the meaning specified in the first
recital to this Guarantee Agreement.

                  "Common Securities" has the meaning specified in the first
recital of this Guarantee Agreement.
                  
                  "Convertible Junior Subordinated Debentures" has the meaning
specified in the second recital of this Guarantee Agreement.

                  "Convertible Preferred Securities" has the meaning specified
in the first recital of this Guarantee Agreement.



                                       2
<PAGE>   8
                  "Debt" means (i) the principal of, premium, if any, unpaid
interest (including interest accruing on or after the filing of any petition in
bankruptcy or for reorganization relating to the Guarantor at the relevant
contracted rate specified in the documentation for the relevant Debt whether or
not such claim for post-petition interest is allowed in such proceeding) on, and
all other Obligations relating to, indebtedness for money borrowed (including
any guarantee relating to the foregoing obligations), (ii) purchase money and
similar obligations, (iii) obligations under capital lease, letters of credit
and reimbursement obligations relating thereto, (iv) guarantees, assumptions or
purchase commitments relating to, or other transactions as a result of which the
Guarantor is responsible for the payment of such indebtedness of others, (v)
renewals, extensions and refundings of any such indebtedness, (vi) interest or
obligations in respect of any such indebtedness accruing after the commencement
of any insolvency or bankruptcy proceedings (at the relevant contractual rate
specified in the documentation therefor, whether or not such claim for
post-petition interest is allowed in such proceeding), (vii) all obligations to
make payment pursuant to the terms of financial instruments, such as (a)
securities contracts and foreign currency exchange contracts, (b) derivative
instruments, such as swap agreements (including interest rate and foreign
exchange rate swap agreements), cap agreements, floor agreements, collar
agreements, interest rate agreements, foreign exchange agreements, options,
commodity futures contracts and commodity options contracts and (c) similar
financial instruments, and (viii) any deferrals, renewals or extensions of any
such Debt.

                  "Declaration" has the meaning specified in the first recital
to this Guarantee Agreement.

                  "Event of Default" means a default by the Guarantor on any of
its payment or other obligations under this Guarantee Agreement; PROVIDED,
HOWEVER, that, except with respect to a default in payment of any Guarantee
Payments, the Guarantor shall have received notice of default and shall not have
cured such default within 60 days after receipt of such notice.

                  "Guarantee Payments" means the following payments or
distributions, without duplication, with respect to the Convertible Preferred
Securities, to the extent not paid or made by or on behalf of the Issuer: (i)
any accrued and unpaid Distributions (as defined in the Declaration) required to
be paid on the Trust Securities, to the extent the Issuer shall have funds on
hand available therefor at such time; (ii) the redemption price, including all
accrued and unpaid Distributions to the date of redemption (the "Redemption
Price"), with respect to the Trust Securities called for redemption by the
Issuer to the extent the Issuer shall have funds on hand available therefor at
such time; and (iii) upon a voluntary or involuntary dissolution, winding-up or
liquidation of the Issuer, unless Convertible Junior Subordinated Debentures are
distributed to the Holders of the Trust Securities or all the Trust Securities
are redeemed, the lesser of (a) the aggregate of the liquidation amount of $50
per Trust Security plus accrued and unpaid Distributions on the Trust Securities
to the date of payment (the "Liquidation Distribution") to the extent the Issuer
shall have funds on hand available to make such payment at such time and (b) the
amount of assets of the Issuer remaining available for distribution to Holders
of the Trust Securities upon liquidation of the Issuer after satisfaction of
liabilities to creditors of the Issuer as required by applicable law.


                                      3
<PAGE>   9
                  "Guarantee Trustee" means The Bank of New York, until a
Successor Guarantee Trustee has been appointed and has accepted such appointment
pursuant to the terms of this Guarantee Agreement and thereafter means each such
Successor Guarantee Trustee.

                  "Guarantor" has the meaning specified in the first recital of
this Guarantee Agreement.

                  "Holder" means any holder, as registered on the books and
records of the Issuer, of any Trust Securities; PROVIDED, HOWEVER, that in
determining whether the holders of the requisite percentage of Trust Securities
have given any request, notice, consent or waiver hereunder, "Holder" shall not
include the Guarantor, the Guarantee Trustee, or any Affiliate of the Guarantor
or the Guarantee Trustee.

                  "Indenture" means the Indenture dated as of April 14, 1998, as
amended or supplemented, between Coltec Industries and The Bank of New York, as
trustee, relating to the issuance of Convertible Junior Subordinated Debentures.

                  "Issuer" has the meaning specified in the first recital of
this Guarantee Agreement.

                  "List of Holders" has the meaning specified in Section 
2.02(a).

                  "Majority in liquidation amount of the Trust Securities"
means, except as provided by the Trust Indenture Act, a vote by the Holders,
voting separately as a class, of more than 50% of the aggregate liquidation
amount of all then outstanding Trust Securities issued by the Issuer.

                  "Obligations" means all obligations for principal, premium,
interest, penalties, fees, indemnifications, reimbursements, damages and other
liabilities payable under, or with respect to, the documentation governing any
Debt.

                  "Officers' Certificate" means, with respect to any Person, a
certificate signed by the Chairman and Chief Executive Officer, the President or
any Vice President, and by the Treasurer, any Assistant Treasurer, the
Controller, the Secretary or an Assistant Secretary of such Person, and
delivered to the Guarantee Trustee. Any Officers' Certificate delivered with
respect to compliance with a condition or covenant provided for in this
Guarantee Agreement shall include:

                  (a) a statement that each officer signing the Officers'
         Certificate has read the covenant or condition and the definitions
         relating thereto;

                  (b) a brief statement as to the nature and scope of the
         examination or investigation upon which the statements or opinions
         contained in the Officers' Certificate are based;


                                       4
<PAGE>   10
                  (c) a statement that each officer has made such examination or
         investigation as, in such officer's opinion, is necessary to enable
         such officer to express an informed opinion as to whether or not such
         covenant or condition has been complied with; and

                  (d) a statement as to whether, in the opinion of each officer,
         such condition or covenant has been complied with.

                  "Person" means a legal person, including any individual,
corporation, estate, partnership, joint venture, association, joint stock
company, limited liability company, trust, unincorporated association, or
government or any agency or political subdivision thereof, or any other entity
of whatever nature.

                  "Responsible Officer," when used with respect to the Guarantee
Trustee, means any officer assigned to the Corporate Trust Office, including any
vice president, assistant vice president, assistant treasurer, assistant
secretary or any other officer of the Guarantee Trustee customarily performing
functions similar to those performed by any of the above designated officers and
having direct responsibility for the administration of this Guarantee Agreement,
and also, with respect to a particular matter, any other officer to whom such
matter is referred because of such officer's knowledge of and familiarity with
the particular subject.

                  "Senior Debt" means any Debt of the Guarantor, whether
outstanding on the date of execution of the Indenture or thereafter created,
assumed or incurred, except such Debt that is expressly stated to rank junior in
right of payment to, or PARI PASSU in right of payment with, the Convertible
Junior Subordinated Debentures (or any guarantee thereof); PROVIDED, HOWEVER,
that Senior Debt shall not be deemed to include (a) any Debt of the Guarantor
which, when incurred and without respect to any election under Section 1111(b)
of the United States Bankruptcy Code of 1978, was without recourse to the
Guarantor, (b) trade accounts payable and accrued liabilities arising in the
ordinary course of business, (c) any Debt of the Guarantor to any of its
subsidiaries, (d) any Debt to any employee of the Guarantor or (e) any
obligations of Guarantor pursuant to a guarantee agreement or any other
agreement or arrangement relating to B.F.Goodrich Capital Trust's 8.3%
Cumulative Quarterly Income Preferred Securities, Series A issued on June 29,
1995 (the "BFG QUIPS(SM)")*.

