PER CURIAM.
The Little Rock School District (LRSD) appeals from an order of the district court awarding the Kaplan group, attorneys for LRSD in school desegregation litigation, attorneys fees in the sum of $555,272.25 with interest at the rate of 6.62% per an-num from February 6, 1991. The Kaplan group cross-appeals from this order. LRSD also appeals from an order of the district court awarding to the Kaplan group an additional sum of $25,562.93 with interest at 6% from May 24, 1991 for its attorneys fees in this action. We affirm the district court’s decision that the Kaplan group is entitled to additional attorneys fees for their services, but reduce the sum awarded to $241,714.59 with interest from February 6, 1991 at 6.62%. We also affirm the district court’s award to the Kaplan group for fees received by them in the district court for prosecuting this action in the sum of $25,562.93 with interest at 6% from May 24, 1991.
[719]*719BACKGROUND
It is agreed by all that the Kaplan group entered into a contract with LRSD on October 8, 1982 to represent the school district in school desegregation litigation. The contract set forth the hourly rates that various members of the Kaplan group were to be paid for their services. It noted that these rates were less than the rate regularly charged to their clients, and it stated that the rates were to be adjusted annually to the satisfaction of LRSD and the Kaplan group. A request to increase hourly fees was approved by LRSD in mid-1984. No further requests to increase the hourly fees were approved. The Kaplan group was dismissed by LRSD in December 1987. The total fee paid to the Kaplan group from the date of employment to termination was $868,829.91.
There was an understanding between LRSD and the Kaplan group at the time of termination that an application would be made to the United States District Court for attorneys fees for services rendered to the Board by the Kaplan group on the basis of prevailing rates and that the Kap-lan group would continue to represent LRSD in making the application. Pursuant to this understanding, the Kaplan group filed an application for attorneys fees with the district court. An evidentiary hearing was held. Based on the evidence produced, the court found that LRSD was a prevailing party, that the parties had agreed that LRSD would prosecute fee petitions at the Kaplan group’s full prevailing rates, and that LRSD would pay the Kaplan group the difference between their billed rates and the proceeds of any attorneys fees award.1 The court further found that the parties had modified their agreement in 1987 to provide that the Kaplan group and LRSD would split evenly any award made by the court. The court found that the appropriate fee was $1,110,544.50 and that the Kaplan group should receive one-half of that sum, or $555,272.25.2
On appeal, LRSD contends that the district court erred in (1) awarding attorneys fees without explaining its reasons for the fee award; (2) holding that the original contract between the parties required LRSD to pay the Kaplan group the difference between the rates set forth in the contract and their “normal rates” from the proceeds of any attorneys fees award; and (3) holding that the parties modified their agreement to require that any attorneys fees recovered by LRSD be shared equally with the Kaplan group.
Size of Fee Award
We do not believe that the district court erred in determining that the total fee should be $1,110,544.50. It is undisputed that the compensable hours were accurately reported by the Kaplan group. The LRSD does not question the district court’s findings as to the Kaplan group’s prevailing rates in 1984 and 1988, and the Kaplan group does not contest the district court’s decision to reduce compensable hours by ten percent to reflect that the Kaplan group was not wholly successful in its action.
Rather, LRSD argues that the district court did not adequately explain why it did not consider several factors which would require a lower fee award. First, LRSD states that the court should have given greater weight to the fact that the Kaplan group failed to achieve one of the most important goals of the litigation, consolidation of three Pulaski County school districts. See Little Rock Sch. Dist. v. Pulaski County Special Sch. Dist., 778 F.2d [720]*720404, 434 (8th Cir.1985) (en banc), cert. denied 476 U.S. 1186, 106 S.Ct. 2926, 91 L.Ed.2d 554 (1986). LRSD also claims that the court should have given greater weight to the fact that the contract between LRSD and the Kaplan group allowed the Kaplan group to amass many billable hours without any significant risk of monetary loss, and allowed the Kaplan group to have the use of the money for several years.
