Document:

<PAGE>   1
                                                                    EXHIBIT 10.4

                               SECOND AMENDMENT TO

                              ACQUISITION AGREEMENT

         THIS SECOND AMENDMENT TO ACQUISITION AGREEMENT (this "Amendment"), made
as of the 30 day of May, 2000, by and among BOYD BROS. TRANSPORTATION INC., a
Delaware corporation (hereinafter referred to as "Boyd"), WELBORN TRANSPORT,
INC., (formerly known as W. T. Acquisition Corp.), an Alabama corporation
(hereinafter referred to as "Boyd Sub"), MILLER WELBORN ("Welborn") and STEVEN
RUMSEY ("Rumsey") (Welborn and Rumsey are hereinafter sometimes collectively
referred to as the "Shareholders").

                              W I T N E S S E T H:

         WHEREAS, Boyd, Boyd Sub and the Shareholders (together with Welborn
Transport, Inc., which was merged into Boyd Sub) entered into an Acquisition
Agreement, dated October 8, 1997, as amended by that certain First Amendment to
Acquisition Agreement, Employment Agreement and Covenant Not to Compete, dated
March 17, 2000 (as amended, the "Acquisition Agreement"); and

         WHEREAS, Boyd, Boyd Sub and the Shareholders desire to amend the
Acquisition Agreement to modify certain terms and conditions contained therein,
all as more particularly set forth herein.

         NOW, THEREFORE, for and in consideration of the premises and the mutual
promises, agreements, representations, warranties and covenants hereinafter set
forth, and the sum of ten dollars and other good and valuable consideration, the
receipt and sufficiency of which is hereby specifically agreed to and
acknowledged, the Acquisition Agreement is hereby amended as follows:

         1. AMENDMENT TO ACQUISITION AGREEMENT. Section 4.5.2. of the
Acquisition Agreement is hereby amended by deleting said Section in its entirety
and substituting in lieu thereof a new 4.5.2 reading as follows:

         "4.5.2. During the Restricted Period, the shares of Boyd Common Stock
         held by Steven Rumsey shall not be voluntarily or involuntarily
         transferred, assigned, sold or conveyed and the certificates
         representing such shares shall bear a legend to that effect. The words
         "transfer, assign, sell or convey" shall have the meaning set forth in
         Section 4.5.1. After the Restricted Period, Steven Rumsey may not,
         during any one (1) calendar quarter, voluntarily or involuntarily
         transfer, assign, sell or convey a number of shares of Boyd Common
         Stock which is greater than one percent of the number of shares of Boyd
         Common Stock outstanding at the beginning of such calendar quarter. In
         the event that during (a) the five (5) calendar quarters immediately
         following the Restricted Period or (b) the five (5) calendar quarters
         immediately following the third (3rd) anniversary of the Closing Date
         (collectively, these two five-quarter periods are hereinafter referred
         to as

<PAGE>   2

         the "Floor Periods") Steven Rumsey sells shares of Boyd Common Stock on
         the open market at a per share price which is less than the Per Share
         Minimum Price, Boyd shall pay to Steven Rumsey the difference between
         the Per Share Minimum Price and the per share price at which such
         shares were sold on the open market, such payment to be made within ten
         (10) days after Steven Rumsey transmits to Boyd confirmation of such
         sale. Notwithstanding anything to the contrary contained in this
         Agreement, in the event Steven Rumsey elects to sell shares of Boyd
         Common Stock on the open market during the Floor Periods at a price
         that is less than the Per Share Minimum Price, then Steven Rumsey must
         first deliver written notice thereof, in the form of Exhibit 4.5.2(a)
         attached hereto (a "Rumsey Offer Notice"), to the Chief Financial
         Officer of the Company in order to provide the Company a right of first
         refusal on the following terms and conditions:

                  (a)      The Rumsey Offer Notice must contain a full
                           description of the proposed sale of Boyd Common Stock
                           by Steven Rumsey, including, without limitation, the
                           number of shares of to be sold (the "Rumsey Affected
                           Shares"), the proposed price per share of the Boyd
                           Common Stock, terms of payment for the Rumsey
                           Affected Shares and the proposed date of such sale. A
                           Rumsey Offer Notice shall constitute Steven Rumsey's
                           binding agreement to sell all of the Rumsey Affected
                           Shares to the Company on the terms and conditions
                           specified therein.