                  "Successor Guarantee Trustee" means a successor Guarantee
Trustee possessing the qualifications to act as Guarantee Trustee under Section
4.01.

                  "Trust Indenture Act" means the Trust Indenture Act of 1939
(15 U.S.C. Sections 77aaa-77bbbb), as amended.

                  "Trust Securities" has the meaning specified in the first
recital of this Guarantee Agreement.




- --------

* QUIPS(SM) is a service mark of Goldman, Sachs & Co.



                                       5
<PAGE>   11

                                   ARTICLE II

                               Trust Indenture Act
                               -------------------

                  SECTION 2.01. TRUST INDENTURE ACT; APPLICATION. (a) This
Guarantee Agreement will be qualified under the Trust Indenture Act upon the
effectiveness of a registration statement with respect to this Guarantee
Agreement. This Guarantee Agreement incorporates certain provisions of the Trust
Indenture Act identified in the Cross-Reference Table set forth in this
Guarantee Agreement.

                  (b) Upon qualification under the Trust Indenture Act as
contemplated in clause (a) above, if and to the extent that any provision of
this Guarantee Agreement limits, qualifies or conflicts with the duties imposed
by Sections 310 to 317, inclusive, of the Trust Indenture Act, such imposed
duties shall control.

                  SECTION 2.02. LIST OF HOLDERS. (a) At the request of the
Guarantee Trustee, the Guarantor shall furnish or cause to be furnished to the
Guarantee Trustee (i) semiannually, on or before February 1st and August 1st of
each year, a list, in such form as the Guarantee Trustee may reasonably require,
of the names and addresses of the Holders ("List of Holders") as of a date not
more than 15 days prior to the delivery thereof, and (ii) at such other times as
the Guarantee Trustee may request in writing, within 30 days after the receipt
by the Guarantor of any such request, a List of Holders as of a date not more
than 15 days prior to the time such list is furnished, in each case to the
extent such information is in the possession or control of the Guarantor and is
not identical to a previously supplied list of Holders or has not otherwise been
received by the Guarantee Trustee in its capacity as such. The Guarantee Trustee
may destroy any List of Holders previously given to it on receipt of a new List
of Holders.

                  (b) The Guarantee Trustee shall comply with its obligations
under Section 311(a), Section 311(b) and Section 312(b) of the Trust Indenture
Act.

                  SECTION 2.03. REPORTS BY THE GUARANTEE TRUSTEE. (a) The
Guarantee Trustee shall transmit to Holders such reports concerning the
Guarantee Trustee and its actions under this Guarantee as may be required
pursuant to the Trust Indenture Act, at the times and in the manner provided
pursuant thereto.

                  (b) Reports so required to be transmitted at stated intervals
of not more than 12 months shall be transmitted no later than May 15th in each
calendar year, commencing with May 15, 2000.

                  (c) A copy of each such report shall, at the time of such
transmission to Holders, be filed by the Guarantee Trustee with each securities
exchange upon which the Convertible Preferred Securities are listed and also
with the Securities and Exchange Commission. The Guarantor will promptly notify
the Guarantee Trustee whenever the Convertible Preferred Securities are listed
on any securities exchange.


                                       6
<PAGE>   12

                  SECTION 2.04. PERIODIC REPORTS TO THE GUARANTEE TRUSTEE. The
Guarantor shall provide to the Guarantee Trustee, and, if required by the Trust
Indenture Act, to the Securities and Exchange Commission and the Holders, such
documents, reports and information, if any, as required by Section 314 of the
Trust Indenture Act and the compliance certificate required by Section 314 of
the Trust Indenture Act, in the form, in the manner and at the times required by
Section 314 of the Trust Indenture Act. The Guarantor shall file annually with
the Guarantee Trustee a certificate as to whether or not the Guarantor is in
compliance with all the conditions and covenants applicable to it under this
Guarantee Agreement.

                  SECTION 2.05. EVIDENCE OF COMPLIANCE WITH CONDITIONS
PRECEDENT. The Guarantor shall provide to the Guarantee Trustee such evidence of
compliance with such conditions precedent, if any, provided for in this
Guarantee Agreement that relate to any of the matters set forth in Section
314(c) of the Trust Indenture Act. Any certificate or opinion required to be
given by any officer pursuant to Section 314(c)(1) may be given in the form of
an Officers' Certificate.

                  SECTION 2.06. EVENTS OF DEFAULT; WAIVER. The Holders of a
Majority in liquidation amount of the Convertible Preferred Securities may, by
vote, on behalf of the Holders, waive any past Event of Default and its
consequences. Upon such waiver, any such Event of Default shall cease to exist,
and any Event of Default arising therefrom shall be deemed to have been cured,
for every purpose of this Guarantee Agreement, but no such waiver shall extend
to any subsequent or other default or Event of Default or impair any right
consequent therefrom.

                  SECTION 2.07. EVENT OF DEFAULT; NOTICE. (a) The Guarantee
Trustee shall, within 90 days after the occurrence of an Event of Default,
transmit by mail, first class postage prepaid, to the Holders, notices of all
Events of Default known to a Responsible Officer of the Guarantee Trustee,
unless such Events of Default actually have been cured before the giving of such
notice; PROVIDED, that, except in the case of a default in the payment of a
Guarantee Payment, the Guarantee Trustee shall be protected in withholding such
notice if and so long as the Board of Directors, the executive committee or a
trust committee of directors and/or Responsible Officers in good faith determine
that the withholding of such notice is in the interests of the Holders.

                  (b) The Guarantee Trustee shall not be deemed to have
knowledge of any Event of Default unless a Responsible Officer charged with the
administration of the Guarantee shall have received written notice of such Event
of Default.

                  SECTION 2.08. CONFLICTING INTERESTS. The Declaration shall be
deemed to be specifically described in this Guarantee Agreement for the purposes
of clause (i) of the first proviso contained in Section 310(b) of the Trust
Indenture Act.


                                       7
<PAGE>   13

                                   ARTICLE III

                        Powers, Duties and Rights of the
                        --------------------------------
                                Guarantee Trustee
                                -----------------

                  SECTION 3.01. POWERS AND DUTIES OF THE GUARANTEE TRUSTEE. (a)
This Guarantee Agreement shall be held by the Guarantee Trustee for the benefit
of the Holders, and the Guarantee Trustee shall not transfer this Guarantee
Agreement to any Person except a Holder exercising his or her rights pursuant to
Section 5.04(iv) hereof or to a Successor Guarantee Trustee on acceptance by
such Successor Guarantee Trustee of its appointment to act as Successor
Guarantee Trustee. The right, title and interest of the Guarantee Trustee shall
automatically vest in any Successor Guarantee Trustee, upon acceptance by such
Successor Guarantee Trustee of its appointment hereunder, and such vesting and
cessation of title shall be effective whether or not conveyancing documents have
been executed and delivered pursuant to the appointment of such Successor
Guarantee Trustee.

                  (b) If an Event of Default has occurred and is continuing, the
Guarantee Trustee shall enforce this Guarantee Agreement for the benefit of the
Holders.

                  (c) The Guarantee Trustee, before the occurrence of any Event
of Default and after the curing of all Events of Default that may have occurred,
shall undertake to perform only such duties as are specifically set forth in
this Guarantee Agreement, and no implied covenants shall be read into this
Guarantee Agreement against the Guarantee Trustee. In case an Event of Default
has occurred (that has not been cured or waived pursuant to Section 2.06), the
Guarantee Trustee shall exercise such of the rights and powers vested in it by
this Guarantee Agreement, and use the same degree of care and skill in its
exercise thereof, as a prudent person would exercise or use under the
circumstances in the conduct of his or her own affairs.