We reject LRSD’s arguments. The district court’s determination of the appropriate attorneys fees was neither clearly erroneous nor an abuse of discretion. The award was based on the compensable hours and prevailing rates as of 1984 and 1988. No additional fee was awarded for the difficulty of the case or any other factor. The court’s lodestar award was presumptively a reasonable fee. Hendrickson v. Branstad, 934 F.2d 158, 162 (8th Cir.1991). Perhaps the district court could have articulated its reasons for the award more thoroughly, see Jenkins v. Missouri, 838 F.2d 260, 264 (8th Cir.), cert. denied 488 U.S. 889, 109 S.Ct. 221, 102 L.Ed.2d 212 (1988), but its reasons were sufficiently explained. It is true, of course, that the Kaplan group did not achieve consolidation, but it did achieve a broadly based desegregation decree which this court found would achieve substantial equality of education opportunity for all students in Pulaski County. See Little Rock Sch. Dist. v. Pulaski County Special Sch. Dist., 921 F.2d 1371, 1377 (8th Cir.1990) (reviewing history of case). Moreover, the district court did consider the Kaplan group’s failure to secure total success when it reduced the group’s compensa-ble hours by ten percent. Although we acknowledge that fees were paid to the Kaplan group during the pendency of the case, it is also true that the original fee agreement called for annual adjustments which were not always made, and the Kap-lan group had to wait from December of 1987 to May of 1991 to be assured of its fee.
Agreement to Pay Kaplan Group the Excess of a Fee Award if LRSD Achieved Prevailing Party Status
LRSD argues that the district court erred when it found that a contract existed between LRSD and the Kaplan group, and that contract
provided that the Kaplan Group would bill at reduced hourly rates and LRSD would pay such rates as billed: however, in the event LRSD achieved “prevailing party status”, LRSD would prosecute fee petitions at the attorneys’ full rates and pay the attorneys the difference between their billed rates and their full normal rates from the proceeds of any attorneys’ fee award.
Little Rock Sch. Dist. v. Pulaski County Special Sch. Dist., No. LR-C-82-866, slip op. at 2, 1991 WL 255004 (Feb. 6, 1991). As the following chronology shows, the district court’s conclusion is supported by the evidence in the record.
On May 27, 1982, LRSD and the Kaplan group entered into a written agreement employing the Kaplan group to seek an interdistrict desegregation remedy.
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PER CURIAM.
The Little Rock School District (LRSD) appeals from an order of the district court awarding the Kaplan group, attorneys for LRSD in school desegregation litigation, attorneys fees in the sum of $555,272.25 with interest at the rate of 6.62% per an-num from February 6, 1991. The Kaplan group cross-appeals from this order. LRSD also appeals from an order of the district court awarding to the Kaplan group an additional sum of $25,562.93 with interest at 6% from May 24, 1991 for its attorneys fees in this action. We affirm the district court’s decision that the Kaplan group is entitled to additional attorneys fees for their services, but reduce the sum awarded to $241,714.59 with interest from February 6, 1991 at 6.62%. We also affirm the district court’s award to the Kaplan group for fees received by them in the district court for prosecuting this action in the sum of $25,562.93 with interest at 6% from May 24, 1991.
[719]*719BACKGROUND
It is agreed by all that the Kaplan group entered into a contract with LRSD on October 8, 1982 to represent the school district in school desegregation litigation. The contract set forth the hourly rates that various members of the Kaplan group were to be paid for their services. It noted that these rates were less than the rate regularly charged to their clients, and it stated that the rates were to be adjusted annually to the satisfaction of LRSD and the Kaplan group. A request to increase hourly fees was approved by LRSD in mid-1984. No further requests to increase the hourly fees were approved. The Kaplan group was dismissed by LRSD in December 1987. The total fee paid to the Kaplan group from the date of employment to termination was $868,829.91.
