
    CEDE & CO. and Cinerama, Inc., Petitioners Below—Appellants, v. TECHNICOLOR, INC., Respondent Below—Appellee.
    No. 357, 2004.
    Supreme Court of Delaware.
    Submitted: Jan. 26, 2005.
    Decided: May 4, 2005.
    Revised: June 28, 2005.
    
      Robert K. Payson, Esq., Arthur L. Dent, Esq., of Potter, Anderson & Corroon LLP, Wilmington, Delaware, Gary J. Greenberg, Esq. (argued), New York, New York for Appellants.
    Thomas J. Allingham, Esq. (argued), Edward B. Micheletti, Esq., James A. Whitney, Esq., of Skadden, Arps, Slate, Meagher & Flom, LLP, Wilmington, Delaware for Appellee.
    Before STEELE, Chief Justice, HOLLAND and RIDGELY, Justices.
   RIDGELY, Justice.

This is an appeal from a final judgment of the Court of Chancery following a retrial of a statutory appraisal action. This matter arises from a cash-out merger of the minority shareholders of Technicolor, Inc. (“Technicolor”), a Delaware corporation. With approval from a majority of Technicolor’s shareholders, MacAndrews & Forbes Group Inc. (“MAF”) merged its wholly-owned subsidiary, Macanfor Corporation (“Maeanfor”), into Technicolor. The only respondent-appellee in this appraisal action is Technicolor, the surviving corporation. The petitioners-appellants are Cinerama, Inc., the beneficial owner of 201,200 shares of Technicolor common stock, and Cede & Company, the record owners of those shares (collectively, “Cinerama”). The Court of Chancery valued each share at $21.98 and entered a judgment in the principal amount of $4,422,376 with pre-judgment and post-judgment interest.

Cinerama raises two arguments for our consideration. First, Cinerama assigns several errors to the Court of Chancery’s appraisal of the fair value of its Technicol- or shares. Second, Cinerama argues that the Court of Chancery erred, as a matter of law, in awarding post-judgment interest of 10.32% compounded annually from the merger date until only August 2, 1991.

We conclude that the Court of Chancery’s valuation model is supported by record evidence and was the product of an orderly and logical deductive process. However, the Court of Chancery’s use of a 19.89% discount rate and $21.3 million corporate debt was contrary to the law of the case. A discount rate of 15.28% and $19.9 million corporate debt are required by the law of the case doctrine. This results in a per share value of $28.41 and a judgment in the principal amount of $5,716,092.

We also find the law of the case doctrine governs Cinerama’s entitlement to prejudgment interest. Cinerama is entitled to prejudgment interest on this principal amount at 10.32% compounded annually consistent with the initial determination of the Court of Chancery which awarded prejudgment interest until the date of judgment.

Accordingly, we affirm in part, reverse in part, and remand with instructions to enter judgment consistent with this opinion.

I.

This is the sixth appeal by Cinerama relating either to its statutory appraisal proceeding (the “appraisal action”) or its shareholder rescissory damages lawsuit for fraud and unfair dealing (the “personal liability action”). As the Court of Chancery correctly noted, the history of this “sempiternal appraisal action” is thoroughly recorded in the annals of Delaware corporate law.

In the late summer of 1982, MAF sought to purchase Technicolor. MAF structured a deal where it would make a tender offer of $23 per share for all of the outstanding common stock of Technicolor, followed by a second-step merger with the remaining outstanding shares converted into $23 per share, with Technicolor becoming the wholly owned subsidiary of MAF. On October 29, 1982, the Technicolor Board agreed to the acquisition proposal made by MAF. On that date, the Technicolor Board approved the Agreement and Plan of Merger with MAF, recommended to its stockholders the acceptance of the offer of $23 per share and recommended the repeal of the super majority provision in Technicolor’s charter. Technicolor also filed forms 14D-9 and 13D with the Securities and Exchange Commission which reflected those Board actions and recommendations.

In November 1982, MAF commenced an all-cash tender offer of $23 per share to the shareholders of Technicolor. When the tender offer closed on November 30, 1982, MAF had gained control of Technicolor. By December 3, 1982, MAF had acquired 82.19% of the Technicolor stock. Thereafter, MAF and Technicolor were consolidated for tax and financial reporting purposes.

