<PAGE>
 
                                                                   EXHIBIT 10(y)

                             UNITED RENTALS, INC.



                SERIES A PERPETUAL CONVERTIBLE PREFERRED STOCK,
                                $.01 Par Value





                      PREFERRED STOCK PURCHASE AGREEMENT








December 21, 1998
<PAGE>
 
                               TABLE OF CONTENTS
                               -----------------
                                                                          Page
                                                                          ----

1.  Authorization of Stock................................................  2

2.  Sale and Purchase of Stock............................................  2

3.  Closing; Payment of Purchase Price....................................  3

4.  Conditions to Closing.................................................  3
    4.1  Representations and Warranties...................................  4
    4.2  Performance; No Default..........................................  4
    4.3  Compliance Certificates..........................................  4
    4.4  Opinion of Counsel...............................................  4
    4.5  Certificate of Designation.......................................  4
    4.6  Registration Rights Agreement....................................  4
    4.7  [omitted]........................................................  4
    4.8  [omitted]........................................................  4
    4.9  No Actions Pending...............................................  5
    4.10 Compliance with Securities Laws..................................  5
    4.11 Proceedings and Documents........................................  5
    4.12 Reservation of Common Stock......................................  5
    4.13 Payment of Fees and Expenses.....................................  5
    4.14 HSR Act..........................................................  5

5.  Representations and Warranties........................................  5
    5.1  Organization, Standing, etc......................................  6
    5.2  Subsidiaries.....................................................  6
    5.3  Qualification....................................................  6
    5.4  Business; Financial Statements...................................  6
    5.5  Changes, etc.....................................................  7
    5.6  Capital Stock and Related Matters................................  7
    5.7  Tax Returns and Payments.........................................  8
    5.8  Indebtedness of the Company......................................  8
    5.9  Title to Properties, Liens.......................................  9
    5.10 Litigation, etc..................................................  9
    5.11 Compliance with Other Instruments, etc...........................  9
    5.12 Governmental Consents, etc....................................... 10



                                      ii
<PAGE>
 
    5.13 Offering of Securities........................................... 11
    5.14 Certain Fees..................................................... 11
    5.15 Investment Company Act........................................... 11
    5.16 Disclosure....................................................... 11
    5.17 Enforceability................................................... 12
    5.18 [omitted]........................................................ 12
    5.19 Integration...................................................... 12
    5.20 Manipulation..................................................... 12
    5.21 Acquired Companies............................................... 12
    5.22 Intellectual Property............................................ 12
    5.23 Government Licenses.............................................. 13
    5.24 Environmental Laws............................................... 13
    5.25 Insurance........................................................ 14
    5.26 Internal Controls................................................ 14
    5.27 ERISA............................................................ 14
    5.28 Year 2000 Compliance............................................. 15

6.  Investment Representations............................................ 15
    6.1  Acquisition for Own Account...................................... 15
    6.2  Ability to Protect Own Interests................................. 15
    6.3  Accredited Investor.............................................. 16
    6.4  Access to Information............................................ 16
    6.5  No Brokers....................................................... 16
    6.6  Compliance with Laws............................................. 16

7.  Affirmative Covenants................................................. 16
    7.1  Exchange Act and Securities Act Filings.......................... 16
    7.2  Certificates; Other Information.................................. 17
    7.3  [omitted]........................................................ 17
    7.4  [omitted]........................................................ 17
    7.5  Inspection of Property; Books and Records; Discussions........... 17
    7.6  Notices.......................................................... 17
    7.7  Reservation of Common Stock...................................... 18
    7.8  Availability of Information...................................... 18
    7.9  Public Announcements............................................. 18

8.  Registration, Transfer and Substitution of Certificates for Stock..... 18
    8.1  Stock Register; Ownership of Stock............................... 18
    8.2  Replacement of Certificates...................................... 19



                                      iii
<PAGE>
 
    8.3  Restrictive Legends.............................................. 19
    8.4  Notice of Proposed Transfer; Opinions of Counsel................. 20
    8.5  Termination of Restrictions...................................... 21

9.  Definitions........................................................... 21
    9.1  Certain Defined Terms............................................ 21
    9.2  Accounting Terms................................................. 25
    9.3  Other Provisions Regarding Definitions........................... 25

10. Expenses, etc......................................................... 25

11. Survival of Representations and Warranties and
    Indemnification; Certain Limitations.................................. 26

12. Amendments and Waivers................................................ 26

13. Notices, etc.......................................................... 26

14. Indemnification....................................................... 27

15. Termination........................................................... 28

16. Miscellaneous......................................................... 28


Exhibit A    Form of Restated Certificate of Incorporation
---------                                                             

Exhibit B    Form of Opinion of Counsel for the Company
---------                                                         

Exhibit C    Form of Opinion of Counsel for the Company
---------                                                         

Exhibit D    Form of Registration Rights Agreement
---------                                                         

Exhibit E    Subsidiaries of the Company, exceptions to representations 
---------    and warranties 

Exhibit F    Indebtedness of the Company and the Subsidiaries
---------                                                            


                                      iv
<PAGE>
 
                             United Rentals, Inc.
                          Four Greenwich Office Park,
                              Greenwich, CT 06830

                                                               December 21, 1998

Apollo Investment Fund IV, L.P.
Apollo Overseas Partners IV, L.P.
c/o Apollo Management IV, L.P.
1301 Avenue of the Americas, 38th Floor
New York, NY 10019

Dear Sirs:

          United Rentals, Inc., a Delaware corporation (the "Company"), agrees
with Apollo Investment Fund IV, L.P. and Apollo Overseas Partners IV, L.P.
(together, the "Purchasers") as follows:

          1.   Authorization of Stock. The Company will authorize the issue
               ----------------------
and sale of 300,000 shares (the "Shares", such term to include any such shares
issued in substitution therefor pursuant to section 8) of its Series A Perpetual
Convertible Preferred Stock, $.01 par value, to be designated as its "Series A
Perpetual Convertible Preferred Stock" (the "Stock"). The relative rights,
preferences and limitations of the Stock, including, without limitation, the
right to convert Shares into shares of the Company's common stock, par value
$.01 per share (the "Common Stock"), will be as set forth in the form of the
Certificate of Designation of the Stock of the Company attached as Exhibit A
hereto (the "Certificate of Designation"). Certain capitalized terms used in
this Agreement are defined in Section 9; references to a "Schedule" or an
"Exhibit" are, unless otherwise specified, to a Schedule or an Exhibit attached
to this Agreement and references to a "section" are, unless otherwise specified,
to one of the sections of this Agreement.

          2.   Sale and Purchase of Stock. The Company will issue and sell
               --------------------------
to the Purchasers and, subject to the terms and conditions of this Agreement,
the

                                       2
<PAGE>
 
Purchasers will purchase from the Company, at the Closing provided for in
section 3, the Shares at a purchase price of $ 1,000 per share.

          3.   Closing, Payment of Purchase Price. The sale of the Shares to
               ----------------------------------
be purchased by the Purchasers shall take place at the offices of Skadden, Arps,
Slate, Meagher & Flom LLP, 919 Third Avenue, New York, New York 10022, at 10: 00
a.m., New York City time, at a closing (the "Closing") on the first Business Day
after the conditions to closing set forth in Section 4 (other than those to be
satisfied at the Closing, which shall be satisfied or waived at the Closing)
have been satisfied or waived by the party entitled to waive such condition or
on such other Business Day thereafter or prior to such date as may be agreed
upon by the Company and the Purchasers, provided that in no event shall the
Closing occur earlier than the 11th Business Day following the date of this
Agreement.