There was an understanding between LRSD and the Kaplan group at the time of termination that an application would be made to the United States District Court for attorneys fees for services rendered to the Board by the Kaplan group on the basis of prevailing rates and that the Kap-lan group would continue to represent LRSD in making the application. Pursuant to this understanding, the Kaplan group filed an application for attorneys fees with the district court. An evidentiary hearing was held. Based on the evidence produced, the court found that LRSD was a prevailing party, that the parties had agreed that LRSD would prosecute fee petitions at the Kaplan group’s full prevailing rates, and that LRSD would pay the Kaplan group the difference between their billed rates and the proceeds of any attorneys fees award.1 The court further found that the parties had modified their agreement in 1987 to provide that the Kaplan group and LRSD would split evenly any award made by the court. The court found that the appropriate fee was $1,110,544.50 and that the Kaplan group should receive one-half of that sum, or $555,272.25.2
On appeal, LRSD contends that the district court erred in (1) awarding attorneys fees without explaining its reasons for the fee award; (2) holding that the original contract between the parties required LRSD to pay the Kaplan group the difference between the rates set forth in the contract and their “normal rates” from the proceeds of any attorneys fees award; and (3) holding that the parties modified their agreement to require that any attorneys fees recovered by LRSD be shared equally with the Kaplan group.
Size of Fee Award
We do not believe that the district court erred in determining that the total fee should be $1,110,544.50. It is undisputed that the compensable hours were accurately reported by the Kaplan group. The LRSD does not question the district court’s findings as to the Kaplan group’s prevailing rates in 1984 and 1988, and the Kaplan group does not contest the district court’s decision to reduce compensable hours by ten percent to reflect that the Kaplan group was not wholly successful in its action.
Rather, LRSD argues that the district court did not adequately explain why it did not consider several factors which would require a lower fee award. First, LRSD states that the court should have given greater weight to the fact that the Kaplan group failed to achieve one of the most important goals of the litigation, consolidation of three Pulaski County school districts. See Little Rock Sch. Dist. v. Pulaski County Special Sch. Dist., 778 F.2d [720]*720404, 434 (8th Cir.1985) (en banc), cert. denied 476 U.S. 1186, 106 S.Ct. 2926, 91 L.Ed.2d 554 (1986). LRSD also claims that the court should have given greater weight to the fact that the contract between LRSD and the Kaplan group allowed the Kaplan group to amass many billable hours without any significant risk of monetary loss, and allowed the Kaplan group to have the use of the money for several years.
We reject LRSD’s arguments. The district court’s determination of the appropriate attorneys fees was neither clearly erroneous nor an abuse of discretion. The award was based on the compensable hours and prevailing rates as of 1984 and 1988. No additional fee was awarded for the difficulty of the case or any other factor. The court’s lodestar award was presumptively a reasonable fee. Hendrickson v. Branstad, 934 F.2d 158, 162 (8th Cir.1991). Perhaps the district court could have articulated its reasons for the award more thoroughly, see Jenkins v. Missouri, 838 F.2d 260, 264 (8th Cir.), cert. denied 488 U.S. 889, 109 S.Ct. 221, 102 L.Ed.2d 212 (1988), but its reasons were sufficiently explained. It is true, of course, that the Kaplan group did not achieve consolidation, but it did achieve a broadly based desegregation decree which this court found would achieve substantial equality of education opportunity for all students in Pulaski County. See Little Rock Sch. Dist. v. Pulaski County Special Sch. Dist., 921 F.2d 1371, 1377 (8th Cir.1990) (reviewing history of case). Moreover, the district court did consider the Kaplan group’s failure to secure total success when it reduced the group’s compensa-ble hours by ten percent. Although we acknowledge that fees were paid to the Kaplan group during the pendency of the case, it is also true that the original fee agreement called for annual adjustments which were not always made, and the Kap-lan group had to wait from December of 1987 to May of 1991 to be assured of its fee.