Between the date the Technicolor Board agreed to MAF’s acquisition proposal (October 29, 1982) and the date the merger was accomplished (January 24,1983), MAF made a strategic decision not to follow the Kamerman Plan. “The Court of Chancery made a factual finding that, ‘upon acquiring control’ of Technicolor, Perelman and his associates ‘began to dismember what they saw as a badly conceived melange of businesses.’” MAF then implemented the Perelman Plan, which would sell off four of Technicolor’s unprofitable business units, thereby generating additional cash flow.

The merger was accomplished on January 24, 1983, at which time a cash-out merger occurred, converting all common stock not owned by MAF into the right to receive $23.00 in cash. Cinerama, dissented from the merger and sought a judicial appraisal of its stock under Delaware’s appraisal statute. Cinerama’s holdings represented 4.405% of the total shares of Technicolor outstanding. During pretrial discovery in the appraisal proceeding, certain deposition testimony caused Cinerama to believe that the Technicolor Board violated their fiduciary duties in connection with the sale of the company.

As a result, on January 22,1986, Cinerama filed the personal liability action against Technicolor, seven of the nine members of Technicolor’s Board at the time of the merger, MAF, Macanfor and Ronald 0. Perelman (collectively, the “defendants”). Cinerama’s personal liability action alleged fraud, breach of fiduciary duty and unfair dealing. Cinerama sought, among other things, rescissory damages. The defendants in the personal liability action filed a motion to dismiss on the ground that Cinerama had no standing to pursue such a claim after petitioning for an appraisal of its shares. The Court of Chancery denied this motion, but later ruled that Cinerama would have to elect which cause of action it intended to pursue. Cinerama filed an interlocutory appeal to this Court. In that appeal, this Court concluded that the Court of Chancery erred, as a matter of law, in requiring Cinerama to make an election of remedies before trial. This Court held that Cinerama was entitled to pursue concurrently through trial its appraisal action and its personal liability action. Both actions were then remanded to the Court of Chancery for a consolidated trial.

Following discovery and an extended trial which lasted 47-days, the Court of Chancery announced its first decision in the appraisal action. In a decision dated October 19, 1990, the Court of Chancery found Technicolor’s fair value to be $21.60 under the Kamerman Plan.

The Court of Chancery then issued its personal liability opinion, entering a judgment in favor of the defendants. In its opinion dated June 24, 1991, the Court of Chancery held that even if there was persuasive evidence that the Technicolor Board had not exercised due care in approving the merger, Cinerama had failed to prove that it had been damaged. In reaching this conclusion, the Court of Chancery relied on its earlier appraisal opinion.

Cinerama appealed from the judgments entered in both the appraisal and personal liability actions. With respect to the personal liability action, this Court affirmed in part, reversed in part, and remanded to the Court of Chancery for an application of the entire fairness standard to the challenged transaction, and to resolve additional issues relating to the duty of loyalty. This Court also noted that Cinerama’s appeal of the Court of Chancery’s original appraisal decision was “moot” pending its resolution of the companion personal liability action.

On remand, the Court of Chancery concluded that the Technicolor Board met their burden of showing entire fairness. The Court of Chancery entered judgment in favor of the Technicolor Board in the personal liability action. Cinerama then filed its third appeal. This Court affirmed the Court of Chancery’s final judgment dismissing the personal liability action. This Court reasoned that there was substantial evidence in the record to support the Court of Chancery’s finding that the $23 deal price was the highest price reasonably available. Consequently, the appraisal action that remained in abeyance following this Court’s remand in Technicolor II was no longer moot. Therefore, the only remaining issue was for the Court of Chancery to determine the fair value of Cinerama’s shares and the appropriate post-judgment interest to be awarded.

The Court of Chancery then entered a Restated Modified Order and Final Judgment in the appraisal action on October 27, 1995. That judgment set the fair value of a share of Technicolor’s stock at $21.60. That judgment awarded Cinerama: (I) the principal amount of $4,345,920; (ii) prejudgment interest on that amount at a rate of 10.32% compounded annually from January 24, 1983 (the date of the merger); and (iii) post-judgment interest thereafter, at the rate of 10.5% simple interest, accruing only on the principal award of $4,345,920.