          The names in which the Company will register the shares of the Stock
to be purchased at the Closing are as set forth in Exhibit 1. At the Closing,
the Company will deliver to the Purchasers the Shares to be purchased by the
Purchasers in the form of a single certificate (or such greater number of
certificates representing such Shares as the Purchasers may request) dated the
date of the Closing and registered in the names aforesaid, and the Purchasers
jointly and severally shall deliver to the Company or its order immediately
available funds in the amount of the purchase price for such Shares. If at the
Closing the Company shall fail to tender to the Purchasers the Shares to be
purchased by the Purchasers, as provided above in this Section 3, or any of the
conditions specified in Section 4 shall not have been fulfilled to the
Purchasers' reasonable satisfaction, the Purchasers shall, at their election, be
relieved of all further obligations under this Agreement, without thereby
waiving any other rights the Purchasers may have by reason of such failure or
such nonfulfillment. If at the Closing, Purchasers shall fail to tender to the
Company the purchase price for the Shares, as provided above in this Section 3,
other than on account of any of the conditions specified in section 4 not having
been fulfilled to the Purchasers' satisfaction or on account of the breach by
the Company of any of its obligations under this Agreement, the Company shall,
at its election, be relieved of all further obligations under this Agreement,
without thereby waiving any other rights the Company may have by reason of such
failure.

          4.   Conditions to Closing. The Purchasers' obligation to purchase
               ---------------------
and pay for the Shares to be sold to the Purchasers at the Closing is subject to
the fulfillment to their reasonable satisfaction, prior to or concurrently with
the Closing, of the following conditions:

                                       3
<PAGE>
 
          4.1    Representations and Warranties. The representations and
                 -------------------------------
          warranties of the Company contained in this Agreement shall be in all
material respects correct when made and at the time of the Closing, except as
affected by the consummation of the transactions contemplated by this Agreement.

          4.2    Performance, No Default. The Company shall have performed
                 -----------------------
          and complied in all material respects with all agreements and
conditions contained in this Agreement required to be performed or complied with
by it prior to or at the Closing.

          4.3    Compliance Certificates. The Company shall have delivered
                 -----------------------
          to the Purchasers an Officers' Certificate, dated the date of the
Closing, certifying that the conditions specified in sections 4.1 and 4.2 have
been fulfilled.

          4.4    Opinion of Counsel. The Purchasers shall have received the
                 ------------------
          favorable opinions, dated the date of the Closing and reasonably
satisfactory in substance and form to the Purchasers from Ehrenreich, Eilenberg
Krause & Zivian LLP and Weil, Gotshal & Manges LLP, counsel for the Company,
substantially in the form set forth in Exhibits B and C and covering such other
matters incident to the transactions contemplated by this Agreement as the
Purchasers or their counsel may reasonably request.

          4.5    Certificate of Designation. The Certificate of Designation 
                 ---------------------------
shall have been duly filed under the laws of the State of Delaware, and the
Restated Certificate of Incorporation of the Company, as amended by the
Certificate of Designation, shall be in full force and effect, and shall not
have been otherwise amended or modified.

          4.6    Registration Rights Agreement. The Purchasers shall have
                 -----------------------------
received a fully executed counter-part of the Registration Rights Agreement
substantially in the form set out in Exhibit D (the "Registration Rights
Agreement"), such agreement shall be in full force and effect and no term or
condition thereof shall have been amended, modified or waived.

          4.7    [omitted]

          4.8    [omitted]

                                       4
<PAGE>
 
          4.9    No Actions Pending. There shall be no suit, action, 
                 ------------------
investigation, inquiry or other proceeding by any Governmental Authority or any
other Person or any other legal or administrative proceeding pending or to the
knowledge of the Company threatened which questions the validity or legality of
the transactions contemplated by this Agreement, or seeks damages in connection
therewith.

          4.10  Compliance with Securities Laws. The offering and sale by the 
                -------------------------------                              
Company, at or prior to the Closing, of the Shares pursuant to this Agreement
shall have been made in compliance with all applicable requirements of federal
and state securities laws and the Purchasers shall have received evidence
thereof in form and substance reasonably satisfactory to the Purchasers.

          4.11  Proceedings and Documents. All corporate and other proceedings
                -------------------------                               
in connection with the transactions contemplated by this Agreement and all
documents and instruments incident to such transactions shall be reasonably
satisfactory to the Purchasers and their counsel, and the Purchasers and their
counsel shall have received all such counterpart originals or certified or other
copies of such documents as the Purchasers or their counsel may reasonably
request.

          4.12  Reservation of Common Stock. The shares of Common Stock
                ---------------------------                                 
initially issuable upon conversion of the Stock shall have been duly authorized
and reserved for issuance upon conversion of the Stock.

          4.13  Payment of Fees and Expenses. The Company shall have paid the 
                ----------------------------                      
Purchasers on or before the Closing (a) a fee equal to 1% of the purchase price
of the Stock and (b) the costs and expenses provided for in Section 10 hereof,
provided that the Purchasers shall have provided to the Company a statement of
its estimated costs and expenses at least one Business Day prior to the Closing.

          4.14  HSR Act. Any waiting period (and any extension thereof) under
                -------
the Hart-Scott-Rodino Antitrust Improvements Act of 1976, as amended, applicable
to this Agreement and the transactions contemplated hereby shall have expired or
been terminated.

          5.    Representations and Warranties. Except as disclosed in
                ------------------------------
Exhibit E, the Company represents and warrants that:

                                       5
<PAGE>
 
          5.1   Organization, Standing, etc. The Company is a corporation
                ---------------------------
duly organized, validly existing and in good standing under the laws of the
State of Delaware and has all requisite corporate power and authority to own and
operate its properties, to carry on its business as now conducted and as
proposed to be conducted, to enter into and perform all of its obligations
under this Agreement and each of the Collateral Agreements to which it is a
party, to issue and sell the Shares to be issued and sold at the Closing and to
carry out the transactions contemplated hereby or thereby.

          5.2   Subsidiaries. Exhibit E correctly lists as to each Subsidiary
                ------------
of the Company on the date of this Agreement (a) its name, (b) the jurisdiction
of its incorporation and (c) the percentage of its issued and outstanding shares
owned by the Company or by another Subsidiary of the Company (specifying such
other Subsidiary), as the case may be. Each Subsidiary of the Company is a
corporation duly organized, validly existing and in good standing under the laws
of the jurisdiction of its incorporation and has all requisite corporate power
and authority to own and operate its properties and to carry on its business as
now conducted and as proposed to be conducted. All the outstanding shares of
capital stock of each Subsidiary of the Company are validly issued, fully paid
and nonassessable, and all such shares indicated in Exhibit E as owned by the
Company or by a Subsidiary of the Company are so owned beneficially and of
record by the Company or by such Subsidiary, as the case may be, free and clear
of any Lien except as indicated in Exhibit E.

          5.3   Qualification. Each of the Company and its Subsidiaries is
                -------------
duly qualified and in good standing as a foreign corporation authorized to do
business in each jurisdiction (other than the jurisdiction of its incorporation)
in which the nature of its activities or the character of the properties it owns
or leases makes such qualification necessary and in which the failure so to
qualify would have a Material Adverse Effect. A "Material Adverse Effect 'shall
mean any effect that is materially adverse to the properties, business, results
of operations or financial condition of the Company and its Subsidiaries taken
as a whole.

          5.4   Business; Financial Statements. The Company has delivered to 
                ------------------------------
the Purchasers complete and correct copies of the audited supplemental
consolidated balance sheets of the Company and its Subsidiaries as of December
31, 1997 and December 31, 1996, and the related audited supplemental
consolidated statements of operations, stockholders' equity and cash flows of
the Company and its Subsidiaries for the years ended December 31, 1997, 1996 and
1995. Such audited

                                       6
<PAGE>
 
financial statements are hereinafter referred to as the "Financial Statements."
The Financial Statements are accompanied by the report of Ernst & Young LLP 1997
and 1996 and by the report of Price Waterhouse Coopers for 1995, which state
that the Financial Statements have been prepared in accordance with GAAP
consistently applied throughout the periods involved (except as otherwise
specified therein) and present fairly the financial position of the corporations
to which they relate as of the respective dates specified and the results of
their operations and changes in financial position for the respective periods
specified, and that the audit by such accountants of the Financial Statements
has been made in accordance with generally accepted auditing standards. The
Company has also delivered to the Purchasers complete and correct copies of the
unaudited consolidated balance sheet of the Company and its Subsidiaries as of
September 30, 1998, and the related unaudited consolidated statement of
operations, stockholders' equity and cash flows of the Company and its
Subsidiaries for the three month period ended on such date. Such unaudited
financial statements are hereinafter referred to as the "Unaudited Statements."
The Unaudited Statements have been prepared in accordance with GAAP consistently
applied throughout the periods involved (except as otherwise specified therein)
and present fairly the financial position of the Company and its Subsidiaries as
of the respective dates specified, and the results of their operations and
changes in cash flows for the respective periods specified. As of the date of
this Agreement, the Purchasers are not aware that this representation is
incorrect in any material respect.

