
765 N.W.2d 108 (2009)
Todd Michael BAUERLY, petitioner, Appellant,
v.
Suzanne Mary BAUERLY, Respondent.
No. A08-0794.
Court of Appeals of Minnesota.
May 5, 2009.
*109 Alan J. Albrecht, Albrecht & Associates, Ltd., Brooklyn Center, MN, for appellant.
Daniel J. Goldberg, Messerli & Kramer, P.A., Minneapolis, MN, for respondent.
Considered and decided by KALITOWSKI, Presiding Judge; LANSING, Judge; and SCHELLHAS, Judge.

OPINION
SCHELLHAS, Judge.
After remand, appellant seeks review of the district court's order recalculating his child-support obligation and denying his request for compensation for overpaid support. We reverse and remand.

FACTS
The marriage of appellant Todd Michael Bauerly (father) and respondent Suzanne Mary Bauerly (mother) was dissolved by judgment entered August 31, 2005. The parties stipulated to joint legal custody of their two minor children and sole physical custody to mother, subject to father's parenting time. Mother was awarded child support from father in the amount of $1,505 per month, which the district court calculated after finding that father's net income was $5,015 per month. Father moved for amended findings of fact and conclusions of law, and an amended dissolution judgment was filed on January 25, *110 2006. The amended judgment changed the formula for computing father's share of daycare costs and added a provision addressing dependency exemptions.
Father appealed from the amended judgment, claiming numerous errors by the district court, including an incorrect calculation of his net income. We reversed the district court's finding of father's net monthly income and child-support obligation and remanded for "recalculation based on the most current income evidence presented at trial, or an explanation of why the use of that evidence would not be appropriate." Bauerly v. Bauerly, No. A06-557, 2007 WL 1053254, at *4 (Minn. App. Apr. 10, 2007) (footnote omitted). We acknowledged that there was mention at oral arguments that father's employment had changed since the judgment was entered, and noted that "a determination of income and the child-support obligation at the time of the dissolution may impact later motions for modification." Id. at *4 n. 4 (emphasis added).
On remand, father moved the district court for an order reducing his child-support obligation "retroactive to the date of entry of the Judgment and Decree" and requiring mother to reimburse him for "[c]hild support erroneously withheld." Father proposed recalculation of his child-support obligation for the period beginning September 2005 and ending December 2006, when he began new employment, and argued that he should receive "credit for overpaid child support" during that period. Father also proposed a calculation of his child-support obligation for the period beginning January 2007 and ending December 2007 and sought "credit for overpaid support" for that period. Additionally, father sought to be reimbursed for his payments on mother's student loan and for a "[j]oint tax liability taken from [him]." Mother asked that any reduction in father's child-support obligation be prospective, arguing that her ability to provide a financially secure household for the children would be jeopardized if support were reduced to reimburse father for overpaid support.
On March 18, 2008, the district court amended the judgment and found that father's net monthly income at the time of trial was $4,173.34, based on the most recent paystub that he submitted at trial. The district court recalculated child support at $1,252.01 per month, which is $252.99 per month less than the amount stated in the original judgment, effective from the date of the March 2008 order. The district court did not apply the reduced child-support obligation as of the date of the dissolution judgment, did not order mother to reimburse father for "previously paid child support," and denied all other motions. This appeal follows.

ISSUE
Did the district court abuse its discretion on remand when it corrected a child-support obligation as of the date of its order on remand rather than the date of the original dissolution judgment?

ANALYSIS
A district court order regarding child support will be reversed only where a district court abused its discretion by resolving the matter in a manner that is against logic and the facts on the record. Putz v. Putz, 645 N.W.2d 343, 347 (Minn. 2002). Misapplying the law is an abuse of discretion. Pikula v. Pikula, 374 N.W.2d 705, 710 (Minn.1985). A district court's duty on remand is to execute the mandate of the remanding court "strictly according to its terms." Duffey v. Duffey, 432 N.W.2d 473, 476 (Minn.App.1988). "When the trial court receives no specific directions as to how it should proceed in *111 fulfilling the remanding court's order, the trial court has discretion ... to proceed in any manner not inconsistent with the remand order." Id.

