
<PAGE>   1


                                                                    EXHIBIT 99.1



                                 January 9, 1999



PERSONAL AND CONFIDENTIAL
-------------------------

Board of Directors
Unitog Company
1300 Washington Street
Kansas City, MO 64105

         Re:  Fairness Opinion

Gentlemen:

In connection with the proposed acquisition through a merger (the "Merger") by
Cintas Corporation ("Cintas" or "Parent") of Unitog Company ("Unitog" or the
"Company"), pursuant to the Agreement and Plan of Merger dated January 9, 1999
(the "Agreement") between Cintas, Cintas Image Acquisition Company ("Merger
Sub"), and Unitog you have requested our opinion as to the fairness, from a
financial point of view, to the Company's shareholders of the Merger
Consideration to be received by such shareholders for their common stock in the
proposed Merger pursuant to the Agreement.

Subject to the provisions of the Agreement, at the Effective Time, each issued
and outstanding share of common stock of the Company ("Company Shares"), by
virtue of the Merger and without any action on the part of the holder thereof,
other than Company Shares owned by Parent, Merger Sub, or any direct or indirect
wholly owned subsidiary of Parent, shall be converted into the right to receive
as Merger Consideration, that number of shares of Parent Common Stock equal to
the Conversion Number upon surrender of the Certificate representing such
Company Share.

The Conversion Number shall be equal to the quotient (rounded to the nearest
1/10,000) determined by dividing $38.00, as adjusted pursuant to Section 8.3 of
the Agreement ("Company Share Price"), by the amount determined by calculating
the average of the high and low sales prices of Parent Common Stock as reported
on the NASDAQ Stock Market for the twenty (20) consecutive trading days ending
on the third trading day preceding the date of the meeting of the Company's
stockholders for the purpose of voting on the adoption of this Agreement
("Parent Share Price"). Notwithstanding the foregoing, if the Parent Share Price
is less than $52.00, the Parent Share Price shall be deemed to be $52.00 (for
purposes of determining the Conversion Number) and, if the Parent Share Price is
greater than $66.43, the Parent Share Price shall be deemed to be $66.43 plus
fifty percent (50%) of the difference between the Parent Share Price and $66.43.

As a customary part of its investment banking business, Goldsmith, Agio, Helms
Securities, Inc. ("GAHS") is engaged in the valuation of businesses and
securities in connection with mergers and acquisitions, private placements, and
valuations for estate, corporate, and other purposes. In return for our services
in connection with providing this opinion, the Company will pay us a fee, which
fee is not contingent upon the consummation of the Merger, and indemnify us
against certain liabilities. We are also acting as a financial advisor to the
Company in connection with the Merger for which we will receive certain other
fees, a significant portion of which is contingent upon the consummation of the
Merger.


<PAGE>   2





In arriving at our opinion, we have undertaken such reviews, analyses and
inquiries as we deemed necessary and appropriate under the circumstances. Among
other things, we have (i) reviewed the Agreement; (ii) analyzed financial and
other information that is publicly available relating to Cintas; (iii) analyzed
financial and other information that is publicly available relating to the
Company; (iv) analyzed certain financial and operating data of the Company that
has been made available to us by Unitog; (v) visited certain facilities of the
Company and discussed with management of the Company the financial condition,
operating results, business outlook and prospects of the Company; (vi) analyzed
the valuations of publicly traded companies that we deemed comparable to the
Company; (vii) performed a discounted cash flow analysis of the Company based on
financial projections that Unitog management provided to us; and (viii) analyzed
the financial terms of certain transactions we deemed similar to the Merger that
have recently been effected.

We have relied upon and assume the accuracy, completeness, and fairness of the
financial statements and other information furnished by, or publicly available
relating to, the Company or Cintas, or otherwise made available to us, and have
not assumed responsibility independently to verify such information. We have
further relied upon assurances by the Company that the information provided to
us has a reasonable basis, and with respect to projections and other business
outlook information, reflects the best currently available estimates, and that
the Company is not aware of any information or fact that would make the
information provided to us incomplete or misleading. In arriving at our opinion,
we have not performed any appraisals or valuations of specific assets or
liabilities of the Company or Cintas and express no opinion regarding the
liquidation value of the Company or Cintas or any of its assets. Our opinion is
based upon the information available to us and the facts and circumstances as
they exist and are subject to evaluation on the date hereof; events occurring
after the date hereof could materially affect the assumptions used in preparing
this opinion.

We have assumed that the Merger will be accounted for as a pooling of interests
in accordance with generally accepted accounting principles ("GAAP") and that
such Merger qualifies for such accounting treatment under GAAP. We have also
assumed that the Merger will constitute a reorganization under Section 368 of
the Internal Revenue Code of 1986, as amended. We have relied, with respect to
legal and accounting matters related to the Agreement, on the advice of the
Company's legal and accounting advisors. We have made no independent
investigation of any legal or accounting matters that may affect the Company and
have assumed the correctness of the legal and accounting advice provided to the
Company and its Board of Directors.

Our opinion is rendered for the benefit and use of the Board of Directors of the
Company in connection with the Board's consideration of the Merger and does not
constitute a recommendation to any holder of Company Common Stock as to how such
stockholder should vote with respect to the Agreement. We have not been asked
to, nor do we, express an opinion as to the relative merits of the Merger as
compared to any alternative business strategies that might exist for the Company
or the effect of any other transaction in which the Company might engage. This
opinion may not be published or otherwise used or referred to publicly without
our written consent; provided, however, that this opinion may be included in its
entirety in any filing with the Securities and Exchange Commission with respect
to the Merger.




<PAGE>   3




Based upon and subject to the foregoing, and based upon such other facts as we
consider relevant, it is our opinion that, as of the date hereof, the Merger
Consideration to be received by the Company's shareholders for their common
stock in the proposed Merger pursuant to the Agreement is fair to such
shareholders from a financial point of view.

                                        Sincerely,

                                        Goldsmith, Agio, Helms Securities, Inc.



                                        By:
                                           ------------------------------------