          5.5   Changes, etc. Since September 30, 1998, neither the Company 
                -------------
nor any of the Subsidiaries has sustained any loss or interference with its
business from fire, explosion, flood or other calamity, whether or not covered
by insurance, or from any labor dispute or court or governmental action, order
or decree which would be material to the Company and the Subsidiaries taken as a
whole, otherwise than as reserved for as disclosed in the Company's financials
statements; and there has not been any change in the capital stock of the
Company or increase in the long-term debt (other than accretion or scheduled
repayments thereof) of the Company and the Subsidiaries taken as a whole, or any
material adverse change which has had a Material Adverse Effect, in each case
otherwise than as set forth on Exhibit E.

          5.6   Capital Stock and Related Matters. At the time of the Closing
                ---------------------------------
and after giving effect to the transactions contemplated by this Agreement, the
authorized capital stock of the Company will consist of (a) 500,000,000 shares
of Common Stock, of which approximately 68,500,000 shares will be outstanding,
(b) 300,000 shares of Series A Perpetual Convertible Preferred Stock, of which

                                       7
<PAGE>
 
300,000 shares will be outstanding, and (c) 4,700,000 shares of preferred stock,
undesignated as to terms, none of which are outstanding. The Company is
obligated to issue Common Stock on conversion of debentures held by United
Rentals Trust 1, a business trust organized under Delaware law. The Common Stock
and the Stock are hereinafter collectively referred to as "Capital Stock". All
of the outstanding shares of Capital Stock are, and at the Closing will be,
validly issued and outstanding, fully paid and non-assessable. Except as set
forth above and on Exhibit E, the Company has no outstanding stock or securities
convertible into or exchangeable for any shares of its Capital Stock, or any
outstanding rights (either preemptive or other) to subscribe for or to purchase,
or any outstanding options for the purchase of, or any agreements providing for
the issuance (contingent or otherwise) of, or any outstanding calls,
commitments or claims of any character relating to, any Capital Stock or any
stock or securities convertible into or exchangeable for any Capital Stock of
the Company. Except as set forth on Exhibit E, the Company is not subject to any
obligation (contingent or otherwise) to repurchase or otherwise acquire or
retire any shares of its Capital Stock or any convertible securities, rights or
options of the type described in the preceding sentence. Neither the Company nor
any of its Subsidiaries is a party to, or has knowledge of, any agreement
(except as set forth on Exhibit E) restricting the transfer of any shares of the
Company's Capital Stock which would affect the transferability of the Common
Stock issuable upon conversion of the Stock.

          5.7   Tax Returns and Payments. The Company and each of the
                ------------------------
Subsidiaries have filed all necessary federal, state, local and foreign income,
payroll, franchise and other tax returns (after giving effect to extensions) and
have paid all taxes shown as due thereon (except where the failure to so file or
pay would not, singly or in the aggregate, have a Material Adverse Effect), and
there is no tax deficiency that has been, or to the knowledge of the Company is
likely to be, asserted against the Company, any of the Subsidiaries or any of
their properties or assets that would result in a Material Adverse Effect,
except for taxes that are being contested in good faith by appropriate
proceedings and with respect to which the Company has established adequate
reserves in accordance with United States generally accepted accounting
principles.

          5.8   Indebtedness of the Company. Exhibit F correctly describes
                ---------------------------
all secured and unsecured Indebtedness of the Company and its Subsidiaries
(other than intercompany items) outstanding, or for which the Company or one of
its Subsidiaries has commitments, which is individually in excess of $5,000,000
("Significant Indebtedness") (excluding operating leases), on the date of this
Agree-

                                       8
<PAGE>
 
ment. The secured and unsecured Indebtedness of the Company and its Subsidiaries
(other than intercompany items, and other than Significant Indebtedness)
outstanding, or for which the Company or one of its Subsidiaries has
commitments does not in the aggregate exceed $1,600,000,000 on the date of this
agreement. Neither the Company nor any of its Subsidiaries is in default with
respect to any Indebtedness or any instrument or agreement relating thereto,
except for such defaults as would not, either in any case or in the aggregate,
have a Material Adverse Effect.

          5.9   Title to Properties; Liens. The Company and each of the
                --------------------------
Subsidiaries have good and marketable title to all real property (other than
property which is leased) material to the conduct of the business of the Company
and the Subsidiaries, taken as a whole, and good and marketable title to all
personal property (other than property which is leased) material to the conduct
of the business of the Company and the Subsidiaries, taken as a whole, in each
case free and clear of all liens, encumbrances and defects except such as are
described on Exhibit E or such as do not in the aggregate have a Material
Adverse Effect; and any real property and buildings held under lease by the
Company and the Subsidiaries, material to the conduct of the business of the
Company and the Subsidiaries, taken as a whole, are held by them under valid,
subsisting and enforceable leases with such exceptions as are described on
Exhibit E and except for such other exceptions as do not have a Material Adverse
Effect.

          5.10  Litigation, etc. There is no action, proceeding or investigation
                ---------------
pending or (to the knowledge of the Company) threatened (or any basis therefor
known to the Company) which questions the validity of this Agreement, the Shares
or any action taken or to be taken pursuant to this Agreement, the Shares or the
Collateral Agreements. Other than as set forth on Exhibit E, there are no legal
or governmental proceedings pending to which the Company or any of the
Subsidiaries is a party or of which any property of the Company or the
Subsidiaries is the subject, which if determined adversely to the Company or any
of the Subsidiaries, would individually or in the aggregate have a Material
Adverse Effect; and, to the Company's knowledge, no such proceedings which
would in the aggregate have a Material Adverse Effect are threatened or
contemplated by governmental authorities or threatened by others.

          5.11  Compliance with Other Instruments, etc. Neither the Company
                --------------------------------------
nor any of its Subsidiaries is in violation of any term of its certificate
or articles of incorporation or by-laws, and neither the Company nor any of its
Subsidiaries is in violation of any term of any agreement or instrument to which
it is a party or by

                                       9
<PAGE>
 
which it is bound or any term of any applicable law, ordinance, rule or
regulation of any Governmental Authority or any term of any applicable order,
judgment or decree of any court, arbitrator or Governmental Authority, the
consequences of which violation could reasonably be expected to have a Material
Adverse Effect. The compliance by the Company with all of the provisions of this
Agreement and the Registration Rights Agreement, the execution, delivery and
performance by the Company of this Agreement and the Registration Rights
Agreement, the issuance by the Company of the Common Stock upon the conversion
of the Shares, and the compliance with the terms of the Certificate of
Designation will not conflict with or result in a breach or violation of any of
the terms and provisions of, or constitute a default under, any indenture,
mortgage, deed of trust, loan agreement (provided the consent of the Company's
lending banks must be obtained before the Company makes an offer to purchase
under Section 5 of the Certificate of Designation) or other agreement or
instrument to which the Company or any of the Subsidiaries is a party or by
which the Company or any of the Subsidiaries is bound or to which any of the
property or assets of the Company or any of the Subsidiaries is subject, or
constitute a Repayment Event thereunder, nor will such actions result in any
violation of the provisions of the certificate of incorporation or bylaws of the
Company or any of the Subsidiaries or any statute or any order, rule or
regulation of any court or governmental agency or body having jurisdiction
over the Company or any of the Subsidiaries or any of their properties except
in each case as would not, individually or in the aggregate have a Material
Adverse Effect. Except as set forth on Exhibit E, the execution, delivery and
performance by the Company of this Agreement and the transactions contemplated
hereby will not subject the Company to or accelerate any obligation to make
payments to any Person.