Cinerama then filed its fourth appeal. In addressing Cinerama’s appeal of the Court of Chancery’s appraisal decision, this Court reversed, finding that the Court of Chancery improperly valued Technicol- or. This Court’s mandate required the Court of Chancery to value Technicolor “on the merger date as it was then ‘operating pursuant to the Perelman Plan,’” rather than valuing Technicolor under the Kamerman Plan. The difference between Perelman’s Technicolor as of the merger date and Kamerman’s Technicolor as of October 29, 1982 was that the former operated pursuant to “business plans and strategies focused on the processing and duplication of film and videotape and the provision of services to the United States Government and which planned and expected to generate $50 million in cash during 1983 from the sale of unwanted and/or unsuccessful businesses,” while the later’s “business plans and strategies assumed diversification away from a concentration on film processing and videotape duplication for the professional market toward consumer oriented businesses....”

Recognizing that that dichotomy “resulted in different factual assumptions” being made by the parties’ respective experts, this Court held that the Court of Chancery “had arrived at an ‘understatement of Technicolor’s fair value’ ... because [it] had ‘valued Technicolor pursuant to a discounted cash flow model with the negative factual input and assumptions from the Kamerman Plan rather than the Perelman Plan.’ ” That model was Technicol- or’s Alear model, which the Court of Chancery adopted as its valuation model. This Court held that when the Court of Chancery adopted the Alear model it excluded from its valuation calculus the “value added to the going concern by the ‘majority acquiror,’ ’’including the value “created by substituting new management” and “redeploying assets.” Quantifying the undervaluation, this Court held that the Court of Chancery’s “attribution of only a $4.43 per share value difference between the Perelman Plan and the Kam-erman Plan should not be considered the law of this case upon remand.”

After this matter was remanded to the Court of Chancery, the Chancellor recused himself sua sponte from further participation and the case was re-assigned. The Court of Chancery then set forth its understanding of this Court’s mandate and decided several significant procedural issues. Specifically, the Court of Chancery decided to: (1) appoint a non-lawyer to serve concurrently as an independent expert witness on valuation matters and as a special appraisal master; (2) defer ruling on several issues presented by Cinerama pursuant to Court of Chancery Rule 63; (3) defer consideration of the admissibility under Delaware Rule of Evidence 702 and 703 of Technicolor’s expert opinion evidence from Bruce Klopfenstein, which Cinerama had moved to exclude; and (4) rule that certain post-merger evidence was inadmissible to establish merger date value.

Cinerama filed a motion in the Court of Chancery for certification of an interlocutory appeal. Technicolor did not oppose that application. The Court of Chancery issued an order granting Cinerama’s request for certification and this Court accepted the interlocutory appeal. This Court then reversed the Court of Chancery’s procedural guidelines, holding that a new trial was required to avoid prejudice, the Court of Chancery could appoint an expert witness but could not delegate authority nor appoint a special master for valuation purposes, the Court of Chancery must determine the reliability and relevance of an expert witness, and post-merger evidence of asset sales was admissible to show value as of the merger. This Court ordered the Court of Chancery to conduct a new appraisal trial.

The Court of Chancery correctly recognized that although a new appraisal trial was ordered, the law of the case doctrine still applied. With regard to the pre and post-judgment interest award, the Court of Chancery decided that its prior ruling regarding pre-judgment interest (at the rate of 10.32% per year compounded annually) was the law of the case. However, the Court of Chancery determined that this interest was only to run from the merger date until August 2, 1991 which was the date of the original appraisal judgment.

The new appraisal trial was held in May 2003. On December 31, 2003, the Court of Chancery issued a post-trial opinion valuing Technicolor at $23.33 per share on the merger date. Both Cinerama and Technicolor filed motions pursuant to Court of Chancery Rule 60, each addressing clerical errors made in the appraisal. The Court of Chancery, acknowledging these clerical errors, issued a corrected opinion on July 9, 2004, revising the valuation of Technicol- or to $21.98 per share. This resulted in a judgment in the principal amount of $4,422,376. The Court of Chancery finally concluded that following August 2, 1991, interest should accrue at a rate of 7% simple interest (on the principal of the award only) until the date of payment.

II.

We will address first whether the Court of Chancery abused its discretion with respect to the “other financial inputs” used in its valuation model. We mil specifically address Cinerama’s request for this Court to revise the Court of Chancery’s figures for (1) Vidtronics’ depreciations, (2) New-bury Park’s revenue and material cost income spread, (3) North Hollywood’s 35mm footage and margin and (4) Technicolor’s fixed capital expense forecast.

A.