                  (d) No provision of this Guarantee Agreement shall be
construed to relieve the Guarantee Trustee from liability for its own negligent
action, its own negligent failure to act or its own willful misconduct, except
that:

                           (i) prior to the occurrence of any Event of Default
                  and after the curing or waiving of all such Events of Default
                  that may have occurred:

                                    (A) the duties and obligations of the
                           Guarantee Trustee shall be determined solely by the
                           express provisions of this Guarantee Agreement, and
                           the Guarantee Trustee shall not be liable except for
                           the performance of such duties and obligations as are
                           specifically set forth in this Guarantee Agreement;
                           and

                                    (B) in the absence of bad faith on the part
                           of the Guarantee Trustee, the Guarantee Trustee may
                           conclusively rely, as to the truth of the statements
                           and the correctness of the opinions expressed
                           therein, upon any certificates or opinions furnished
                           to the Guarantee Trustee and conforming to the
                           requirements of this Guarantee Agreement; but in the
                           case of any 


                                       8
<PAGE>   14

                           such certificates or opinions that by any provision
                           hereof or of the Trust Indenture Act are specifically
                           required to be furnished to the Guarantee Trustee,
                           the Guarantee Trustee shall be under a duty to
                           examine the same to determine whether or not they
                           conform to the requirements of this Guarantee
                           Agreement (but need not confirm or investigate the
                           accuracy of mathematical calculations or other facts
                           stated therein);

                           (ii) the Guarantee Trustee shall not be liable for
                  any error of judgment made in good faith by a Responsible
                  Officer of the Guarantee Trustee, unless it shall be proved
                  that the Guarantee Trustee was negligent in ascertaining the
                  pertinent facts upon which such judgment was made;

                           (iii) the Guarantee Trustee shall not be liable with
                  respect to any action taken or omitted to be taken by it in
                  good faith in accordance with the direction of the Holders of
                  not less than a Majority in liquidation amount of the Trust
                  relating to the time, method and place of conducting any
                  proceeding for any remedy available to the Guarantee Trustee,
                  or exercising any trust or power conferred upon the Guarantee
                  Trustee under this Guarantee Agreement; and

                           (iv) no provision of this Guarantee Agreement shall
                  require the Guarantee Trustee to expend or risk its own funds
                  or otherwise incur personal financial liability in the
                  performance of any of its duties or in the exercise of any of
                  its rights or powers.

                  SECTION 3.02. CERTAIN RIGHTS OF GUARANTEE TRUSTEE. (a) Subject
to the provisions of Section 3.01:

                           (i) The Guarantee Trustee may conclusively rely and
                  shall be fully protected in acting or refraining from acting
                  upon any resolution, certificate, statement, instrument,
                  opinion, report, notice, request, direction, consent, order,
                  bond, debenture, note, other evidence of indebtedness or other
                  paper or document (whether in its original or facsimile form)
                  reasonably believed by it to be genuine and to have been
                  signed, sent or presented by the proper party or parties.

                           (ii) Any direction or act of the Guarantor
                  contemplated by this Guarantee Agreement shall be sufficiently
                  evidenced by an Officers' Certificate unless otherwise
                  prescribed herein.

                           (iii) Whenever, in the administration of this
                  Guarantee Agreement, the Guarantee Trustee shall deem it
                  desirable that a matter relating to compliance by the
                  Guarantor with any of its obligations contained in this
                  Guarantee Agreement be proved or established before taking,
                  suffering or omitting to take any action hereunder, the
                  Guarantee Trustee (unless other evidence is herein
                  specifically prescribed) may, in the absence of bad faith on
                  its part, request and conclusively rely upon an Officers'
                  Certificate (with respect to the Guarantor) which, upon


                                       9
<PAGE>   15

                  receipt of such request from the Guarantee Trustee, shall be
                  promptly delivered by the Guarantor.

                           (iv) The Guarantee Trustee may consult with legal
                  counsel of its selection, and the advice or written opinion of
                  such legal counsel with respect to legal matters shall be full
                  and complete authorization and protection in respect of any
                  action taken, suffered or omitted to be taken by it hereunder
                  in good faith and in accordance with such advice or opinion.
                  Such legal counsel may be legal counsel to the Guarantor or
                  any of its Affiliates and may be one of its employees. The
                  Guarantee Trustee shall have the right at any time to seek
                  instructions concerning the administration of this Guarantee
                  Agreement from any court of competent jurisdiction.

                           (v) The Guarantee Trustee shall be under no
                  obligation to exercise any of the rights or powers vested in
                  it by this Guarantee Agreement at the request or direction of
                  any Holder, unless such Holder shall have provided to the
                  Guarantee Trustee such security and indemnity reasonably
                  satisfactory to it, against the costs, expenses (including
                  attorneys' fees and expenses) and liabilities that might be
                  incurred by it in complying with such request or direction,
                  including such reasonable advances as may be requested by the
                  Guarantee Trustee; PROVIDED that nothing contained in this
                  Section 3.02(a)(v) shall be taken to relieve the Guarantee
                  Trustee, upon the occurrence of an Event of Default, of its
                  obligation to exercise the rights and powers vested in it by
                  this Guarantee Agreement.

                           (vi) The Guarantee Trustee shall not be bound to make
                  any investigation into the facts or matters stated in any
                  resolution, certificate, statement, instrument, opinion,
                  report, notice, request, direction, consent, order, bond,
                  debenture, note, other evidence of indebtedness or other paper
                  or document, but the Guarantee Trustee, in its discretion, may
                  make such further inquiry or investigation into such facts or
                  matters as it may see fit and, if the Trustee shall determine
                  to make such further inquiry or investigation, it shall be
                  entitled to examine the books, records and premises of the
                  Guarantor, personally or by agent or attorney at the sole cost
                  of the Guarantor and shall incur no liability or additional
                  liability of any kind by reason of such inquiry or
                  investigation.

                           (vii) The Guarantee Trustee may execute any of the
                  trusts or powers hereunder or perform any duties hereunder
                  either directly or by or through its agents or attorneys, and
                  the Guarantee Trustee shall not be responsible for any
                  misconduct or negligence on the part of any such agent or
                  attorney appointed with due care by it hereunder.

                           (viii) Whenever in the administration of this
                  Guarantee Agreement the Guarantee Trustee shall deem it
                  desirable to receive instructions with respect to enforcing
                  any remedy or right or taking any other action hereunder, the
                  Guarantee Trustee (A) may request instructions from the
                  Holders, (B) may refrain from enforcing such remedy or right
                  or taking such other action until such instructions 


                                       10
<PAGE>   16

                  are received and (C) shall be fully protected in acting in
                  accordance with such instructions.

                  (b) No provision of this Guarantee Agreement shall be deemed
to impose any duty or obligation on the Guarantee Trustee to perform any act or
acts or exercise any right, power, duty or obligation conferred or imposed on it
in any jurisdiction in which it shall be illegal, or in which the Guarantee
Trustee shall be unqualified or incompetent in accordance with applicable law,
to perform any such act or acts or to exercise any such right, power, duty or
obligation. No permissive power or authority available to the Guarantee Trustee
shall be construed to be a duty to act in accordance with such power and
authority.

                  SECTION 3.03. INDEMNITY. The Guarantor agrees to indemnify
each of the Guarantee Trustee, any predecessor Guarantee Trustee and its
directors, officers, agents and employees for, and to hold them harmless
against, any and all loss, damage, claim, liability or expense (including taxes
other than taxes based upon the income of the Guarantee Trustee) incurred
without negligence or bad faith on the part of the Guarantee Trustee, arising
out of or in connection with the acceptance or administration of this Guarantee
Agreement, including the costs and reasonable expenses of defending itself
against any claim or liability in connection with the exercise or performance of
any of its powers or duties hereunder. The Guarantee Trustee will not claim or
exact any lien or charge on any Guarantee Payments as a result of any amount due
to it under this Guarantee Agreement. This indemnity shall survive the
termination of this Guarantee Agreement or the resignation or removal of the
Guarantee Trustee.