          5.12  Governmental Consents, etc. Except as required under the
                --------------------------
HSR Act, no consent, approval or authorization of, or declaration or filing
with, any Governmental Authority on the part of the Company is required for the
valid execution and delivery of this Agreement, the valid offer, issue, sale and
delivery of the Shares pursuant to this Agreement or the valid issue and
delivery of shares of Common Stock issuable upon conversion of the Stock. Except
for (a) the requirements of the HSR Act and applicable state securities or blue
sky laws, and (b) consents, approvals, filings or notices that will be given or
made at or prior to the time of the Closing, neither the Company nor any of its
Subsidiaries is required to obtain any consent, approval or authorization of, or
to make any declaration or filing with, any Governmental Authority as a
condition to the valid execution, delivery or performance of any of the
Collateral Agreements or the consummation of the transactions contemplated
thereby.

                                       10
<PAGE>
 
          5.13  Offering of Securities. Neither the Company nor any Person
                ----------------------
acting on its behalf has offered the Stock or any similar securities of the
Company to, or solicited any offers to buy any thereof from, or otherwise
approached or negotiated with respect thereto with, any Person or Persons other
than the Purchasers in such manner as would subject the offering, issuance or
sale of any of the Stock to the provisions of Section 5 of the Securities Act.
Neither the Company nor any Person acting on behalf of the Company has taken or
will take any action which would subject the offering, issuance or sale of any
of the Stock to the provisions of Section 5 of the Securities Act.

          5.14  Certain Fees. Except for the fee payable by the Company to
                ------------
Goldman Sachs & Co., the amount of which will be disclosed to the Purchasers in
writing prior to the Closing, no broker's or finder's fees or commissions will
be payable by the Company with respect to the transactions contemplated by this
Agreement and the Collateral Agreements, and the Company hereby indemnifies the
Purchasers against and agrees that it will hold the Purchasers harmless from any
claim, demand or liability for broker's or finder's fees alleged to have been
incurred at the instance of the Company or any Person acting on behalf of or at
the request of the Company or any agent of the Company in connection with any of
the transactions contemplated by this Agreement and the Collateral Agreements,
and from any expenses, including reasonable legal fees, arising in connection
with any such claim, demand or liability.

          5.15  Investment Company Act. The Company is not an "investment 
                ----------------------
company" or a company "controlled" by an "investment company" within the meaning
of the Investment Company Act of 1940, as amended.

          5.16  Disclosure. None of this Agreement, the Financial Statements,
                ----------
the Annual Report on Form 10K for the year ended December 31, 1997, any document
filed by the Company with the Securities and Exchange Commission pursuant to the
Securities Exchange Act of 1994 (the "Exchange Act") since the Annual Report on
Form 10K for the year ended December 31, 1997, the Unaudited Statements, or the
Company's Offering Circular dated December 8, 1998 in respect of its 9-1/4%
Senior Subordinated Notes due 2009, contains (in each case, as of its date, and,
in the case of the Offering Circular, also as of the date of this Agreement) any
untrue statement of a material fact or omits to state a material fact necessary
in order to make the statements contained herein or therein, in light of the
circumstances under which they are made, not misleading.

                                       11
<PAGE>
 
          5.17  Enforceability. This Agreement and the Registration Rights
                --------------
Agreement have been duly authorized and when validly executed and delivered by
the Company (assuming the due authorization, execution and delivery thereof by
the other parties thereto) will constitute the valid and binding obligations of
the Company, enforceable in accordance with their respective terms, except as
the enforcement thereof may be limited by bankruptcy, insolvency (including,
without limitation, all laws relating to fraudulent transfers), reorganization,
moratorium or other similar laws relating to or affecting enforcement of
creditors' rights generally, or by general principles of equity (regardless of
whether enforcement is considered in a proceeding in equity or at law).

          5.18  [omitted]

          5.19  Integration. Neither the Company nor any affiliate (as such
                -----------
term is defined in Rule 501 (b) under the Securities Act) has, directly or
through any agent, sold, offered for sale, solicited offers to buy or
otherwise negotiated in respect of, any security (as defined in the Securities
Act) which is or will be integrated with the sale of the Shares, in a manner
that would require the registration of the Securities under the Securities Act.

          5.20  Manipulation. Prior to the date hereof, neither the Company
                ------------                                             
nor any of its affiliates has taken any action which is designed to or which has
constituted or which might have been expected to cause or result in
stabilization or manipulation of the price of any security of the Company in
connection with the sale of the Shares.

          5.21  Acquired Companies. To the best knowledge of the Company, the 
                ------------------                                     
representations and warranties made by each of the Acquired Companies (as
defined in Section 9) and the selling stockholders in the respective agreements
pursuant to which the Company or another Subsidiary acquired the Acquired
Companies did not as of the respective dates thereof contain any inaccuracies
that would, singly or in the aggregate, have a Material Adverse Effect.

          5.22  Intellectual Property. The Company and the Subsidiaries own
                ---------------------
possess, or can acquire on reasonable terms, adequate patents, patent rights,
licenses, inventions, copyrights, know-how (including trade secrets and other
unpatented and/or unpatentable proprietary or confidential information, systems
or procedures), trademarks, service marks, trade names or other intellectual
property

                                       12
<PAGE>
 
(collectively, "Intellectual Property") necessary to carry on the business now
operated by them, and neither the Company nor any of the Subsidiaries has
received any notice or is otherwise aware of any infringement of or conflict
with asserted rights of others with respect to any Intellectual Property or of
any facts or circumstances which would render any Intellectual Property invalid
or inadequate to protect the interest of the Company or any of the Subsidiaries
therein, and which infringement or conflict (if the subject of any unfavorable
decision, ruling or finding) or invalidity or inadequacy, singly or in the
aggregate, would result in a Material Adverse Effect.

          5.23  Government Licenses. The Company and the Subsidiaries possess 
                -------------------                                
such permits, licenses, approvals, consents and other authorizations
(collectively, "Governmental Licenses") issued by the appropriate federal,
state, local or foreign regulatory agencies or bodies necessary to conduct the
business now operated by them, except where the failure to so possess such
Government Licenses would not, singly or in the aggregate, have a Material
Adverse Effect; the Company and the Subsidiaries are in compliance with the
terms and conditions of all such Governmental Licenses, except where the failure
so to comply would not, singly or in the aggregate, have a Material Adverse
Effect; all of the Governmental Licenses are valid and in full force and effect,
except when the invalidity of such Governmental Licenses or the failure of such
Governmental Licenses to be in full force and effect would not have, singly or
in the aggregate, a Material Adverse Effect; and neither the Company nor any of
the Subsidiaries has received any notice of proceedings relating to the
revocation or modification of any such Governmental Licenses which, singly or in
the aggregate, if the subject of an unfavorable decision, ruling or finding,
would result in a Material Adverse Effect.

          5.24  Environmental Laws. Except as described on Exhibit E or
                ------------------                                         
except as would not, singly or in the aggregate, result in a Material Adverse
Effect: (a) neither the Company nor any of the Subsidiaries is in violation of
any federal, state, local or foreign statute, law, rule, regulation, ordinance,
code, policy or rule of common law or any judicial or administrative
interpretation thereof, including any judicial or administrative order, consent,
decree or judgment, relating to pollution or protection of human health, the
environment (including, without limitation, ambient air, surface water,
groundwater, land surface or subsurface strata) or wildlife, including, without
limitation, laws and regulations relating to the release or threatened release
of chemicals, pollutants, contaminants, wastes, toxic substances, hazardous
substances, petroleum or petroleum products (collectively, "Hazardous
Materials") or to the manufacture, processing, distribution, use, treatment,
storage, disposal, transport or handling of Hazardous Materials (collectively,
"Environmental

                                       13
<PAGE>
 
Laws"), (b) neither the Company nor any of the Subsidiaries is lacking any
permits, authorizations and approvals required under any applicable
Environmental Laws or are in violation of the requirements of such Environmental
Laws, (c) there are no pending or, to the best knowledge of the Company,
threatened administrative, regulatory or judicial actions, suits, demands,
demand letters, claims, liens, notices of noncompliance or violation,
investigation or proceedings relating to any Environmental Law against the
Company or any of the Subsidiaries and (d) to the knowledge of the Company there
are no events or circumstances that might reasonably be expected to form the
basis of an order for clean-up or remediation, or an action, suit or proceeding
by any private party or governmental body or agency, against or affecting the
Company or any of the Subsidiaries relating to Hazardous Materials or any
Environmental Laws.