Effective Date of Child-Support Correction
Mother argues that the district court properly exercised its discretion by making the effective date of its correction of father's child-support obligation the date of its order on remand rather than the date of the dissolution judgment. We disagree. Based on our instructions, the district court on remand should have corrected father's child-support obligation as of "the time of the dissolution," not the date of the district court's order on remand. By correcting father's child-support obligation effective as of the date of the order on remand, the district court functionally eliminated any support overpayment by father. This was an abuse of the district court's discretion. Father's child-support obligation must be corrected as of the child-support award in the original dissolution judgment.

Compensation for Child-Support Overpayment
A child-support overpayment exists if the amount of father's support obligation is corrected as of the date of the original dissolution judgment. Father argues that he overpaid child support because of the district court's error in the original dissolution judgment and that he should be compensated for the overpayment under Minn.Stat. § 518A.52 (2008). Section 518A.52 requires that if an obligor has overpaid child support because of a modification or error in the amount owed, the public authority shall: (1) apply the amount of the overpayment to reduce the amount of child-support arrearages or debts owed to the obligee and (2) reduce the amount of child support remitted to the obligee by an amount no greater than 20 percent of current monthly support and remit the amount of the reduction to the obligor until the overpayment is reduced to zero.
At oral argument, mother argued that section 518A.52 does not apply to father's request for compensation for child-support overpayment because the statute applies only to cases in which the public authority is involved because a recipient of child support receives public assistance. Mother's reading of section 518A.52 is too narrow. In addition to cases involving public assistance, the public authority can be involved in cases in which a party applies for collection services. See Minn.Stat. § 518A.50 (b) (2008) (stating that child support must be paid to the public authority responsible for child-support enforcement where the obligee has applied for public assistance or has applied for child-support-collection services); Minn.Stat. § 518A.53, subd. 4(a)-(d) (2008) (addressing income-withholding services available through public authority on application of either party). We conclude that section 518A.52 reflects a policy in favor of compensation where overpayment has occurred, but constitutes a mandate only as to the public authority. Section 518A.52 does not limit a district court's inherent power to grant equitable relief. See DeLa Rosa v. DeLa Rosa, 309 N.W.2d 755, 758 (Minn.1981) (stating that a district court has inherent power to grant equitable relief).
Both parties argue that equity favors their position, with mother focusing on her financial hardship and father focusing on the unfairness of denying him compensation for overpayment. We agree that father acted properly by complying with the district court's order while seeking correction of it, and we are sympathetic to father's *112 argument that the district court's functional elimination of his child-support overpayment seems to penalize him for his compliance. But we leave the determination of whether father must be compensated for his overpayment to be addressed by the district court in light of the concerns articulated in this opinion, the equities of this case, and the child's best interests. Therefore, we reverse and remand for further proceedings. The district court shall make findings justifying the exercise of its equitable powers to grant or deny father compensation for overpaid child support. See Nelson v. Nelson, 384 N.W.2d 468, 471 (Minn.App.1986) (stating that a district court must explain exercise of equitable powers with findings).

Other Arguments
Father and mother make arguments that are distinct from their arguments regarding compensation for overpaid child support. Father argues that he should receive "credit" against future child-support payments for a joint tax refund spent by mother. He argues that the parties agreed that the tax refund would be used to pay a separate joint tax liability that father ultimately paid without contribution from mother. The district court denied father's request, and father has not presented any legal authority to support his argument that child support should be reduced to compensate an obligor for money allegedly owed him by the obligee. We reject father's argument because no prejudicial error is obvious. See Grigsby v. Grigsby, 648 N.W.2d 716, 726 (Minn.App. 2002) (deeming an argument waived where a party failed to cite authority supporting his argument and no prejudice from the alleged error was obvious).
Mother argues for the first time on appeal that we should correct a "typographical error" in the dissolution judgment regarding the percentage by which father's child-support obligation is reduced when the parties' first child emancipates. Mother failed to file a notice of review and concedes that she has not properly raised the issue. We therefore decline to address mother's argument.

DECISION
The district court abused its discretion by failing to correct father's child-support obligation as of the date of the dissolution judgment. On remand, the district court shall: (1) correct father's child-support obligation as of the date of the dissolution judgment; (2) calculate father's child-support overpayment; and (3) address whether, to what extent, and how father will be compensated for his child-support overpayment. While we express no opinion regarding whether, to what extent, and how father will be compensated for his child-support overpayment, the district court on remand must make adequate findings of fact to support its decision. We deny all other requests made by the parties.
Reversed and remanded.