                  SECTION 3.04. EXPENSES. The Guarantor shall from time to time
reimburse the Guarantee Trustee for its reasonable expenses and costs incurred
in connection with the performance of its duties hereunder. This reimbursement
obligation shall survive the termination of this Guarantee Agreement or the
resignation or removal of the Guarantee Trustee.


                                   ARTICLE IV

                                Guarantee Trustee
                                -----------------

                  SECTION 4.01. GUARANTEE TRUSTEE; ELIGIBILITY. (a) There shall
at all times be a Guarantee Trustee which shall:

                  (i)  not be an Affiliate of the Guarantor; and

                  (ii) be a Person that is eligible pursuant to the Trust
         Indenture Act to act as such and has a combined capital and surplus of
         at least $50,000,000, and shall be a corporation meeting the
         requirements of Section 310(c) of the Trust Indenture Act. If such
         corporation publishes reports of condition at least annually, pursuant
         to law or to the requirements of the supervising or examining
         authority, then, for the purposes of this Section and to the extent
         permitted by the Trust Indenture Act, the combined capital and surplus
         of such corporation shall be deemed to be its combined capital and
         surplus as set forth in its most recent report of condition so
         published.


                                       11
<PAGE>   17

                  (b) If at any time the Guarantee Trustee shall cease to be
eligible to so act under Section 4.10(a), the Guarantee Trustee shall
immediately resign in the manner and with the effect set out in Section 4.02(c).

                  (c) If the Guarantee Trustee has or shall acquire any
"conflicting interest" within the meaning of Section 310(b) of the Trust
Indenture Act, the Guarantee Trustee and Guarantor shall in all respects comply
with the provisions of Section 310(b) of the Trust Indenture Act.

                  SECTION 4.02. APPOINTMENT, REMOVAL AND RESIGNATION OF THE
GUARANTEE TRUSTEE. (a) Subject to Section 4.02(b), in the absence of the
existence of an Event of Default, the Guarantee Trustee may be appointed or
removed without cause at any time by the Guarantor.

                  (b) The Guarantee Trustee shall not be removed until a
Successor Guarantee Trustee has been appointed and has accepted such appointment
by written instrument executed by such Successor Guarantee Trustee and delivered
to the Guarantor.

                  (c) The Guarantee Trustee appointed hereunder shall hold
office until a Successor Guarantee Trustee shall have been appointed or until
its removal or resignation. The Guarantee Trustee may resign from office
(without need for prior or subsequent accounting) by an instrument in writing
executed by the Guarantee Trustee and delivered to the Guarantor, which
resignation shall not take effect until a Successor Guarantee Trustee has been
appointed and has accepted such appointment by instrument in writing executed by
such Successor Guarantee Trustee and delivered to the Guarantor and the
resigning Guarantee Trustee.

                  (d) If no Successor Guarantee Trustee shall have been
appointed and accepted appointment as provided in this Section 4.02 within 30
days after delivery to the Guarantor of an instrument of resignation, the
resigning Guarantee Trustee may petition, at the expense of the Guarantor, any
court of competent jurisdiction for appointment of a Successor Guarantee
Trustee. Such court may thereupon, after prescribing such notice, if any, as it
may deem proper, appoint a Successor Guarantee Trustee.


                                    ARTICLE V

                                    Guarantee
                                    ---------

                  SECTION 5.01. GUARANTEE. The Guarantor irrevocably and
unconditionally agrees (i) to pay in full on a subordinated basis to the
Holders the Guarantee Payments (without duplication of amounts theretofore paid
by or on behalf of the Issuer), as and when due, regardless of any defense,
right of set-off or counterclaim which the Issuer may have or assert other than
the defense of payment and (ii) to otherwise pay or perform on a subordinated
basis all obligations of Coltec Industries under the Coltec Guarantee Agreement,
the Indenture, the Convertible Junior Subordinated Debentures, and the
Declaration, to the extent not paid or performed by Coltec Industries. The
Guarantor's obligation to make a Guarantee Payment may  


                                       12
<PAGE>   18
be satisfied by direct payment of the required amounts by the Guarantor to the
Holders or by causing the Issuer to pay such amounts to the Holders. The
Guarantor shall give written notice to the Guarantee Trustee as promptly as
practicable in the event it makes any direct payment hereunder.

                  SECTION 5.02. WAIVER OF NOTICE AND DEMAND. The Guarantor
hereby waives notice of acceptance of the Guarantee Agreement and, with respect
to its obligations under Section 5.01, hereby waives presentment, demand for
payment, any right to require a proceeding first against the Guarantee Trustee,
Issuer or any other Person before proceeding against the Guarantor, protest,
notice of nonpayment, notice of dishonor, notice of redemption and all other
notices and demands.

                  SECTION 5.03. OBLIGATIONS NOT AFFECTED. The obligations,
covenants, agreements and duties of the Guarantor under this Guarantee Agreement
shall in no way be affected or impaired by reason of the happening from time to
time of any of the following:

                  (a) the release or waiver, by operation of law or otherwise,
         of the performance or observance by the Issuer of any express or
         implied agreement, covenant, term or condition relating to the Trust
         Securities to be performed or observed by the Issuer;

                  (b) the extension of time for the payment by the Issuer of all
         or any portion of the Distributions (other than any extension of time
         for payment of Distributions that results from the extension of any
         interest payment period on the Convertible Junior Subordinated
         Debentures as so provided in the Indenture), Redemption Price,
         Liquidation Distribution or any other sums payable under the terms of
         the Trust Securities or the extension of time for the performance of
         any other obligation under, arising out of, or in connection with, the
         Trust Securities;

                  (c) any failure, omission, delay or lack of diligence on the
         part of the Holders to enforce, assert or exercise any right,
         privilege, power or remedy conferred on the Holders pursuant to the
         terms of the Trust Securities, or any action on the part of the Issuer
         granting indulgence or extension of any kind;

                  (d) the voluntary or involuntary liquidation, dissolution,
         sale of any collateral, receivership, insolvency, bankruptcy,
         assignment for the benefit of creditors, reorganization, arrangement,
         composition or readjustment of debt of, or other similar proceedings
         affecting, the Issuer or any of the assets of the Issuer;

                  (e) any invalidity of, or defect or deficiency in, the Trust
         Securities;

                  (f) the settlement or compromise of any obligation guaranteed
         hereby or hereby incurred; or

                  (g) any other circumstance whatsoever that might otherwise
         constitute a legal or equitable discharge or defense of a guarantor, it
         being the intent of this Section 5.03 


                                       13
<PAGE>   19
that the obligations of the Guarantor hereunder shall be absolute and
unconditional under any and all circumstances.

                  There shall be no obligation of the Holders to give notice to,
or obtain the consent of, the Guarantor with respect to the happening of any of
the foregoing.

                  SECTION 5.04. RIGHTS OF HOLDERS. The Guarantor expressly
acknowledges that: (i) this Guarantee Agreement will be deposited with the
Guarantee Trustee to be held for the benefit of the Holders; (ii) the Guarantee
Trustee has the right to enforce this Guarantee Agreement on behalf of the
Holders; (iii) the Holders of a Majority in aggregate liquidation amount of the
Trust Securities have the right to direct the time, method and place of
conducting any proceeding for any remedy available to the Guarantee Trustee in
respect of this Guarantee Agreement or exercising any trust or power conferred
upon the Guarantee Trustee under this Guarantee Agreement; and (iv) any Holder
may institute a legal proceeding directly against the Guarantor to enforce its
rights under this Guarantee Agreement, without first instituting a legal
proceeding against the Issuer or any other Person.