                  (b)      If the Company elects to purchase all, and not less
                           than all, of the Rumsey Affected Shares from Steven
                           Rumsey, the Company shall have until 5 p.m. Clayton,
                           Alabama time on the first business day following the
                           Company's receipt of the Rumsey Offer Notice (the
                           "Rumsey Offer Deadline") to deliver to Steven Rumsey,
                           in writing, notice of its election to so purchase the
                           Rumsey Affected Shares (the "Company Rumsey
                           Acceptance"). Upon such election by the Company, the
                           Company shall purchase, and Steven Rumsey shall sell,
                           of the Rumsey Affected Shares to the Company upon the
                           terms and conditions contained in the Rumsey Offer
                           Notice within three (3) business days following
                           Steven Rumsey's receipt of the Company Rumsey
                           Acceptance. At the closing, Steven Rumsey shall
                           deliver to the Company his confirmation that he has
                           transferred the Rumsey Affected Shares free and clear
                           of any and all pledges, liens, claims, security
                           interests or other encumbrances (other than
                           restrictions imposed by this Agreement or applicable
                           securities laws) and the Company shall pay to Steven
                           Rumsey the consideration set forth in the Rumsey
                           Offer Notice in accordance with the terms described
                           therein, as well as any additional payments in
                           connection with the Per Share Minimum Price
                           contemplated by the first paragraph of this Section
                           4.5.2.

         If the Company fails to provide Steven Rumsey notice of its election to
         purchase or not to purchase the Rumsey Affected Shares on or before the
         Rumsey Offer Deadline, or if the Company notifies that it has elected
         not to purchase the Rumsey Affected Shares, Steven Rumsey shall be free
         to sell the Rumsey Affected Shares on the open market in strict
         accordance with the terms set forth in the Rumsey Offer Notice at any
         time within

<PAGE>   3

         ninety (90) days after the Rumsey Offer Deadline (the "Rumsey Transfer
         Period Termination Date"). In the event that Steven Rumsey does not
         sell or otherwise dispose of all of such Rumsey Affected Shares in the
         manner set forth in the immediately preceding sentence prior to the
         Rumsey Transfer Period Termination Date, the right of first refusal
         provided for in this Section 4.5.2 shall continue to be applicable to
         any subsequent sale or transfer of such Rumsey Affected Shares."

         2. NO OTHER MODIFICATIONS. Except to the extent expressly amended
herein, all terms and conditions of the Acquisition Agreement are hereby
affirmed and shall remain in full force and effect.

         3. GOVERNING LAW. This Amendment shall be governed by and construed and
interpreted in accordance with, the laws of the State of Alabama without giving
effect to any conflict or choice of laws principles.

         4. COUNTERPARTS. This Amendment may be executed in two or more
counterparts, each of which shall be deemed an original, but all of which
together shall constitute one and the same instrument.

                      [SIGNATURES BEGIN ON FOLLOWING PAGE]

<PAGE>   4

         IN WITNESS WHEREOF, each party hereto has executed or caused this
Amendment to be executed on its behalf, all on the day and year first above
written.

                                    BOYD BROS. TRANSPORTATION INC.

                                    "Boyd"

                                By: /s/ Richard Bailey
                                    --------------------------------------------
                                    Name: Richard Bailey
                                          --------------------------------------
                                    Title: CFO
                                           -------------------------------------

                                    WELBORN TRANSPORT, INC.

                                    "Boyd Sub"

                                By: /s/ Richard Bailey
                                    --------------------------------------------
                                    Name: Richard Bailey
                                          --------------------------------------
                                    Title: CFO
                                           -------------------------------------

                                    SHAREHOLDERS

                                    /s/ Miller Welborn
                                    --------------------------------------------
                                    Miller Welborn

                                    /s/ Steven Rumsey
                                    --------------------------------------------
                                    Steven Rumsey<PAGE>   1
                                                                    EXHIBIT 10.5

                               SECOND AMENDMENT TO
                              EMPLOYMENT AGREEMENT

         THIS SECOND AMENDMENT TO EMPLOYMENT AGREEMENT (this "Amendment"), made
as of the 22 day of May, 2000, by and among BOYD BROS. TRANSPORTATION INC., a
Delaware corporation (hereinafter referred to as "Boyd"), and STEVEN RUMSEY
("Rumsey").