          5.25  Insurance. Neither the Company nor any Subsidiary has received 
                ---------
notice from any insurer providing insurance coverage for the Company and the
Subsidiaries or agent of such insurer that capital improvements or other
expenditures will have to be made in order to continue present insurance
coverage, except such as could not reasonably be expected, singularly or in the
aggregate, to have a Material Adverse Effect.

          5.26  Internal Controls. The Company and the Subsidiaries maintain 
                -----------------                                     
a system of internal accounting controls sufficient to provide reasonable
assurances that (a) transactions are executed in accordance with management's
general or specific authorization; (b) transactions are recorded as necessary
(i) to permit preparation of financial statements in conformity with generally
accepted accounting principles and (ii) to maintain accountability for assets;
(c) access to assets is permitted only in accordance with management's general
or specific authorization; and (d) the recorded accountability for assets is
compared with existing assets at reasonable intervals and appropriate action is
taken with respect to any material differences. Any exceptions to this
representation would not render the representation in Section 5.4 incorrect in
any material respect or have a Material Adverse Effect.

          5.27  ERISA. Neither the Company nor any of the Subsidiaries has
                -----
violated any provisions of the Employee Retirement Income Security Act of 1974,
as amended ("ERISA"), or the rules and regulations promulgated thereunder,
except for such violations which, singly or in the aggregate, would not have a
Material Adverse Effect. If any plan subject to ERISA is adopted, the execution
and delivery of this Agreement and the sale of the Securities will not involve
any non-exempt prohibited

                                       14
<PAGE>
 
transaction within the meaning of Section 406 of ERISA or Section 4975 of the
Internal Revenue Code of 1986, as amended.

          5.28  Year 2000 Compliance. With such exceptions as would not
                --------------------
have a Material Adverse Effect, the Company has been advised by its vendors (and
has no reason to believe that such advice is not correct) that as of the date of
this Agreement, all Date Data and Date-Sensitive Systems used by the Company and
its Subsidiaries are Year 2000 Compliant. "Date-Sensitive System" means any
software, microcode or hardware system or component, including any electronic
or electronically controlled system or component, that uses or processes any
Date Data and that is installed, in development or on order by the Company or
any of its subsidiaries for their internal use or for the use of third parties,
or which the Company or any of its subsidiaries sell, lease, license, assign
or otherwise provide to any third party. "Year 2000 Compliant" means (i) with
respect to Date Data, that such data is in proper format and accurate for all
dates, including for those before, on and after December 31, 1999 and (ii) with
respect to Date-Sensitive Systems, that each such system accurately processes
all Date Data, including for dates before, on and after December 31, 1999,
without loss of any functionality or performance, including but not limited to
calculating, comparing, sequencing, storing and displaying such Date Data
(including all leap year considerations), when used as a stand-alone system or
in combination with other software or hardware.

          6.    Investment Representations. The Purchasers understand that
                --------------------------
neither the Shares nor any Common Stock issuable upon conversion, if any, of the
Shares has been registered under the Securities Act and that the certificates
for the Shares and such Common Stock will bear a legend to that effect. The
Purchasers also understand that the Shares are being, offered and sold pursuant
to an exemption from registration contained in the Securities Act, based in part
upon their representations contained in this Agreement. The Purchasers hereby
represent and warrant as follows:

          6.1   Acquisition for Own Account. The Purchasers are acquiring
                ---------------------------
the Shares for their own account for investment and not with a view toward
distribution in a manner which would violate the Securities Act.

          6.2   Ability to Protect Own Interests. The Purchasers represent
                --------------------------------
that by reason of their business or financial experience, or the business and
financial experience of their management, the Purchasers have the capacity to
protect their own interests in connection with the transaction contemplated in
this Agreement.

                                       15
<PAGE>
 
The Purchasers are not a corporation formed for the specific purpose of
consummating this transaction.

          6.3   Accredited Investor. The Purchasers represent that they are an
                -------------------                                         
"accredited investor" as that term is defined in Regulation D promulgated under
the Securities Act.

          6.4   Access to Information. The Purchasers have been given access 
                ---------------------                              
to all Company documents, records, and other information, have received physical
delivery of all those which the Purchasers have requested, and have had adequate
opportunity to ask questions of, and receive answers from, the Company's
officers, employees, agents, accountants, and representatives concerning the 
Company's business, operations, financial condition, assets, liabilities, and
all other matters relevant to its investment in the Shares.

          6.5   No Brokers. Purchasers represent and warrant to the Company 
                ----------
that no broker's or finder's fees or commissions will be payable by the
Purchasers with respect to the transactions contemplated by this Agreement and
the Collateral Agreements, and the Purchasers hereby jointly and severally
indemnify and hold the Company harmless from any claim, demand or liability for
broker's or finder's fees alleged to have been incurred at the instance of the
Purchasers, their affiliates or agents or any Person acting on behalf of or at
the request of the Purchasers, their affiliates or agents.

          6.6   Compliance with Laws. Purchasers and their transferees will
                --------------------                                           
comply with all filing and other reporting obligations under all Requirements of
Law which shall be applicable to Purchasers with respect to the Shares and to
the Common Stock issuable or issued on conversion of the Shares.

          7.    Affirmative Covenants. The Company covenants that from
                ---------------------                                          
and after the date of this Agreement through the Closing and thereafter so long
as the Purchasers own at least 25,000 Shares or 1,000,000 shares of Common Stock
which have been acquired upon conversion of any Shares:

          7.1   Exchange Act and Securities Act Filings. The Company will
                ---------------------------------------
deliver to the Purchasers, within three Business Days of their filing with the
Securities and Exchange Commission, all documents filed by it with the
Securities and Exchange Commission pursuant to the Securities Act or the
Exchange Act, including exhibits thereto.

                                       16
<PAGE>
 
          7.2   Certificates, Other Information. The Company will deliver to
                -------------------------------
the Purchasers: (a) promptly upon receipt thereof, copies of all final reports
submitted to the Company or any of its Subsidiaries by independent certified
public accountants in connection with each annual, interim or (but only if the
holders of the Shares are then entitled under the Certificate of Designation to
elect as a class at least one member of the Company's Board of Directors)
special audit of the books of the Company or any of its Subsidiaries made by
such accountants, including, without limitation, any final comment letter
submitted by such accountants to management in connection with their annual
audit; and (b) promptly upon their becoming available, copies of all financial
statements, reports, notices and proxy statements sent or made available
generally by the Company to all of its security holders in their capacity as
such or by any Subsidiary of the Company to its security holders.

          7.3   [omitted]

          7.4   [omitted]

          7.5   Inspection of Property, Books and Records, Discussions. The
                ------------------------------------------------------
Company will, and will cause each of its Subsidiaries to keep proper books of
record and account in which entries in conformity with GAAP and all Requirements
of Law shall be made of all dealings and transactions in relation to its
business and activities

          7.6   Notices. The Company will, within 48 hours of occurrence, give
                -------
notice to the Purchasers: (a) of any (i) default or event of default under any
instrument or other agreement of the Company or any of its Subsidiaries which
default or event of default would have a Material Adverse Effect or (ii)
litigation, investigation or proceeding which may exist at any time between the
Company or any of its Subsidiaries and any Governmental Authority, which in any
such case, if adversely determined, could reasonably be expected to have a
Material Adverse Effect; and (b) of any litigation or proceeding affecting the
Company or any of its Subsidiaries (i) in which the amount claimed is $2,000,000
or more and not covered by insurance or covered by reserves on the Company's
balance sheet, or (ii) in which injunctive or similar relief is sought which if
obtained could reasonably be expected to have a Material Adverse Effect.