                  SECTION 5.05. GUARANTEE OF PAYMENT. This Guarantee Agreement
creates a guarantee of payment and not of collection. If the Issuer fails to
make payments as required, any Holder may immediately bring suit directly
against the Guarantor for payment of all amounts due and payable under this
Guarantee Agreement. This Guarantee Agreement will apply only to the extent that
the Issuer has funds sufficient to make such payments. If Coltec Industries does
not make interest payments on the Convertible Junior Subordinated Debentures
held by the Issuer, the Issuer will not be able to pay Distributions on the
Trust Securities and will not have funds legally available therefor. This
Guarantee Agreement will not be discharged except by payment of the Guarantee
Payments in full (without duplication of amounts theretofore paid by the Issuer)
or upon distribution of Convertible Junior Subordinated Debentures to Holders as
provided in the Declaration.

                  SECTION 5.06. SUBROGATION. The Guarantor shall be subrogated
to all (if any) rights of the Holders against the Issuer in respect of any
amounts paid to the Holders by the Guarantor under this Guarantee Agreement and
shall have the right to waive payment by the Issuer pursuant to Section 5.01;
PROVIDED, HOWEVER, that the Guarantor shall not (except to the extent required
by mandatory provisions of law) be entitled to enforce or exercise any rights
which it may acquire by way of subrogation or any indemnity, reimbursement or
other agreement, in all cases as a result of payment under this Guarantee
Agreement, if at the time of any such payment, any amounts are due and unpaid
under this Guarantee Agreement. If any amount shall be paid to the Guarantor in
violation of the preceding sentence, the Guarantor agrees to hold such amount in
trust for the Holders and to pay over such amount to the Holders. Any amounts
paid over to and not subsequently recovered from the Holders pursuant to any
insolvency law shall be deemed to have been applied by the Holders to the
Guarantee Payments.

                  SECTION 5.07. INDEPENDENT OBLIGATIONS. The Guarantor
acknowledges that its obligations hereunder are independent of the obligations
of the Issuer with respect to the Trust Securities and that the Guarantor shall
(without duplication of amounts paid by or on behalf of the Issuer) be liable as
principal and as debtor hereunder to make Guarantee Payments pursuant 

                                       14
<PAGE>   20
to the terms of this Guarantee Agreement notwithstanding the occurrence of any
event referred to in subsections (a) through (g), inclusive, of Section 5.03
hereof.


                                   ARTICLE VI

                           Covenants and Subordination
                           ---------------------------

                  SECTION 6.01. SUBORDINATION. This Guarantee Agreement will
constitute an unsecured obligation of the Guarantor and will rank subordinate
and junior in right of payment to all Senior Debt of the Guarantor.

                  SECTION 6.02. PARI PASSU GUARANTEES. The obligations under
this Guarantee Agreement shall rank PARI PASSU with the obligations of the
Guarantor relating to the BFG QUIPS(SM) and any similar guarantee agreements
issued by the Guarantor on behalf of the holders of securities issued by a
trust or similar entity created by the Guarantor and similar to Coltec  Capital
Trust, which securities have substantially equivalent terms to those of the
Trust Securities.


                                   ARTICLE VII

              Consolidation, Merger, Conveyance, Transfer or Lease
              ----------------------------------------------------

                  SECTION 7.01. GUARANTOR MAY CONSOLIDATE, ETC., ONLY ON CERTAIN
TERMS. The Guarantor shall not consolidate with or merge with or into any other
Person or sell or lease its assets as, or substantially as, an entirety to any
Person, unless:

                  (a) the Person formed by such consolidation or into which the
         Guarantor is merged or the Person which acquires by sale or lease, the
         assets of the Guarantor as, or substantially as, an entirety, shall be
         a corporation, partnership or trust, shall be organized under the laws
         of the United States of America, any State thereof or the District of
         Columbia and (if other than the Company) such successor Person shall
         expressly assume the performance or observance of every covenant of
         this Guarantee on the part of the Guarantor to be performed or
         observed;

                  (b) immediately after giving effect to such transaction, no
         Event of Default, and no event which, after notice or lapse of time or
         both, would become an Event of Default, shall have happened and be
         continuing; and

                  (c) the Guarantor has delivered to the Trustee an Officers'
         Certificate and an Opinion of Counsel, each stating that such
         consolidation, merger, sale or lease comply with this Article and that
         all conditions precedent herein provided for relating to such
         transaction have been complied with.


                                       15
<PAGE>   21


                                  ARTICLE VIII

                                   Termination
                                   -----------

                  SECTION 8.01. TERMINATION. This Guarantee Agreement shall
terminate and be of no further force and effect upon (i) full payment of the
Redemption Price of all Trust Securities, (ii) the distribution of Convertible
Junior Subordinated Debentures to the Holders in exchange for all of the Trust
Securities or (iii) full payment of the amounts payable in accordance with the
Declaration upon liquidation of the Issuer. Notwithstanding the foregoing, this
Guarantee Agreement will continue to be effective or will be reinstated, as the
case may be, if at any time any Holder must repay any sums paid with respect to
Trust Securities or this Guarantee Agreement.


                                   ARTICLE IX

                                  Miscellaneous
                                  -------------

                  SECTION 9.01. SUCCESSORS AND ASSIGNS. All guarantees and
agreements contained in this Guarantee Agreement shall bind the successors,
assigns, receivers, trustees and representatives of the Guarantor and shall
inure to the benefit of the Holders of the Trust Securities then outstanding.
Except in connection with a consolidation, merger or sale involving the
Guarantor that is permitted under Article VIII of the Indenture and pursuant to
which the assignee agrees in writing to perform the Guarantor's obligations
hereunder, the Guarantor shall not assign its obligations hereunder.

                  SECTION 9.02. AMENDMENTS. Except with respect to any changes
which do not materially adversely affect the rights of the Holders of
Convertible Preferred Securities (in which case no consent of the Holders will
be required), this Guarantee Agreement may only be amended with the prior
approval of the Holders of not less than a Majority of the aggregate liquidation
amount of the outstanding Convertible Preferred Securities. The provisions of
Article VI of the Declaration concerning meetings of the Holders shall apply to
the giving of such approval.

                  SECTION 9.03. NOTICES. Any notice, request or other
communication required or permitted to be given hereunder shall be in writing,
duly signed by the party giving such notice, and delivered, telecopied
(confirmed by delivery of the original) or mailed by first class mail as
follows:

                  (a) if given to the Guarantor, to the address set forth below
         or such other address, facsimile number or to the attention of such
         other Person as the Guarantor may give notice to the Holders:


                                       16
<PAGE>   22

                           The B.F.Goodrich Company
                           4020 Kinross Lakes Parkway
                           Richfield, Ohio  44286-9368

                           Facsimile No.: (330) 659-7727
                           Attention:  Corporate Secretary

                  (b) if given to the Issuer, in care of the Guarantee Trustee,
         at the Issuer's (and the Guarantee Trustee's) address set forth below
         or such other address as the Guarantee Trustee on behalf of the Issuer
         may, at the Issuer's direction, give notice to the Holders:

                           Coltec Capital Trust
                           c/o Coltec Industries Inc
                           3 Coliseum Centre
                           2550 West Tyvola Road
                           Charlotte, North Carolina  28217

                           Facsimile No.: (704) 423-7011
                           Attention:  Corporate Secretary

                           with a copy to:

                           The Bank of New York
                           101 Barclay Street
                           New York, NY 10286

                           Facsimile No.:
                           Attention:  Corporate Trust Administration

                  (c)      if given to the Guarantee Trustee:

                           The Bank of New York
                           101 Barclay Street, Floor 21 West
                           New York, NY 10286

                           Facsimile No.:  (212) 815-5915
                           Attention:  Corporate Trust Administration

                  (d) if given to any Holder, at the address set forth on the
         books and records of the Issuer.