The parties dispute the applicable standard of appellate review of a determination of fair value made by the Court of Chancery in a statutory appraisal proceeding. Cinerama advances a de novo standard of review. It contends that the Court of Chancery committed legal error in determining the fair value of Technicolor and therefore should not be accorded a high level of deference on appeal. The appellee, on the other hand, advocates for an abuse of discretion standard of review.

The determination of fair value in a statutory appraisal proceeding at the Court of Chancery level “is accorded a high level of deference on appeal.” This Court reviews appraisal valuations pursuant to the abuse of discretion standard, so long as the Court of Chancery has committed no legal error. The Court of Chancery abuses its discretion only if its factual findings do not have support in the record or its valuation is not the result of an orderly and logical deductive process.

This deferential standard of review is based on the recognition “that the Court of Chancery, over time, has developed an expertise” in statutory appraisal proceedings. This Court will defer to the Court of Chancery’s factual findings so long as they are supported by the record, even if this Court might independently reach an opposite conclusion.

It is often the case in statutory appraisal proceedings that a valuation dispute becomes a battle of experts. This is evidenced by the fact that the Court of Chancery is frequently presented with conflicting expert testimony. The Court of Chancery, as the finder of fact in an appraisal case, enjoys the unique opportunity to examine the record and assess the demeanor and credibility of witnesses. Thus, the Court of Chancery is “the sole judge of the credibility of live witness testimony.” This Court will accept the Court of Chancery’s factual determinations if they turn on a question of credibility and the acceptance or rejection of particular pieces of testimony. A factual finding made by the Court of Chancery based on a weighing of expert opinion may be overturned only if arbitrary or lacking evidential support. This Court will only make contradictory findings of fact when the findings below are clearly wrong and the doing of justice requires their overturn.

A less deferential standard of review applies to law of the case determinations. These determinations involve questions of law. A trial court’s application of the law of the case doctrine is therefore subject to de novo review.

B.

We now turn to the merits of Cinerama’s argument that the Court of Chancery abused its discretion with regard to several financial inputs.

1. Vidtronics’Depreciation

Cinerama claims that the Court of Chancery’s ratio of Vidtronics’ depreciation to fixed capital investments was logically impossible. Cinerama points to the fact that for all other divisions of Technicolor, the annual depreciation figure averaged 92.6% of fixed capital investment. Cinerama also points to the fact that Vid-tronics’ forecasted depreciation as a percentage of fixed capital investment varied between 43.1% and 60.0% from 1983 through 1989. It contends that the only explanation for such a low percentage is when new equipment and machinery has a very long useful life (e.g., 25 to 40 years). Cinerama maintains that in a business experiencing rapid obsolescence, like Vid-tronics’ business, a depreciation percentage in this range is logically impossible and is contrary to the nature of the enterprise.

Cinerama’s position is refuted by the present record. The Court of Chancery’s findings for Vidtronics’ forecasted depreciation were based on a historical ratio of depreciation to sales. This historical ratio reveals that Vidtronics was able to accomplish the so-called “logically impossible” feat of maintaining low depreciation to fixed capital expenditures. Thus, the Court of Chancery’s findings did not constitute an abuse of discretion because they were supported by the record and were the product of an orderly and logical deductive process.

2. Newbury Park’s Revenue & Material Cost Income Spread

Cinerama also challenges the Court of Chancery’s valuation of Newbury Park. First, Cinerama argues that the Court of Chancery miscalculated Newbury Park’s revenue based on a 33.1% growth rate. It points to the fact that Newbury Park’s revenue in 1982 was $4,304,259. At a growth rate of 33.1%, Cinerama maintains that the 1983 forecast for Newbury Park’s revenue should have been $5,728,969. Cinerama contends that the Court of Chancery erroneously used a $5,323,000 figure for Newbury Park’s 1983 revenue forecast, which represented only a 23.66% growth rate over 1982 and was $405,969 too low. Second, Cinerama criticizes the Court of Chancery’s finding that, as of the merger date, Newbury Park would not continue to benefit from the material cost spread income stream. This income stream was attributed to rebates on raw material stock.