          Each notice pursuant to this section 7.6 shall be accompanied by a
statement of the chief executive officer or chief financial officer of the
Company

                                       17
<PAGE>
 
setting forth details of the occurrence referred to therein and stating what
action the Company proposes to take with respect thereto.

          7.7   Reservation of Common Stock. The Company will at all times 
                ---------------------------
reserve and keep available, solely for issuance and delivery upon conversion of
the Stock, the number of shares of Common Stock from time to time issuable upon
conversion of all shares of the Stock at the time outstanding. All shares of
Common Stock issuable upon conversion of the Stock shall be duly authorized and,
when issued upon such conversion, shall be validly issued, fully paid and non-
assessable.

          7.8   Availability of Information. The Company will comply with the 
                ---------------------------
reporting requirements of Sections 13 and 15(d) of the Exchange Act and will
comply with all other public information reporting requirements of the
Securities and Exchange Commission (including Rule 144 promulgated by the
Securities and Exchange Commission under the Securities Act) from time to time
in effect and relating to the availability of an exemption from the Securities
Act for the sale of any Restricted Securities. The Company will also reasonably
cooperate with each holder of any Restricted Securities in supplying such
information as may be necessary for such holder to complete and file any
information reporting forms presently or hereafter required by the Securities
and Exchange Commission as a condition to the availability of an exemption from
the Securities Act for the sale of any Restricted Securities.

          7.9   Public Announcements. Attached hereto is the text of the press
                --------------------
releases which the parties shall issue publicly to announce the execution of
this Agreement.

          8.    Registration, Transfer and Substitution of Certificates for
                ------------------------------------------------------------
          Stock.
          ------

          8.1   Stock Register, Ownership of Stock. (a) The Company will keep 
                -----------------------------------                    
at its principal office a register in which the Company will provide for the
registration of the stock and the registration of transfers or conversion of the
Stock. The Company may treat the Person in whose name any of the Shares or
shares issued upon conversion of any of the Stock are registered on such
register as the owner thereof and the Company shall not be affected by any
notice to the contrary. All references in this Agreement to a "holder" of any
Shares or shares issued upon conversion of any of the Stock shall mean the
Person in whose name such Shares or

                                       18
<PAGE>
 
shares issued upon conversion of any of the Stock are at the time registered on
such register.

                (b) Upon the surrender of any certificate for Stock, properly
endorsed, for registration of transfer or for conversion at the office of the
Company maintained pursuant to subdivision (a) of this section 8.1, the Company
at its expense will (subject to compliance with section 8.2 hereof, if
applicable) execute and deliver to or upon the order of the holder thereof (i) a
new certificate or certificates for the same aggregate number of shares of
Stock less the number of shares of Stock being converted, if any, in the name of
such holder or as such holder (upon payment by such holder of any applicable
transfer taxes) may direct, and (ii) a certificate or certificates for the
number of shares of Common Stock to be issued upon conversion of the shares of
Stock so surrendered.

          8.2   Replacement of Certificates. Upon receipt of evidence 
                ---------------------------
reasonably satisfactory to the Company of the loss, theft, destruction or
mutilation of any certificate representing shares of Stock or Common Stock
issued upon the conversion of shares of Stock and, in the case of any such loss,
theft or destruction of any certificate representing shares of Stock or Common
Stock issued upon the conversion of shares of Stock held by a Person other than
the Purchasers, upon delivery of indemnity reasonably satisfactory to the
Company in form and amount or, in the case of any such mutilation, upon
surrender of such certificate representing shares of Stock or Common Stock
issued upon the conversion of shares of Stock for cancellation at the office of
the Company maintained pursuant to subdivision (a) of section 8.1 hereof, the
Company at its expense will execute and deliver, in lieu thereof, a new
certificate representing shares of Stock or Common Stock of like tenor.

          8.3   Restrictive Legends. Except as otherwise permitted by this
                -------------------
section 8, each certificate for Stock (including each certificate for Stock
issued upon the transfer of any certificate for Stock) shall be stamped or
otherwise imprinted with a legend in substantially the following form:

                "The shares represented by this Certificate and any shares of
          Common Stock issuable upon conversion of any such shares have not been
          registered under the Securities Act of 1933 and may not be transferred
          in the absence of such registration or an exemption there from under
          such Act. Such shares and any such shares of Common Stock may be
          transferred only in compliance with the conditions

                                       19
<PAGE>
 
          specified in the Preferred Stock Purchase Agreement dated December __,
          1998 between United Rentals, Inc. (the "Company") and the purchasers
          identified therein. A complete and correct copy of such Agreement is
          available for inspection at the principal office of the Company and
          will be furnished without charge to the holder of such shares upon
          written request."

Except as otherwise permitted by this section 8, each certificate for Common
Stock issued upon the conversion of any of the Stock, and each certificate
issued upon the transfer of any such Common Stock, shall be stamped or otherwise
imprinted with a legend in substantially the following form:

               "The shares represented by this certificate have not been
          registered under the Securities Act of 1933 and may not be transferred
          in the absence of such registration or an exemption therefrom under
          such Act. Such shares may be transferred only in compliance with the
          conditions specified in the Preferred Stock Purchase Agreement dated
          December , 1998 between United Rentals, Inc. (the "Company") and the
          purchasers identified therein. A complete and correct copy of such
          Agreement is available for inspection at the principal office of the
          Company and will be furnished without charge to the holder of such
          shares upon written request."

          8.4   Notice of Proposed Transfer; Opinions of Counsel. Prior to
                ------------------------------------------------
any transfer of any Restricted Securities which are not registered under an
effective registration statement under the Securities Act, the holder thereof
will give written notice to the Company of such holder's intention to effect
such transfer and to comply in all other respects with this section 8.4. Each
such notice shall describe the manner and circumstances of the proposed transfer
and shall be accompanied by an opinion of counsel for such holder, which counsel
and opinion shall each be reason ably satisfactory to the Company, that the
proposed transfer may be effected without registration of such shares of
Restricted Securities under the Securities Act. Such holder shall thereupon be
entitled to transfer such shares in accordance with the terms of the notice
delivered by such holder to the Company. Each certificate representing such
shares issued upon or in connection with such transfer shall bear the
restrictive legends required by section 8.3, unless the related restrictions on
transfer shall have ceased and terminated as to such shares pursuant to section
8.5 hereof

                                       20
<PAGE>
 
          8.5   Termination of Restrictions. The restrictions imposed by this
                ---------------------------
section 8 upon the transferability of Restricted Securities shall cease and
terminate as to any particular Restricted Securities when such restrictions are
no longer required in order to insure compliance with the Securities Act.
Whenever such restrictions shall cease and terminate as to any Restricted
Securities, the holder thereof shall be entitled to receive from the Company,
without expense (other than applicable transfer taxes, if any), new certificates
for such securities of like tenor not bearing the applicable legends required by
section 8.3 hereof.

          9.    Definitions.
                -----------

          9.1   Certain Defined Terms. As used in this Agreement the
                ---------------------
following terms have the following respective meanings:

          Acquired Companies: The companies United Rentals, Inc. has acquired
since its formation in September 1997.

          Affiliate: With reference to any Person, a spouse of such Person, any
relative (by blood, adoption or marriage) of such Person within the second
degree, any director, officer or employee of such Person, any other Person of
which such Person is a member, director, officer or employee, and any other
Person directly or indirectly controlling or controlled by or under direct or
indirect common control with such Person.

          Business Day: Any day except a Saturday, a Sunday, or any day on
which banking institutions in New York, New York are required or authorized by
law or other governmental action to be closed.