                  All notices hereunder shall be deemed to have been given when
received in person, telecopied with receipt confirmed, or mailed by first class
mail, postage prepaid, except that if a notice or other document is refused
delivery or cannot be delivered because of a changed address of which no notice
was given, such notice or other document shall be deemed to have been delivered
on the date of such refusal or inability to deliver.


                                       17
<PAGE>   23

                  SECTION 9.04. BENEFIT. This Guarantee Agreement is solely for
the benefit of the Holders and is not separately transferable from the
Convertible Preferred Securities.

                  SECTION 9.05. INTERPRETATION. In this Guarantee Agreement,
unless the context otherwise requires:

                  (a) capitalized terms used in this Guarantee Agreement but not
         defined in the preamble hereto have the respective meanings assigned to
         them in Section 1.01;

                  (b) a term defined anywhere in this Guarantee Agreement has
         the same meaning throughout;

                  (c) all references to "the Guarantee Agreement" or "this
         Guarantee Agreement" are to this Guarantee Agreement as modified,
         supplemented or amended from time to time;

                  (d) all references in this Guarantee Agreement to Articles and
         Sections are to Articles and Sections of this Guarantee Agreement
         unless otherwise specified;

                  (e) a term defined in the Trust Indenture Act has the same
         meaning when used in this Guarantee Agreement unless otherwise defined
         in this Guarantee Agreement or unless the context otherwise requires;

                  (f) a reference to the singular includes the plural and vice
         versa; and

                  (g) the masculine, feminine or neuter genders used herein
         shall include the masculine, feminine and neuter genders.

                  SECTION 9.06. GOVERNING LAW. THIS GUARANTEE AGREEMENT SHALL BE
GOVERNED BY AND CONSTRUED AND INTERPRETED IN ACCORDANCE WITH THE LAWS OF THE
STATE OF NEW YORK WITHOUT REGARD TO THE CONFLICT OF LAW PRINCIPLES THEREOF.

                  This instrument may be executed in any number of counterparts,
each of which so executed shall be deemed to be an original, but all such
counterparts shall together constitute but one and the same instrument.




                                       18
<PAGE>   24


                  This GUARANTEE AGREEMENT is executed as of the day and year
first above written.

                                    THE B.F.GOODRICH COMPANY



                                    By
                                      ------------------------------
                                      Name:
                                      Title:


                                    THE BANK OF NEW YORK,
                                    AS GUARANTEE TRUSTEE



                                    By
                                      ------------------------------
                                      Name:
                                      Title:





<PAGE>   1
                                                                     Exhibit 4.4

                             COLTEC INDUSTRIES INC,

                            THE B.F.GOODRICH COMPANY,

                                       AND

                              THE BANK OF NEW YORK,

                                   as Trustee

                          FIRST SUPPLEMENTAL INDENTURE

                           Dated as of April    , 1999
                                            ----

<PAGE>   2



                                            FIRST SUPPLEMENTAL INDENTURE, dated
                           as of April __, 1999, among Coltec Industries Inc, a
                           Pennsylvania corporation (the "Company"), The
                           B.F.Goodrich Company, a New York corporation
                           ("BFGoodrich"), and The Bank of New York, a New York
                           banking corporation, as trustee (herein called the
                           "Trustee"). Terms not defined herein shall have the
                           meanings assigned to them in the Indenture (as
                           defined below).

                  RECITALS OF THE COMPANY AND BFGOODRICH

                  WHEREAS, the Company and the Trustee are parties to an
Indenture, dated as of April 14, 1998 (the "Indenture"), relating to the
Company's 5 1/4% Convertible Junior Subordinated Deferrable Interest Debentures
due 2028 (the "Securities");

                  WHEREAS, on November 22, 1998, the Company, BFGoodrich, and a
wholly owned Pennsylvania subsidiary of BFGoodrich entered into an Agreement and
Plan of Merger (the "Merger Agreement"). Pursuant to the Merger Agreement,
BFGoodrich's subsidiary merged with and into the Company, with the Company being
the surviving corporation in the merger (the "Merger"), and each outstanding
share of common stock of the Company (other than shares held by the Company,
BFGoodrich or any of their direct or indirect subsidiaries) was converted into
the right to receive 0.56 of a fully paid and nonassessable share of common
stock, par value $5 per share, of BFGoodrich ("BFGoodrich Common Stock");

                  WHEREAS, BFGoodrich agrees to be bound by the conversion and
adjustment provisions set forth in the Indenture;

                  WHEREAS, Section 9.01 of the Indenture provides that the
Company, when authorized by a Board Resolution, and the Trustee may enter into a
supplemental indenture, without the consent of any Holder, to, among other
things, make provision with respect to the conversion rights of Holders pursuant
to the requirements of Article XIII of the Indenture; and

                  WHEREAS, the Company and the Trustee have determined that this
First Supplemental Indenture complies with Section 9.01 of the Indenture and
does not require the consent of any Holders and, on the basis of the foregoing,
the Trustee has determined that this First Supplemental Indenture is in form
satisfactory to it.

                  NOW, THEREFORE, for and in consideration of the premises, it
is mutually covenanted and agreed, for the equal and ratable benefit of the
Holders, as follows:


<PAGE>   3

                                    ARTICLE I

                          CONVERSION RIGHTS OF HOLDERS
                          IN CONNECTION WITH THE MERGER


                  SECTION 1.1. CONVERSION RIGHTS. The Company, as the surviving
corporation of the Merger, and BFGoodrich hereby provide in accordance with
Section 13.04 of the Indenture that the Holder of each Security outstanding at
the effective time of the Merger shall have the right, during the period such
Security shall be convertible as specified in Section 13.01 of the Indenture, to
convert such Security only into that number of shares of BFGoodrich Common Stock
equal to the product of 0.955248 and the number of Securities the Holder owns.

                                   ARTICLE II

                          ADJUSTMENT OF CONVERSION RATE

                  SECTION 2.1. ADJUSTMENT. BFGoodrich hereby unconditionally
agrees, as required by Section 13.04 of the Indenture, to make any adjustments
provided for in Article XIII of the Indenture. Notwithstanding anything herein
to the contrary, the Company shall remain obligated under the Indenture and the
Securities, in accordance with the terms of the Indenture, as supplemented
hereby. "Effective Date" shall mean                   , 1999.
                                   -------------------

                                   ARTICLE III

                      ACCEPTANCE OF SUPPLEMENTAL INDENTURE

                  SECTION 3.1. TRUSTEE'S ACCEPTANCE. The Trustee hereby accepts
this First Supplemental Indenture and agrees to perform the same under the terms
and conditions set forth in the Indenture.

                                   ARTICLE IV

                               GENERAL PROVISIONS

                  SECTION 4.1. EFFECT OF SUPPLEMENTAL INDENTURE. On the date
hereof, the Indenture shall be supplemented in accordance herewith, and this
First Supplemental Indenture shall form a part of the Indenture for all
purposes, and every Holder heretofore or hereafter authenticated and delivered
under the Indenture shall be bound thereby.

                  SECTION 4.2. INDENTURE REMAINS IN FULL FORCE AND EFFECT.
Except as supplemented hereby, all provisions in the Indenture shall remain in
full force and effect.