Both of the Court of Chancery’s findings have support in the record. The Court of Chancery’s calculation of Newbury Park’s revenue was supported by Technicolor’s management predictions for revenues from the CY 1983 Plan. The Court of Chancery used the CY 1983 Plan in valuing every other Technicolor entity. Furthermore, the Court of Chancery’s conclusion that Newbury Park’s material cost spread income stream at the time of the merger would not be expected to continue was supported by evidence contained in the present record. First, the record consisted of testimonial evidence that the rebates on raw material stock was not expected to continue. Second, the present record revealed that Technicolor’s contract with Warner Brothers provided that Warner Brothers (not Technicolor) was entitled to all discounts and thus had a right to all rebate income. Finally, income from material rebates was not included in the CY 1983 Plan for Newbury Park. Thus, the Court of Chancery did not abuse its discretion in valuing Newbury Park.

3. North Hollywood’s 35mm Footage & Margin

Cinerama launches numerous attacks on the Court of Chancery’s valuation of North Hollywood. Despite its breadth, Cinerama’s challenge essentially takes issue with the Court of Chancery’s reliance on the CY 1983 Plan in valuing North Hollywood. However, Cinerama’s attack on the Court of Chancery’s valuation of North Hollywood is foreclosed by its own admission that the valuation was based on evidence contained in the record. In its opening brief, Cinerama concedes that “the Court of Chancery reliefd] on Technicolor’s [CY 1983] Plan for North Hollywood .... ” Because the Court of Chancery’s factual findings have record support, we will not independently make the contrary factual findings needed to support Cinerama’s arguments. Thus, the Court of Chancery did not abuse its discretion in valuing North Hollywood.

4. Technicolor’s Fixed Capital Expenses

Cinerama finally challenges the Court of Chancery’s fixed capital expenditure inputs for Technicolor on two grounds. First, it contends that while the Court of Chancery relied on the CY 1983 Plan in all other respects, its fixed capital expense projection of $37.7 million over the five year period of 1983 through 1987 was well in excess of the CY 1983 Plan. Second, Cinerama argues that the Court of Chancery’s fixed capital expenditure inputs was in excess of certain contractual limitations. It bases this argument on the fact that Technicolor’s controlling shareholder was contractually restricted to spend no more than $25.5 million on fixed capital investments. Cinerama’s challenges are not persuasive.

From 1984 forward, the Court of Chancery forecasted Technicolor’s fixed capital expenditures based on a percentage of the following year’s sales for Technicolor’s operating entities, with the exception of Newbury Park. For Newbury Park, the Court of Chancery based its forecast on the testimony of James Wilson, a Technicolor executive, as well as estimates from analysts, all of which stated that Newbury Park required additional capital expenditures to add to its capacity. For Technicolor’s remaining divisions, the Court of Chancery relied on historical data to forecast fixed capital expenditures. The dramatic jumps in Technicolor’s fixed capital expenditures from 1983 to 1987 were primarily attributed to Newbury Park, where that entity’s forecasted net sales increased greater than threefold. Other causes for the increase in Technicolor’s fixed capital expenditures forecast were attributed to Vidtronics’ and North Hollywood’s capital expenditures returning to their historical levels. The Court of Chancery made these findings based on evidence located in the present record.

Cinerama’s attempt to limit Technicol- or’s fixed capital expenditures to a loan agreement restricting Technicolor’s controlling shareholder to spend no more than $25.5 million in fixed capital expenses is also improper. The Court of Chancery appropriately determined that these restrictions were not binding in perpetuity. These restrictions were capable of being amended or waived pursuant to contract. Thus, the Court of Chancery did not abuse its discretion in forecasting Technicolor’s fixed capital expenditures as its findings were supported by the record and were the product of an orderly and logical deductive process.

III.

We must next decide whether the Court of Chancery erred, as a matter of law, by utilizing a 19.89% discount rate and $21.3 million corporate debt. Cinerama argues that the Court of Chancery’s use of a 19.89% discount rate and $21.3 million corporate debt was contrary to the law of the case. As previously stated, our review of an application of the law of the case doctrine is de novo.

A.

It is well-settled that when an appellate court remands for further proceedings, the trial court must proceed in accordance with the appellate court’s mandate as well as the law of the case established on appeal. The trial court must implement “both the letter and the spirit of the mandate ... taking into account the appellate court’s opinion ... and the circumstances it embraces.” The appellate court’s opinion becomes part of the mandate, and the trial court must consider everything as one. Although the trial court on remand is not constrained by the mandate as to issues not addressed on appeal, the trial court is required to comply with the appellate court’s determinations as to all issues expressly or implicitly disposed of in its decision.