Agreement to Pay Kaplan Group the Excess of a Fee Award if LRSD Achieved Prevailing Party Status
LRSD argues that the district court erred when it found that a contract existed between LRSD and the Kaplan group, and that contract
provided that the Kaplan Group would bill at reduced hourly rates and LRSD would pay such rates as billed: however, in the event LRSD achieved “prevailing party status”, LRSD would prosecute fee petitions at the attorneys’ full rates and pay the attorneys the difference between their billed rates and their full normal rates from the proceeds of any attorneys’ fee award.
Little Rock Sch. Dist. v. Pulaski County Special Sch. Dist., No. LR-C-82-866, slip op. at 2, 1991 WL 255004 (Feb. 6, 1991). As the following chronology shows, the district court’s conclusion is supported by the evidence in the record.
On May 27, 1982, LRSD and the Kaplan group entered into a written agreement employing the Kaplan group to seek an interdistrict desegregation remedy. The agreement set forth the hourly fees that various members of the group were to receive, provided that the hourly fees were to be good for one contract year and were to be renegotiated annually to the satisfaction of LRSD and the Kaplan group. On June 12, 1984, the Kaplan group requested and received an increase in hourly rates. On August 8 of the same year, attorney Philip Kaplan of the Kaplan group wrote the following letter to the superintendent of schools:
This letter is to request an increase in the attorneys’ fees set forth in our original contract dated October, 1982. Those rates were applicable for a one year period of time and were considerably below the normal and regular rate charged by any of the four lawyers involved in the case.
Some eight months after expiration of that agreement, we find that we must ask for an increase in rates. These new rates are still considerably below the regular hourly rate charged by any of us to our regular clients and considerably below the rate being paid by the other school districts. These reduced rates reflect our continued commitment to public [721]*721interest aspects of the litigation set forth in our original proposal. The requested rates are as follows:
Philip E. Kaplan $85.00
P.A. Hollingsworth 85.00
John M. Bilheimer 75.00
Janet L. Pulliam 70.00
Others Lawyers 55.00
Law Clerks & Paralegals 25.00
We would appreciate your bringing this matter to the Board for consideration at their next board meeting. Hopefully, the new rates would go into effect July 1, 1984, and will be applicable for a period of one year.
On December 14, 1984, LRSD, through the Kaplan group, submitted a motion to the district court for an award of attorneys fees. The fee application was consistent with the August 8 letter and was based on “the prevailing rate in Little Rock for attorneys with comparable experience.” The court did not take action on the fee petition until 1987.
On September 15, 1987, the Kaplan group wrote to the chief administrator of LRSD stating that the district court was now ready to consider the question of attorneys fees and requesting that any fee approved be shared equally with LRSD. A copy of this letter was furnished to the superintendent of schools.
On October 22, 1987, the superintendent made the following recommendation to the board:
I have studied the issue of attorneys fees paid to the District’s legal counsel on the desegregation lawsuit. I recognize that Mr. Kaplan, Mr. Hollingsworth, Mr. Bil-heimer, and Ms. Pulliam have provided legal services to the District at a reduced hourly rate since the inception of the desegregation litigation in 1982. In addition, I recognize that the fees paid by the Little Rock School District for legal counsel in this case are below the fees paid by the other parties in the case. Conversely, I am mindful that whatever fees are paid for legal counsel are funds which are entrusted to the District by the public and must be administered with prudence.
Keeping in mind the responsibility of fairness to those with whom the District does business while at the same time managing District funds with restraint and discretion, I recommend that Mr. Kaplan, Mr. Hollingsworth, Mr. Bilheimer, and Ms. Pulliam be paid on a pro rata share only where fees recovered by court order are in excess of the total amount paid by the District.
The board adopted the superintendent’s recommendation on October 29, 1987 by a vote of five to one. By this time relations between the Kaplan group and the board had deteriorated. The board asked the court to approve substitution of counsel, and on December 28, 1987, the district court approved the substitution of counsel for reasons of “irreconcilable differences.” It noted, however, that “the LRSD has requested that [the Kaplan group] continue to represent LRSD on the sole issue of attorneys’ fees, and current counsel have agreed.” Little Rock Sch. Dist. v. Pulaski County Special Sch. Dist., No. LR-C-82-866, slip op. at 1, 1991 WL 255004 (Dec. 28, 1987). Rather than withdraw, the Kaplan group did continue to represent LRSD on the attorneys fees issue, and subsequent to the vote of the board the Kaplan group submitted a fee application to the court.