                              W I T N E S S E T H:

         WHEREAS, Boyd and Rumsey entered into an Employment Agreement, dated as
of December 8, 1997, as amended by that certain First Amendment to Acquisition
Agreement, Employment Agreement and Covenant Not to Compete by and between Boyd,
Rumsey, Miller Welborn and Welborn Transport, Inc., an Alabama corporation,
dated March 17, 2000 (as amended, the "Rumsey Employment Agreement"); and

         WHEREAS, Boyd and Rumsey desire to amend the Rumsey Employment
Agreement to modify certain terms and conditions contained therein, all as more
particularly set forth herein.

         NOW, THEREFORE, for and in consideration of the premises and the mutual
promises, agreements, representations, warranties and covenants hereinafter set
forth, and the sum of ten dollars and other good and valuable consideration, the
receipt and sufficiency of which is hereby specifically agreed to and
acknowledged, the Rumsey Employment Agreement is hereby amended as follows:

         1. AMENDMENT TO RUMSEY EMPLOYMENT AGREEMENT. The parties acknowledge
that the Rumsey Employment Agreement has been extended for each of the two
one-year extension periods set forth in Section 1 of the Rumsey Employment
Agreement, as such Section exists prior to being amended hereby. Section 1 of
the Rumsey Employment Agreement is hereby amended by deleting said Section in
its entirety and substituting in lieu thereof a new Section 1 reading as
follows:

         "1. Term of Employment. Boyd hereby employs Employee and Employee
         hereby accepts such employment upon the terms and conditions set forth
         in this Agreement. The term ("Term") of Employee's employment under
         this Agreement shall be for a period commencing from the date hereof
         (the "Effective Date") and terminating on the first anniversary of the
         Effective Date (the "Termination Date"), unless such employment is
         terminated or extended prior to the expiration of said period as
         hereinafter provided. Employee shall have the right to extend the Term
         for up to three (3) additional one year periods by providing notice to
         Boyd, in the case of the first such extension, within thirty (30) days
         prior to the Termination Date, in the case of the second such
         extension, within thirty (30) days prior to the anniversary of the
         Termination Date, and in the case of the third such extension, within
         thirty (30) days prior to the second (2nd) anniversary of the
         Termination Date."

<PAGE>   2

         2. NO OTHER MODIFICATIONS. Except to the extent expressly amended
herein, all terms and conditions of the Rumsey Employment Agreement are hereby
affirmed and shall remain in full force and effect.

         3. GOVERNING LAW. This Amendment shall be governed by and construed and
interpreted in accordance with, the laws of the State of Alabama without giving
effect to any conflict or choice of laws principles.

         4. COUNTERPARTS. This Amendment may be executed in two or more
counterparts, each of which shall be deemed an original, but all of which
together shall constitute one and the same instrument.

                      [SIGNATURES BEGIN ON FOLLOWING PAGE]

<PAGE>   3

         IN WITNESS WHEREOF, each party hereto has executed or caused this
Amendment to be executed on its behalf, all on the day and year first above
written.

                                    BOYD BROS. TRANSPORTATION INC.

                                    "Boyd"

                                    By: /s/ Richard Bailey
                                        ----------------------------------------
                                    Name: Richard Bailey
                                          --------------------------------------
                                    Title: CFO
                                           -------------------------------------

                                    /s/ Steven S. Rumsey
                                    --------------------------------------------
                                    Steven Rumsey

Source: [{"source": "alea-institute/alea-institute/kl3m-data-edgar-agreements/train-00022-of-00352.parquet"}, [{"source": "alea-institute/alea-institute/kl3m-data-edgar-agreements/train-00022-of-00352.parquet"}]]