The law of the case doctrine embraces the same principles arising from the mandate rule. The law of the case doctrine posits that “findings of fact and conclusions of law by an appellate court are generally binding in all subsequent proceedings in the trial court or in a later appeal.” The law of the case doctrine, much like the stare decisis doctrine, is founded on the principles of efficiency, finality, stability and respect for the judicial system. The doctrine is meant to bring “some closure to matters already decided in a given case by the highest court of a particular jurisdiction.” Under the principles governing the law of the case doctrine, a trial court may make any order or direction in further progress of the case so long as it is not inconsistent with the decision of the appellate court, as to any question not settled by the decision.

The law of the case doctrine, however, is not inflexible in that, unlike res judicata, it is not an absolute bar to a prior decision that is clearly wrong, produces an unjust result or should be revisited because of changed circumstances. This Court has recognized these three instances as exceptions to the law of the case doctrine.

B.

In light of these governing principles, we turn to the issue of whether the 15.28% discount rate and $19.9 million corporate debt are the law of the case. If so, we must next determine whether any exception to the law of the case doctrine justifies the Court of Chancery’s use of a 19.89% discount rate and $21.3 million corporate debt at the retrial of this appraisal action.

When the Court of Chancery originally calculated the cost of capital, or discount rate, both parties accepted this calculation as reasonable and neither party challenged the calculation on appeal to this Court. In fact, Cinerama argued that under these circumstances the 15.28% discount rate was the law of the case. Both parties employed the 15.28% discount rate during their initial (1998) briefing to the Court of Chancery. Subsequently, the Court of Chancery acknowledged that “[t]he discount rate and Technicolor’s cost of debt may well be the law of the case.”

At the retrial of this appraisal action, Cinerama’s expert computed a 14.6% cost of capital, while Technicolor’s expert computation was 15.8%. Thus, the parties presented the Court of Chancery with a 14.6% to 15.8% range, with the 15.28% cost of capital in the middle. Notwithstanding these presentations, the Court of Chancery disregarded its prior determination of 15.28% and calculated a 19.89% cost of capital.

Although the appellee argues in this appeal that the 15.28% discount rate and $19.9 million corporate debt were not binding law of the case determinations, that is a new position for the appellee which is directly contrary to its prior position in this case. Initially, the appellee recognized that it “lost” those issues at the first trial, where it argued for a mixture of two rates, 20.4% and 17.3%, so it filed a notice of cross-appeal challenging those determinations. However, it abandoned that cross-appeal. After this Court’s decision in Technicolor TV, the appellee recognized that those two determinations were the law of the case because they were unrelated to the Court of Chancery’s erroneous majority acquiror principle and had no relation to the Alear cash flow inputs that were rejected and had to be retried. The appellee took this position in briefs it filed in 1998 with the Court of Chancery. For example, in its Answering Brief to the Court of Chancery on remand from Technicolor TV, the appellee wrote: “As we have shown in our Opening Brief, the Al-ear model can be modified to value Perelman’s Technicolor using the law of the ease discount rate of 15.28% and the law of the case corporate debt of $19.9 million.”

After this Court’s decision in Technicol- or V, the appellee became concerned that it was bound by the law of the case rulings relating to the discount rate and corporate debt. It filed a motion for reargument with this Court requesting that this Court’s decision in Technicolor V be modified “to establish that matters previously resolved as law of the case ... must be determined anew in the course of the new Perelman Plan trial.” This Court resolved appellee’s motion by summarily denying it. In light of the foregoing record, the 15.28% discount rate and $19.9 million corporate debt were clearly established as the law of the case.

We next examine whether any exceptions to the law of the case doctrine applies which would permit the use of a 19.89% discount rate and $21.3 million corporate debt. When the Court of Chancery determined the 15.28% discount rate in 1991, it took a historic perspective, employed objective facts including a $19.9 million corporate debt listed in a filing with the Securities Exchange Commission. The Court of Chancery further noted that the discount rate and the corporate debt were “free standing” from the competing discounted cash flow models.

After the new trial, the Court of Chancery did not cite any exception to the law of the case doctrine. It did state that the $19.9 million corporate debt was “not necessarily an accurate reflection of the true outstanding Technicolor debt.” But that is not the standard for an exception to the law of the case doctrine. To avoid the 15.28% discount rate and $19.9 million corporate debt which are the law of the case, the Court of Chancery had to determine that the findings were “clearly wrong.” It did not.

