PRICING SUPPLEMENT NO. 31A Rule 424(b)(3) DATED: September 1, 2004+ File No. 333-109793 October 27, 2004++ (To Prospectus dated November 17, 2003, and Prospectus Supplement dated November 17, 2003) $10,668,950,162 THE BEAR STEARNS COMPANIES INC. Medium-Term Notes, Series B Principal Amount: $450,000,000 Floating Rate Notes [x] Book Entry Notes [x] Original Issue Date: 9/9/2004^ Fixed Rate Notes [ ] Certificated Notes [ ] 11/1/2004^^ Initial Public Offering Price: 100%> 100.033%>> Maturity Date: 9/9/2009 CUSIP#: 073928G56 Euroclear and Clearstream Common Code: 020066784 Option to Extend Maturity: No [x] Yes [ ] Final Maturity Date: Optional Optional Redemption Repayment Repayment Redeemable On Price(s) Date(s) Price(s) ------------- -------------- ------------- ----------- N/A N/A N/A N/A Applicable Only to Fixed Rate Notes: ----------------------------------- Interest Rate: Interest Payment Dates: Applicable Only to Floating Rate Notes: -------------------------------------- Interest Rate Basis: Maximum Interest Rate: N/A [ ] Commercial Paper Rate Minimum Interest Rate: N/A [ ] Federal Funds Effective Rate [ ] Federal Funds Open Rate Interest Reset Date(s): * [ ] Treasury Rate Interest Reset Period: Quarterly [ ] LIBOR Reuters Interest Payment Date(s): ** [x] LIBOR Telerate [ ] Prime Rate [ ] CMT Rate Initial Interest Rate: 2.13% Interest Payment Period: Quarterly Index Maturity: Three Months Spread (plus or minus): +0.27% + $400,000,000 was traded on September 1, 2004. ++ $50,000,000 was traded on October 27, 2004. ^ $400,000,000 was issued on September 9, 2004. ^^ $50,000,000 was issued on November 1, 2004. These Notes will have interest accrued from September 9, 2004 for the Interest Payment Date on December 9, 2004. > The Notes issued on September 9, 2004 had an Initial Public Offering Price of 100%. >> The Notes issued on November 1, 2004 had an Initial Public Offering Price of 100.033%. * On the 9th of each December, March, June and September prior to Maturity. ** On the 9th of each December, March, June and September, including the maturity date. CERTAIN US FEDERAL INCOME TAX CONSIDERATIONS The following discussion supplements the section captioned "Certain US Federal Income Tax Considerations" in the Prospectus Supplement dated November 17, 2003. Qualified Reopening We will treat the Notes issued on November 1, 2004 as part of the same issue as the Notes issued on September 9, 2004 (the "Original Notes") for US federal income tax purposes. Accordingly, for purposes of the Treasury regulations governing original issue discount on debt instruments (the "OID Regulations"), we will treat the Notes issued on November 1, 2004 as having the same issue date, the same issue price and, with respect to holders, the same adjusted issue price as the Original Notes. Consequently, the "issue price" of the Notes issued on November 1, 2004 for US federal income tax purposes will be the first price at which a substantial amount of the Original Notes were sold to the public (excluding sales to bond houses, brokers, or similar persons or organizations acting in the capacity of underwriters, placement agents, or wholesalers). The purchase price for the Notes issued on November 1, 2004 will reflect interest accrued from September 9, 2004 ("pre-issuance accrued interest"), which will be included in accrued interest to be paid on December 9, 2004. In accordance with the OID Regulations, we will exclude pre-issuance accrued interest from the issue price of the Notes issued on November 1, 2004. Accordingly, US Holders of the Notes issued on November 1, 2004 should treat a corresponding portion of the interest payable on December 9, 2004 as a return of the excluded pre-issuance accrued interest, rather than as an amount payable on the Notes issued on November 1, 2004. The distribution of Notes will conform to the requirements set forth in Rule 2720 of the NASD Conduct Rules. -2-