After a hearing, the district court found that the parties had at a point in time agreed to modify the 1982 agreement so as to give the Kaplan group the difference between the fee allowed by the court and the amount paid prior to such allowance by LRSD. LRSD argues that the Kaplan group never approved this modification and that the Board’s action of October 29, 1987 was simply an offer that was never accepted by the Kaplan group. The district court, however, found that the contract had been modified by the parties, and we cannot say this finding was clearly erroneous. There is evidence in the record, primarily the testimony of the president of the board at the time the fee agreement was signed, that the parties intended this result from the beginning. Moreover, we think it clear that LRSD, by a five to one vote of its board, voted to have the Kaplan group submit a fee application to the district [722]*722court at prevailing rates, and decided that it would retain an amount from the award equal to the sum it had paid the Kaplan group and pay the balance to the Kaplan group.
Fifty/Fifty Split of Fee Award Between LRSD and the Kaplan Group
The district court found that the contract had been modified a second time to provide that any fee award should be evenly split between the parties, and thus the Kaplan group was entitled to a judgment in the sum of $555,272. We believe this finding is clearly erroneous and contrary to law.
According to the Kaplan group, the superintendent of LRSD agreed to a fifty/fifty split of the fee award. Even if we assume that the superintendent of schools agreed to this change, we find no evidence to support a finding that the board ratified the superintendent’s action. LRSD never ratified the fifty/fifty modification by “accepting the services with full knowledge of [an unauthorized contract].” Beckley-Cardy Co., Inc. v. West Point Special Sch. Dist. No. 3, 209 Ark. 792, 192 S.W.2d 540, 543 (1946) (citing cases). See also Responsive Environments Corp. v. Pulaski County Special Sch. Dist., 366 F.Supp. 241, 243 (E.D.Ark.1973) (no legal contract found where contract in question never approved or sanctioned by school board). Instead, the board specifically rejected the fifty/fifty proposal and affirmed its intention to pay the Kaplan group whatever was left after LRSD had reimbursed itself for monies it had already paid to the Kaplan group.
The Kaplan group argues, however, that the district court’s decision can be supported on an estoppel theory, the theory being that the superintendent agreed to the Kaplan group’s proposal for a fifty/fifty split and subsequently told the Kaplan group that the board had also agreed to the fifty/fifty split. Even if one assumes that a board of education in appropriate circumstances could be estopped by the superintendent’s representation, we cannot find sufficient evidence of estoppel here. The board’s action rejecting the fifty/fifty split was spread on the record of the board’s minutes. The Kaplan group had access to this public record.
Moreover, the majority of work done by the Kaplan group was before the purported fifty/fifty agreement, and the group represented the board for only two months after the October 29, 1987 board meeting, so the detriment to the group was insignificant at best. In sum, there is insufficient evidence to support a conclusion that the Kaplan group changed its position in reliance on the superintendent’s report that the board had accepted their proposal. See Christmas v. Raley, 260 Ark. 150, 539 S.W.2d 405, 410 (1976) (party claiming estoppel must prove he has changed his position to his detriment).
CONCLUSION
We find no merit to the parties’ further contentions. We thus affirm the judgment of the district court that a total fee of $1,110,544.50 was appropriate. We also affirm the district court’s finding that the original fee agreement was modified to provide that the Kaplan group would receive the difference between the fee awarded by the court ($1,110,544.50) and the fee paid by the board ($868,829.91), or $241,714.59, together with interest from February 6, 1991 at 6.62%. We finally affirm the district court’s award of the sum of $25,562.93 with interest at the rate of 6% from May 24, 1991 for attorneys fees incurred by the Kaplan group in the district court. Each party to this appeal will bear its own costs and attorneys fees.