We find no evidence in the record to show that these findings of the Court of Chancery in 1991 were clearly wrong, or that they produce an injustice. The only circumstance that has changed since 1991 was the remand for a new trial. This was not a basis to change matters already decided and not appealed. Because there was no available exception to the law of the case doctrine, these findings on the discount rate and corporate debt of Technicolor were binding upon the Court of Chancery. When the discount rate of 15.28% and corporate debt figure of $19.9 million required by the law of the case are applied, Technicolor’s per share value as of the date of the merger equals $28.41. This translates to a judgment against Technicolor in the principal amount of $5,716,092.

IV.

We must finally decide whether the Court of Chancery erred, as a matter of law, when it decided to accrue post-judgment interest from the date of the reversed 1991 judgment. Cinerama further argues that the Court of Chancery further erred by awarding only simple interest post-judgment, with interest to accrue on the principal amount of the judgment only. Cinerama urges us to vacate the Court of Chancery’s interest ruling under the law of the case doctrine because a 10.32% annual compound interest through the date of payment or, alternatively, until the date of the entry of a final judgment entered after compliance with the remand instructions on July 21, 2004 is required.

A.

The parties again differ on the standard of review to be applied to the Court of Chancery’s interest award. The appellee advances an abuse of discretion standard of review, while Cinerama argues for a de novo standard of review.

The Court of Chancery is vested with broad discretion to fashion an interest award in an appraisal proceeding. This Court generally reviews an interest award in an appraisal proceeding for abuse of discretion. An interest award made arbitrarily or capriciously would be an abuse of discretion. However, when the Court of Chancery’s interest award involves questions of law, that award will be subject to a de novo standard of review. In this case, we are asked to review the Court of Chancery’s law of the case determinations regarding its post-judgment interest award. Since this is a question of law, we again will apply a de novo standard of review to the Court of Chancery’s law of the case determinations.

B.

The Court of Chancery ruled that the 10.32% annual compound interest was the law of the case and was applicable to the period of January 24, 1983 through August 2, 1991 (the date of the original appraisal judgment). It limited the retrial evidence to “the rate and form of post-judgment interest” and “the relevant post-judgment period.” In its post-trial opinion, the Court of Chancery held that its prior pre-judgment interest award constituted a binding law of the case determination, but ruled that the pre-judgment period ended on August 2, 1991 which was the date of the original appraisal judgment. The Court of Chancery concluded that post-judgment interest would accrue from that date. Because that judgment was vacated on appeal, the date of August 2, 1991 cannot be used to calculate the parameters of the prejudgment period.

When this Court reversed the Court of Chancery’s valuation in Technicolor IV, the original appraisal judgment was vacated. When a judgment is completely reversed on its merits, post-judgment interest commences on the date of the remand judgment. Conversely, the prejudgment interest period precedes the same date of the remand judgement. We therefore hold that Cinerama is entitled to the law of the case pre-judgment interest award of 10.32% compounded annually until the entry of a judgment on remand. Cinerama is entitled to a legal rate of interest thereafter as the Court of Chancery held.

Y.

We commend the Court of Chancery for its careful analysis. Its discretion was limited on remand, however, by the law of the case doctrine which in this case required a 15.28% discount rate, $19.9 million corporate debt and prejudgment interest at the rate of 10.32% compounded annually. Accordingly, we affirm in part and reverse in part the judgments of the Court of Chancery. We remand this case with instructions to enter judgment consistent with this opinion so that this litigation, at long last, is brought to an end. 
      
      . See Cede & Co. v. Technicolor, Inc., 542 A.2d 1182 (Del.1988) (‘'Technicolor I"); Cede & Co. v. Technicolor, Inc., 634 A.2d 345 (Del. 1993), modified, 636 A.2d 956 (Del.1994) {“Technicolor II ”); Cinerama, Inc. v. Technicolor, Inc., 663 A.2d 1156 (Del. 1995) (“Technicolor III Cede & Co. v. Technicolor, Inc., 684 A.2d 289 (Del. 1996) (''Technicolor IV"); Cede & Co. v. Technicolor, Inc., 758 A.2d 485 (Del.2000) (“Technicolor V ").
     