          Capital Stock: As defined in section 5.6 of this Agreement.

          Certificate of Designation: As defined in section I of this Agreement.

          Closing: As defined in section 3 of this Agreement.

          Closing Date: The date of the Closing.

          Code: The Internal Revenue Code of 1986, as amended from time to
time.

                                       21
<PAGE>
 
          Collateral Agreements: The Registration Rights Agreement and the
Certificate of Designation.

          Common Stock: As defined in section I of this Agreement.

          Company: As defined in the introduction to this Agreement.

          Exchange Act: At any time, the Securities Exchange Act of 1934 as
then in effect or any similar federal statute then in effect, and any reference
to a particular section of such Act shall be deemed to include a reference to
the comparable section, if any, in any such similar federal statute.

          Financial Statements: As defined in section 5.4 of this Agreement.

          GAAP: Generally accepted accounting principles set forth in the
Opinions of the Accounting Principles Board of the American Institute of
Certified Public Accountants and in statements by the Financial Accounting
Standards Board or in such other statement by such other entity as may be
approved by a significant segment of the accounting profession; and the
requisite that such principles be applied on a consistent basis shall mean that
the accounting principles observed in a current period are comparable in all
material respects to those applied in a preceding period.

          Governmental Authority: Any nation or government, any state or
other political subdivision thereof and any entity exercising executive,
legislative, judicial, regulatory or administrative functions of or pertaining
to government.

          Indebtedness: With respect to any Person, at a particular time (a) all
indebtedness of such Person for borrowed money or for the deferred purchase
price of property, (b) the face amount of all letters of credit issued for the
account of such Person and, without duplication, all drafts drawn thereunder,
(c) all liabilities secured by any Lien on any property owned by such Person, to
the extent attributable to such Person's interest in such property, even though
such Person has not assumed or become liable for the payment thereof, and (d)
lease obligations of such Person which, in accordance with GAAP, should be
capitalized; but excluding trade and other accounts payable in the ordinary
course of business in accordance with customary trade terms and which are not
overdue for a period of more than 60 days or, if overdue for more than 60 days,
as to which a dispute exists and adequate reserves in conformity with GAAP have
been established on the books of such

                                       22
<PAGE>
 
Person. The term "Indebtedness" shall not include amounts which have not been
drawn under credit facilities, notwithstanding that such amounts when drawn will
automatically be secured by an existing Lien.

          Lien: Any mortgage, pledge, hypothecation, assignment, security
interest, lien, charge or encumbrance, or preference, priority or other security
agreement or preferential arrangement of any kind or nature whatsoever
(including, without limitation, any conditional sale or other title retention
agreement, any financing lease having substantially the same economic effects as
any of the foregoing, and the filing of, or agreement to give, any financing
statement under the Uniform Commercial Code or comparable law of any
jurisdiction). For the purposes of this Agreement, the Company or one of its
Subsidiaries shall be deemed to be the owner of any property which it has placed
in trust for the benefit of the holders of Indebtedness of the Company or its
Subsidiaries which Indebtedness is deemed to be extinguished under GAAP but for
which the Company or its Subsidiaries remain legally liable, and such trust
shall be deemed to be a Lien.

          Majority in Interest: At any time, the holders of a majority, by
number of shares, of the outstanding Shares and the outstanding shares of Common
Stock issued upon conversion of any Shares, such majority to be determined by
reference to the number of shares of Common Stock into which all outstanding
Shares are at the time convertible. 

          Officers' Certificate: As to the Company, a certificate executed on
behalf of the Company by its Chief Executive Officer, and any one of its Vice
Chairman, Chief Acquisition Officer, or Chief Financial Officer. 

          Person: An individual, a partnership, a joint venture, a corporation,
a limited liability company, a trust, an unincorporated organization or a
government or any department or agency thereof.

          Registration Rights Agreement: As defined in section 4.6 of this
Agreement.

          Repayment Event: Any event or condition which gives the holder of any
note, debenture or other evidence of indebtedness (or any person acting on such
holder's behalf) the right to require the repurchase, redemption or repayment of
all or a portion of such indebtedness by the Company or any of the Subsidiaries.

                                       23
<PAGE>
 
          Requirement of Law: As to any Person, the Certificate of 
Incorporation and by-Laws or other organizational or governing documents of such
Person, and any law, treaty, rule or regulation, or determination of an
arbitrator or a court or other Governmental Authority, in each case applicable
to or binding upon such Person or any of its property or to which such Person or
any of its property is subject.

          Restricted Securities: All of the following: (a) any certificates for
Stock bearing the applicable legend or legends referred to in section 8.3
hereof, (b) any shares of Common Stock which have been issued upon the
conversion of any of the Stock and which are evidenced by a certificate or
certificates bearing the applicable legend or legends referred to in such
section and (c) unless the context otherwise requires, any shares of Common
Stock which are at the time issuable upon the conversion of Stock and which,
when so issued, will be evidenced by a certificate or certificates bearing the
applicable legend or legends referred to in such section.

          Securities Act: At any time, the Securities Act of 1933 as then in
effect or any similar federal statute then in effect, and any reference to a
particular section of such Act shall be deemed to include a reference to the
comparable section, if any, in any such similar federal statute.

          Securities and Exchange Commission: The U.S. Securities and
Exchange Commission, or any other federal agency at the time administering the
Securities Act or the Exchange Act, whichever is the relevant statute for the
particular purpose.

          Shares: As defined in section 1 of this Agreement.

          Stock: As defined in section 1 of this Agreement.

          Subsidiaries: With respect to any Person, any corporation with respect
to which more than 50% of the outstanding shares of stock of each class having
ordinary voting power (other than stock having such power only by reason of the
happening of a contingency) is at the time owned by such Person or by one or
more Subsidiaries of such Person or by such Person and one or more Subsidiaries
of such Person.

          Any of the above-defined terms may, unless the context otherwise
requires, be used in the singular or plural depending on the reference.

                                       24
<PAGE>
 
          9.2   Accounting Terms. As used in this Agreement, and in any
                ----------------
certificate, report or other document made or delivered pursuant to this
Agreement, accounting terms not defined in section 9.1 and accounting terms
partly defined in said section 9.1 to the extent not defined, shall have the
respective meanings given to them under GAAP.

          9.3   Other Provisions Regarding Definitions: (1) Unless otherwise
                --------------------------------------
defined therein, all terms defined in this Agreement shall have the defined
meanings when used in any certificate, report or other document made or
delivered pursuant to this Agreement.

                    (2)  The words "hereof, "herein", and "hereunder" and words
of similar import when used in this Agreement shall refer to this Agreement as
a whole and not to any particular provision of this Agreement.

          10.   Expenses, etc. Whether or not the transactions contemplated
                --------
by this Agreement shall be consummated, the Company will pay all of its expenses
in connection with such transactions and in connection with any amendments or
waivers (whether or not the same become effective) under or in respect of this
Agreement or the Shares purchased by the Purchasers hereunder, including,
without limitation: (a) the cost and expenses of reproducing this Agreement and
the Shares purchased by the Purchasers, of furnishing all opinions of counsel
for the Company (including any opinions requested by the Purchasers' special
counsel as to any legal matter arising hereunder) and all certificates on behalf
of the Company, and of the Company's performance of and compliance with all
agreements and conditions contained herein to be performed or complied with by
it; and (b) the cost (other than any applicable stock transfer taxes) of
delivering to their principal office, insured to their satisfaction, the Shares
sold to the Purchasers hereunder and any Shares delivered to the Purchasers upon
any substitution of Shares pursuant to section 8 and of the Purchasers
delivering any Shares, insured to their satisfaction, upon any such
substitution. In addition, if the transactions contemplated hereby have been
consummated, the Company shall pay 50% of the reasonably itemized out-of-pocket
expenses incurred by the Purchasers in connection with such transactions
(including the fees and disbursements of their counsel), provided that the
Company's liability under this sentence shall not exceed $500,000. Reference is
made to Section 5 of this Agreement for certain agreements among the parties
regarding the fees, if any, of brokers and finders.