                                       2

<PAGE>   4

                  SECTION 4.3. INCORPORATION OF INDENTURE. All the provisions of
this First Supplemental Indenture shall be deemed to be incorporated in, and
made a part of, the Indenture; and the Indenture, as supplemented and amended by
this First Supplemental Indenture, shall be read, taken and construed as one and
the same instrument.

                  SECTION 4.4. HEADINGS. The headings of the Articles and
Sections of this First Supplemental Indenture are inserted for convenience of
reference and shall not be deemed to be a part thereof.

                  SECTION 4.5. COUNTERPARTS. This First Supplemental Indenture
maybe executed in any number of counterparts, each of which so executed shall be
deemed to be an original, but all such counterparts shall together constitute
but one and the same instrument.

                  SECTION 4.6. CONFIRMATION AND PRESERVATION OF INDENTURE. The
Indenture as supplemented by this First Supplemental Indenture is in all
respects confirmed and preserved.

                  SECTION 4.7. CONFLICT WITH TRUST INDENTURE ACT. If any
provision of this First Supplemental Indenture limits, qualifies or conflicts
with any provision of the Trust Indenture Act that is required under the Trust
Indenture Act to be part of and govern any provision of this First Supplemental
Indenture, the provision of the Trust Indenture Act shall control. If any
provision of this First Supplemental Indenture modifies or excludes any
provision of the Trust Indenture Act that may be so modified or excluded, the
provision of the Trust Indenture Act shall be deemed to apply to the Indenture
as so modified or to be excluded by this First Supplemental Indenture, as the
case may be.

                  SECTION 4.8. SUCCESSORS. All covenants and agreements in this
First Supplemental Indenture by the Company and BFGoodrich shall be binding upon
and accrue to benefit of their respective successors. All covenants and
agreements in this First Supplemental Indenture by the Trustee shall be binding
upon and accrue to the benefit of its successors.

                  SECTION 4.9. SEPARABILITY CLAUSE. In case any provision in
this First Supplemental Indenture shall be invalid, illegal or unenforceable,
the validity, legality and enforceability of the remaining provisions shall not
in any way be affected or impaired thereby.

                  SECTION 4.10. BENEFITS OF FIRST SUPPLEMENTAL INDENTURE.
Nothing in this First Supplemental Indenture or the Securities, express or
implied, shall give to any Person, other than the parties hereto and thereto and
their successors hereunder and thereunder and the Holders, any benefit of any
legal or equitable right, remedy or claim under the Indenture, this First
Supplemental Indenture or the Securities.



                                        3

<PAGE>   5

                  SECTION 4.11. TRUSTEE NOT RESPONSIBLE FOR RECITALS. The
recitals contained herein shall be taken as the statements of the Company and
BFGoodrich, and the Trustee assumes no responsibility for their correctness. The
Trustee makes no representations as to, and shall not be responsible for, the
validity or sufficiency of this First Supplemental Indenture.

                  SECTION 4.12. CERTAIN DUTIES AND RESPONSIBILITIES OF THE
TRUSTEES. In entering into this First Supplemental Indenture, the Trustee shall
be entitled to the benefit of every provision of the Indenture relating to the
conduct or affecting the liability or affording protection to the Trustee,
whether or not elsewhere herein so provided.

                  SECTION 4.13. GOVERNING LAW. THIS FIRST SUPPLEMENTAL INDENTURE
SHALL BE GOVERNED BY, AND CONSTRUED IN ACCORDANCE WITH, THE LAWS OF THE STATE OF
NEW YORK, WITHOUT REGARD TO PRINCIPLES OF CONFLICTS OF LAWS.

                    [Remainder of page intentionally blank.]


                                      4
<PAGE>   6


                  IN WITNESS WHEREOF, the parties hereto have caused this First
Supplemental Indenture to be duly executed, all as of the day and year first
above written.

                                 COLTEC INDUSTRIES INC

                                 By: 
                                     --------------------------------------
                                      Name:
                                      Title:

                                 THE B.F.GOODRICH COMPANY

                                 By: --------------------------------------
                                      Name:
                                      Title:

                                 THE BANK OF NEW YORK, as Trustee

                                 By: --------------------------------------
                                      Name:
                                      Title:

<PAGE>   1


                                                                     Exhibit 5.1

                    [LETTERHEAD OF THE B.F. GOODRICH COMPANY]

                                                                   April 7, 1999


Board of Directors
The B.F. Goodrich Company
4020 Kinross Lakes Parkway
Richfield, Ohio  44286-9368

Directors:

         This opinion is being furnished in connection with the proposed
registration under the Securities Act of 1933, as amended, of (1) up to
2,865,744 shares of common stock (collectively, the "Shares") of The
B.F.Goodrich Company, a New York corporation (the "Company"), which are to be
issued from time to time by the Company following the consummation of the merger
(the "Merger") of Runway Acquisition Corporation, a Pennsylvania corporation and
a wholly owned subsidiary of the Company, with and into Coltec Industries Inc, a
Pennsylvania corporation, to the holders of convertible preferred securities
issued by Coltec Capital Trust and (2) the Guarantee Agreement (the "Guarantee")
and the Supplemental Indenture (the "Supplemental Indenture"), each to be dated
as of April __, 1999, between the Company and The Bank of New York, as trustee.
I have examined such corporate records and other documents, including the
pre-effective Amendment No. 1 to the Registration Statement on Form S-3 relating
to the Shares, the forms of the Guarantee and the Supplemental Indenture,
together with the Prospectus contained in such Registration Statement and any
amendments or supplements thereto (the "Registration Statement"), and have
reviewed such matters of law as I have deemed necessary or appropriate for this
opinion.

         Based on such examination and review, it is my opinion that, (a) when
issued as contemplated by the Registration Statement, the Shares will be duly
authorized, validly issued, fully paid and nonassessable and (b) each of the
Guarantee and the Supplemental Indenture, when duly authorized, executed and
delivered, will be a valid and binding agreement of the Company, enforceable
against the Company in accordance with its terms. The opinion in clause (b) of
the preceding sentence is limited to the extent that the enforceability of the
Guarantee and the Supplemental Indenture may be limited by bankruptcy,
insolvency or similar laws affecting the enforcement of the rights of creditors
generally and by general principles of equity (regardless of whether such
enforceability is sought in a proceeding in equity or at law).

         I consent to be named in the Registration Statement as the attorney who
passed upon the validity of the Shares and the enforceability of the Guarantee
and the Supplemental Indenture, and to the filing of a copy of this opinion as
an exhibit to the Registration Statement.


                                                 Sincerely,


                                                 /s/ Nicholas J. Calise
                                                 ------------------------------
                                                 Nicholas J. Calise
                                                 Vice President, Associate
                                                  General Counsel and Secretary

<PAGE>   1
                                                                      Exhibit 25
================================================================================
                                    FORM T-1

                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

                            STATEMENT OF ELIGIBILITY
                   UNDER THE TRUST INDENTURE ACT OF 1939 OF A
                    CORPORATION DESIGNATED TO ACT AS TRUSTEE

                      CHECK IF AN APPLICATION TO DETERMINE
                      ELIGIBILITY OF A TRUSTEE PURSUANT TO
                             SECTION 305(b)(2) |__|

                                 ---------------

                              THE BANK OF NEW YORK
               (Exact name of trustee as specified in its charter)


New York                                            13-5160382
(State of incorporation                             (I.R.S. employer
if not a U.S. national bank)                        identification no.)

One Wall Street, New York, N.Y.                     10286
(Address of principal executive offices)            (Zip code)

                                 ---------------

                            The B.F.Goodrich Company
               (Exact name of obligor as specified in its charter)


New York                                             34-0252680
(State or other jurisdiction of                      (I.R.S. employer
incorporation or organization)                       identification no.)


