Ernest Gremillion appeals from the initial decision of the Merit Systems Protection Board (“Board”) affirming a decision on reconsideration by the Office of Personnel Management (“OPM”) denying Mr. Gremillion’s request to have a lump sum back pay award included in his average pay for retirement annuity calculation purposes. Gremillion v. OPM, No. DA-0831-01-0306-1-1, slip, op at 1 (MSPB June 20, 2001). The initial decision became final on October 25, 2001, when the Board denied Mr. Gremillion’s petition for review. We affirm.
Mr. Gremillion worked as a Special Agent with the Internal Revenue Service (“IRS”) and was covered by the Civil Ser*794vice Retirement System (“CSRS”). Id. at 2. In 1981, Mr. Gremillion was removed from his job. Id. After successfully appealing his removal to the Board, Petitioner was reinstated and received back pay for the period from December 11, 1981, through October 27, 1984. This back pay award amounted to $123,287.00, less applicable deductions, and it was granted to Mr. Gremillion in January 1985. Id. For income tax purposes, the IRS added the award to Petitioner’s regular salary for 1985. Mr. Gremillion was therefore required to pay taxes on the entire amount of $164,856.00. Id. Petitioner retired from his employment with the IRS on December 30,1989. Id.
As a law enforcement officer, Mr. Gremillion is entitled to a retirement annuity as calculated according to 5 U.S.C. § 8339(d)(1). Section 8339(d)(1) provides that:
The annuity of an employee retiring under section 8335(b) or 8336(c) of this title is -
(A) 2)6 percent of his average pay multiplied by so much of his total service as does not exceed 20 years; plus
(B) 2 percent of his average pay multiplied by so much of his total service as exceeds 20 years.
5 U.S.C. § 8339(d)(1) (emphases added). Under 5 U.S.C. § 8331(4), “average pay” is “the largest annual rate resulting from averaging an employee’s ... rates of basic pay in effect over any three consecutive years of creditable service.” 5 U.S.C. § 8331(4) (emphasis added). 5 U.S.C. § 8331(3) further clarifies that “basic pay” “does not include bonuses, allowances, overtime pay, military pay, [or] pay given in addition to the base pay of the position as fixed by law or regulation,” except as provided by various subparagraphs that do not apply to Mr. Gremillion’s case. 5 U.S.C. § 8331(3).
To determine Mr. Gremillion’s retirement annuity, the OPM averaged Petitioner’s annual rate of pay for 1987, 1988, and 1989 and arrived at a figure of $49,411.00. Id. Petitioner subsequently asked the OPM to recalculate his retirement benefits, using the gross wages stated on his 1985 W-2 form, $164,856.36, to determine his average pay. Id. at 3. The OPM denied this request, as well as Mr. Gremillion’s request for reconsideration, and Petitioner appealed to the Board. Id.
Before the Board, Mr. Gremillion argued that the OPM should be required to calculate his retirement annuity in a manner consistent with the IRS’s handling of his back pay award. Id. at 5. According to Petitioner, it was discriminatory and unfair for the two federal agencies to treat his reported wages differently for retirement and for tax purposes. Id. at 3. The administrative judge rejected Mr. Gremillion’s arguments and affirmed the OPM’s decision. Id. at 7. Relying on the Supreme Court’s decision in Office of Personnel Management v. Richmond, 496 U.S. 414, 110 S.Ct. 2465, 110 L.Ed.2d 387 (1990), the administrative judge held that Petitioner’s entitlements under the CSRS are determined by statute, and that the OPM cannot be ordered to grant benefits not otherwise permitted by law. Id. at 6. The administrative judge concluded that 5 U.S.C. § 8331(4) governs the “average pay” used to calculate an employee’s retirement annuity, id. at 6, and that under the statute, “average pay” does not necessarily encompass an employee’s total annual income, id. at 7. As such, the administrative judge held that the OPM lacked authority to provide the relief Mr. Gremillion sought. Id. A full Board affirmed the administrative judge’s decision, and Mr. Gremillion timely appealed to this court. We have jurisdiction pursuant to 28 U.S.C. § 1295(a)(9).
*795The scope of our review in an appeal from a decision of the Board is limited. This court must affirm the Board’s decision unless it is arbitrary, capricious, an abuse of discretion, not in accordance with law, obtained without procedures required by rule, law, or regulation, or unsupported by substantial evidence. 5 U.S.C. § 7703(c) (1988). See Phillips v. United States Postal Serv., 695 F.2d 1389, 1390 (Fed.Cir.1982).
On appeal, Mr. Gremillion reiterates his argument that if the IRS considered him to have received $164,856.00 in gross earnings for 1985, so should the OPM. Petitioner challenges the administrative judge’s holding that under Richmond, the OPM lacks authority to adjust his “average pay” accordingly, and he urges us to find in his favor in order to alert the relevant federal agencies to what he perceives as their inequitable lack of uniformity.
We conclude that the Board did not err when it affirmed the OPM’s decision that Mr. Gremillion’s back pay award should not be included in his annual average pay for retirement annuity considerations. In Richmond, the Supreme Court held that “the payment of money from the Treasury must be authorized by a statute.” Richmond, 496 U.S. at 424, 110 S.Ct. 2465. Here, not only does the statutory scheme fail to authorize the relief that Mr. Gremillion seeks, but § 8331(3) explicitly excludes “pay given in addition to [an employee’s] base pay” from retirement benefit calculations. 5 U.S.C. § 8331(3). As the administrative judge correctly held, therefore, the OPM cannot be compelled to determine Petitioner’s retirement annuity on the basis of his entire income for 1985, id. at 6, regardless of how the IRS treated this income for tax purposes.
Because the Board’s decision was supported by substantial evidence and was not arbitrary, capricious, an abuse of discretion, or otherwise not in accordance with law, we affirm.