                                       25
<PAGE>
 
          11.   Survival of Representations and Warranties and 
                ----------------------------------------------
Indemnification, Certain Limitations. The Company's indemnification obligations
------------------------------------
and all representations and warranties contained in this Agreement shall survive
the execution and delivery of this Agreement, any investigation at any time
made by the Purchasers or on their behalf, and the purchase of the Shares by the
Purchasers under this Agreement and any conversion of any of the Stock or any
disposition of any shares of Common Stock issued upon conversion of any of the
Stock; provided that all such representations and warranties (and the
indemnities in respect thereof with respect to claims not made prior to such
date) shall expire on the later of March 31, 1999 and 30 days after the date
the Company's audited financial statements for the year ended December 31, 1998,
including a signed audit report of the Company's independent accountants, are
publicly filed with the Commission or delivered to Purchasers. No written
(except as explicitly stated therein) or oral statements made by or on behalf of
the Company, other than in this Agreement, the Collateral Agreements and the
exhibits hereto and thereto, shall constitute representations or warranties
within the meaning of this Agreement. In no event shall Purchasers be entitled
to the remedy of rescission.

          12.    Amendments and Waivers. Any term of this Agreement may
                 -----------------------
be amended or modified and the observance of any term of this Agreement may be
waived (either generally or in a particular instance and either retroactively or
prospectively) only with the written consent of the Company and (a) in the case
of any such action prior to the Closing, the Purchasers; and (b) in the case of
any other such action, a Majority in Interest.

          13.   Notices, etc. Except as otherwise provided in this Agreement,
                ------------
notices and other communications under this Agreement shall be in writing and
shall be delivered, or mailed by first-class mail, postage pre-paid, addressed,
(a) if to the Purchasers, at the address set forth at the beginning of this
Agreement, or at such other address as the Purchasers shall have furnished to
the Company in writing, or (b) if to any other holder of any Shares or shares of
Common Stock into which any of the Shares have been converted, at such address
as such other holder shall have furnished to the Company in writing, or, until
any such other holder so furnishes to the Company an address, then to and at the
address of the last holder of such Shares or shares of Common Stock into which
such Shares have been converted who has furnished an address to the Company, or
(c) if to the Company at the address of the Company set forth at the beginning
of this Agreement, to the attention of its President, or at such other address,
or to the attention of such other officer, as the Company shall have furnished
to the Purchasers and each such other holder in writing.

                                       26
<PAGE>
 
          14.   Indemnification. (a) The Company shall indemnify, defend and 
                ---------------
hold harmless the Purchasers, their affiliates, partners, officers, employees
and agents (each, an "Indemnified Person") from and against any and all losses,
liabilities, damages, judgments, settlements and expenses (including interest
and penalties recovered by a third party with respect thereto and reasonable
attorneys' fees and expenses and reasonable accountants' fees and expenses
incurred in the investigation or defense of any of the same or in asserting,
preserving or enforcing any of rights hereunder), that arise out of:

                    (i) any breach by the Company of any of its representations,
warranties or covenants contained in this Agreement or in the Registration
Rights Agreement; or

                    (ii) any litigation, investigation or proceeding instituted
by any Governmental Agency or any other Person with respect to this Agreement or
the collateral Agreements or the transactions contemplated hereby or thereby and
requiring the Purchasers participation or involvement, excluding, however, any
such litigation, investigation or proceeding which arises solely from the acts
or omissions of Purchasers or their affiliates.

                (b) The Purchasers shall give the Company prompt notice of any
third-party claim that may give rise to any indemnification obligation under
this Section 14 and the Company shall (except as set forth below) have the right
to assume and control the defense (at its expense) and settlement of any such
claim through the Company's own counsel or through other counsel reasonably
acceptable to the Purchasers. The Purchasers may retain additional counsel at
their own expense. If, under applicable standards of professional conduct, a
conflict with respect to any significant issue between the Purchasers and the
Company exists in respect of such third-party claim, the Company shall not
assume the defense of such claim and shall also pay the reasonable fees and
expenses of one counsel selected by Purchasers in respect of such claim.
Notwithstanding the foregoing, without the Purchasers' consent, the Company will
not settle any action or proceeding which does not provide the Purchasers a
full, unconditional release from all liability with respect to such claim by
each claimant or plaintiff in a form acceptable to the Purchasers' counsel, nor
will the Company consent to any injunctive or other non-monetary relief
affecting any Indemnified Person.

                                       27
<PAGE>
 
          15.   Termination. This Agreement may be terminated (a) by the mutual 
                -----------
written consent of the Purchasers and the Company at any time or (b) by the
Purchasers or the Company if the Closing shall not have been consummated on or
before January 31, 1999; provided, however, that the right to terminate this
Agreement pursuant to (b) of this Section 15 shall not be available to any
party whose failure to perform any of its obligations under this Agreement
results in the failure to consummate the transactions by such time.

          16.   Miscellaneous. This Agreement shall be binding upon and inure 
                -------------
to the benefit of and be enforceable by the respective successors and assigns
and affiliates of the parties hereto, whether so expressed or not, and, in
particular, shall inure to the benefit of and be enforceable by any holder or
holders at the time of the Shares or shares of Common Stock into which any of
the Shares have been converted; except as aforesaid, this Agreement shall not
inure to the benefit of any third party. This Agreement embodies the entire
agreement and understanding between the Purchasers and the Company and
supersedes all prior agreements and understandings relating to the subject
matter hereof. This Agreement shall be construed and enforced in accordance with
and governed by the law of the State of New York without regard to the
principles regarding conflicts of laws. The headings in this Agreement are for
purposes of reference only and shall not limit or otherwise affect the meaning
hereof. This Agreement may be executed in any number of counterparts, each of
which shall be an original, but all of which together shall constitute one
instrument.

                                       28
<PAGE>
 
          If the Purchasers are in agreement with the foregoing, please sign
the form of agreement on the accompanying counterparts of this letter and return
one of the same to the Company, whereupon this letter shall become a binding
agreement between the Purchasers and the Company.


                                Very truly yours,

                                UNITED RENTALS, INC.

                                By: /s/ 
                                    ----------------------------
                                    Title: CEO

The foregoing Agreement is hereby
agreed to as of the date thereof.

APOLLO INVESTMENT FUND IV, L.P.

By:    Apollo Advisors, IV, L.P.,
       its general partner

       By:  Apollo Capital Management IV, Inc.,
            its general partner

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

APOLLO OVERSEAS PARTNERS IV, L.P.

BY:    Apollo Advisors, IV, L.P.,
       its general partner

       By:  Apollo Capital Management IV,
            Inc., its general partner

            By:
               ----------------------------
               Title:
<PAGE>
 
                If the Purchasers are in agreement with the foregoing, please
sign the form of agreement on the accompanying counterparts of this letter and
return one of the same to the Company, whereupon this letter shall become a
binding agreement between the Purchasers and the Company.


                                Very truly yours,

                                UNITED RENTALS, INC.

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

The foregoing Agreement is hereby
agreed to as of the date thereof.

APOLLO INVESTMENT FUND IV, L.P.

By:    Apollo Advisors, IV, L.P.,
       its general partner

       By:  Apollo Capital Management IV, Inc.,
            its general partner

            By: /s/ 
               ----------------------------
               Title: Vice President

APOLLO OVERSEAS PARTNERS IV, L.P.

BY:    Apollo Advisors, IV, L.P.,
       its general partner

       By:  Apollo Capital Management IV,
            Inc., its general partner

            By: /s/ 
               ----------------------------
               Title: Vice President
<PAGE>
 
                                   EXHIBIT 1



                                                  Shares of Series A
                                                  Perpetual Convertible
                                                  Preferred Stock
Purchaser                                         to be Purchased
---------                                         ---------------
                                       
Apollo Investment Fund IV, L.P..................  284,726
                                                
Apollo Overseas Partners IV, L.P................   15,274
                                                  -------
                                       
  TOTAL                                           300,000
                                                  =======