4020 Kinross Lakes Parkway
Richfield, Ohio                                      44286-9368
(Address of principal executive offices)             (Zip code)

                                 ---------------

                  Guarantee of Convertible Preferred Securities
                             of Coltec Capital Trust
                       (Title of the indenture securities)
================================================================================

<PAGE>   2


1.       GENERAL INFORMATION. FURNISH THE FOLLOWING INFORMATION AS TO THE
         TRUSTEE:

         (a)     NAME AND ADDRESS OF EACH EXAMINING OR SUPERVISING AUTHORITY TO
                 WHICH IT IS SUBJECT.
<TABLE>
- --------------------------------------------------------------------------------
                Name                                 Address
- --------------------------------------------------------------------------------
<S>                                               <C> 
         Superintendent of Banks of the State of   2 Rector Street, New York,
         New York                                  N.Y. 10006, and Albany, N.Y. 12203

         Federal Reserve Bank of New York          33 Liberty Plaza, New York,
                                                   N.Y.  10045

         Federal Deposit Insurance Corporation     Washington, D.C.  20429

         New York Clearing House Association       New York, New York   10005
</TABLE>

         (b)     WHETHER IT IS AUTHORIZED TO EXERCISE CORPORATE TRUST POWERS.

         Yes.

2.       AFFILIATIONS WITH OBLIGOR.

         IF THE OBLIGOR IS AN AFFILIATE OF THE TRUSTEE, DESCRIBE EACH SUCH 
         AFFILIATION.

         None.

16.      LIST OF EXHIBITS.

         EXHIBITS IDENTIFIED IN PARENTHESES BELOW, ON FILE WITH THE COMMISSION,
         ARE INCORPORATED HEREIN BY REFERENCE AS AN EXHIBIT HERETO, PURSUANT TO
         RULE 7A-29 UNDER THE TRUST INDENTURE ACT OF 1939 (THE "ACT") AND 17
         C.F.R. 229.10(d).

         1.      A copy of the Organization Certificate of The Bank of New York
                 (formerly Irving Trust Company) as now in effect, which
                 contains the authority to commence business and a grant of
                 powers to exercise corporate trust powers. (Exhibit 1 to
                 Amendment No. 1 to Form T-1 filed with Registration Statement
                 No. 33-6215, Exhibits 1a and 1b to Form T-1 filed with 
                 Registration Statement No. 33-21672 and Exhibit 1 to Form T-1
                 filed with Registration Statement No. 33-29637.)

         4.      A copy of the existing By-laws of the Trustee. (Exhibit 4 to
                 Form T-1 filed with Registration Statement No. 33-31019.)

         6.      The consent of the Trustee required by Section 321(b) of the
                 Act. (Exhibit 6 to Form T-1 filed with Registration Statement
                 No. 33-44051.)

         7.       A copy of the latest report of condition of the Trustee
                  published pursuant to law or to the requirements of its
                  supervising or examining authority.


                                       2
<PAGE>   3


                                    SIGNATURE

         Pursuant to the requirements of the Act, the Trustee, The Bank of New
York, a corporation organized and existing under the laws of the State of New
York, has duly caused this statement of eligibility to be signed on its behalf
by the undersigned, thereunto duly authorized, all in The City of New York, and
State of New York, on the 6th day of April, 1999.


                                                THE BANK OF NEW YORK



                                                By: /s/ Michele L. Russo
                                                   ---------------------------
                                                    Name: Michele L. Russo
                                                    Title: Assistant Treasurer
<PAGE>   4
- --------------------------------------------------------------------------------
                       Consolidated Report of Condition of

                              THE BANK OF NEW YORK

                    of One Wall Street, New York, N.Y. 10286
                     And Foreign and Domestic Subsidiaries,
a member of the Federal Reserve System, at the close of business December 31,
1998, published in accordance with a call made by the Federal Reserve Bank of
this District pursuant to the provisions of the Federal Reserve Act.


<TABLE>
<CAPTION>

                                                                                               Dollar Amounts
ASSETS                                                                                          in Thousands
<S>                                                                                            <C>   
Cash and balances due from depository institutions:
   Noninterest-bearing balances and currency and coin.                                           $3,951,273
   Interest-bearing balances..........................                                            4,134,162
Securities:
   Held-to-maturity securities........................                                              932,468
   Available-for-sale securities......................                                            4,279,246
Federal funds sold and Securities purchased under                                                 
   agreements to resell...............................                                            3,161,626
Loans and lease financing receivables:
   Loans and leases, net of unearned
     income...............37,861,802
   LESS: Allowance for loan and
     lease losses............619,791
   LESS: Allocated transfer risk
     reserve........................3,572
   Loans and leases, net of unearned income,                                                   
     allowance, and reserve...........................                                           37,238,439
Trading Assets........................................                                            1,551,556
Premises and fixed assets (including 
   capitalized leases)................................                                              684,181
Other real estate owned...............................                                               10,404
Investments in unconsolidated subsidiaries and                                                     
   associated companies...............................                                              196,032
Customers' liability to this bank on acceptances                                                    
   outstanding........................................                                              895,160
Intangible assets.....................................                                            1,127,375
Other assets..........................................                                            1,915,742
                                                                                                -----------
Total assets..........................................                                          $60,077,664
                                                                                                ===========
</TABLE>

<PAGE>   5

<TABLE>
<CAPTION>

LIABILITIES
Deposits:
<S>                                                                                        <C>        
   In domestic offices................................                                          $27,020,578
   Noninterest-bearing......................11,271,304
   Interest-bearing.........................15,749,274
   In foreign offices, Edge and Agreement                                                        
     subsidiaries, and IBFs...........................                                           17,197,743
   Noninterest-bearing.........................103,007
   Interest-bearing.........................17,094,736
Federal funds purchased and Securities sold 
   under agreements to repurchase.....................                                            1,761,170
Demand notes issued to the U.S.Treasury...............                                              125,423
Trading liabilities...................................                                            1,625,632
Other borrowed money:
   With remaining maturity of one year or 
     less.............................................                                            1,903,700
   With remaining maturity of more than one 
     year through three years.........................                                                    0
   With remaining maturity of more than 
     three years......................................                                               31,639
Bank's liability on acceptances executed and                                                        
   outstanding........................................                                              900,390
Subordinated notes and debentures.....................                                            1,308,000
Other liabilities.....................................                                            2,708,852
                                                                                                 ----------
Total liabilities.....................................                                           54,583,127
                                                                                                 ==========
EQUITY CAPITAL
Common stock..........................................                                            1,135,284
Surplus...............................................                                              764,443
Undivided profits and capital reserves................                                            3,542,168
Net unrealized holding gains (losses) on                                                          
   available-for-sale securities......................                                               82,367
Cumulative foreign currency translation 
   adjustments........................................                                              (29,725)
                                                                                                -----------
Total equity capital..................................                                            5,494,537
                                                                                                -----------
Total liabilities and equity capital..................                                          $60,077,664
                                                                                                ===========
</TABLE>

<PAGE>   6

         I, Thomas J. Mastro, Senior Vice President and Comptroller of the
above-named bank do hereby declare that this Report of Condition has been
prepared in conformance with the instructions issued by the Board of Governors
of the Federal Reserve System and is true to the best of my knowledge and
belief.

                                                         Thomas J. Mastro

         We, the undersigned directors, attest to the correctness of this Report
of Condition and declare that it has been examined by us and to the best of our
knowledge and belief has been prepared in conformance with the instructions
issued by the Board of Governors of the Federal Reserve System and is true and
correct.

Thomas A. Reyni    -
Gerald L. Hassell  -                Directors
Alan R. Griffith   -

- --------------------------------------------------------------------------------



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