      
      . At that time, Technicolor consisted of several distinct business units, including: (i) Professional Services, which provided film processing for movie studios and television; (ii) Newbury Park, which duplicated pre-record-ed videocassettes; (iii) Vidtronics, which provided videotape post-production and film-to-tape transfer services; (iv) Government Services, which provided contract support services to the United States government; (v) Corporate Headquarters, which provided managerial support for the other business units; (vi) One Hour Photo, which provided one-hour retail photo finishing; (vii) Consumer Photo Processing, which provided retailers with photo processing services; (viii) Gold Key, which licensed a library, consisting primarily of B-movies, to independent television stations; and (ix) Audio Visual, which sold camera equipment directly to consumers. MAF, as the acquiror, planned certain changes to Technicolor. Under the Perelman Plan (named after MAF’s Chairman and controlling shareholder Ronald O. Perelman), MAF was to sell four of Technicolor’s business units, including One Hour Photo, Consumer Processing Photo, Gold Key and Audio Visual. Two of those business units, Gold Key and Audio Visual, were already in the process of being sold prior to MAF's tender offer. MAF's planned to operate the remaining business units exactly as they had been prior to the merger. Thus, the Perelman Plan took into consideration the cash flow generated by selling off these four unprofitable business units.
     
      
      . Technicolor TV, 684 A.2d at 293.
     
      
      . The parties have previously agreed that the appraised value of Technicolor must be fixed as of January 24, 1983. This was the stipulated date of the merger. See Technicolor TV, 684 A.2d at 293 (citing Alabama By-Products Corp. v. Neal, 588 A.2d 255, 256-57 (Del. 1991)).
     
      
      . Cinerama also argued that the merger was void ab initio because it violated a super majority provision in Technicolor’s charter that required either unanimous director approval or a 95% vote of the shareholders. This Court later affirmed the Court of Chancery’s "rejection of Cinerama’s claim that the merger was void ab initio because [a director] had cast an opposing vote.” See Technicolor II, 634 A.2d at 371-72.
     
      
      . Cede & Co. v. Technicolor, Inc. C.A. Nos. 7129, 8358, 1987 WL 4768 (Jan. 13, 1987), reprinted in 13 Del. J. Corp. L. 225 (1988).
     
      
      . Technicolor I, 542 A.2d at 1184 — 85.
     
      
      . Id. at 1192.
     
      
      . Id.
      
     
      
      . Cede & Co. v. Technicolor, Inc., 1990 WL 161084 (Del.Ch.).
     
      
      . Cinerama, Inc. v. Technicolor, Inc., 1991 WL 111134 (Del.Ch.).
     
      
      . Technicolor II, 634 A.2d at 351.
     
      
      . Id.
      
     
      
      . Cinerama, Inc. v. Technicolor, Inc., 663 A.2d 1134, 1144 (Del.Ch.1994).
     
      
      . Technicolor III, 663 A.2d at 1180.
     
      
      . Id. at 1177.
     
      
      . Although the personal liability action had been resolved in favor of the Technicolor Board, Cinerama was still entitled to receive the fair value of its Technicolor shares. See Technicolor I, 542 A.2d at 1191.
     
      
      . Technicolor TV, 684 A.2d at 298-301.
     
      
      . Technicolor V, 758 A.2d at 489 (quoting Technicolor IV, 684 A.2d at 299).
     
      
      . Technicolor TV, 684 A.2d at 294.
     
      
      . Id.
      
     
      
      . Technicolor V, 758 A.2d at 489 (quoting Technicolor TV, 684 A.2d at 299) (emphasis added).
     
      
      . Id.
      
     
      
      . Technicolor TV, 684 A.2d at 298-99.
     
      
      
        .Id. at 299-300.
     
      
      . Technicolor V, 758 A.2d at 487.
     
      
      . Id. at 492.
     
      
      . Id.
      
     
      
      . Cede & Co. v. Technicolor, Inc., 2003 WL 23700218, at *45, 2003 Del.Ch. LEXIS 146, at *185.
     
      
      . Id. at *48, *48-*49, 2003 Del.Ch. LEXIS at *196, *198-*99.
     
      
      . Id. at *1, 2003 Del.Ch. LEXIS at *2.
     
      
      . Id. at *48-*49, 2003 Del.Ch. LEXIS at *198.
     
      
      . Technicolor, 2003 WL 23700218, *48-*49, 2003 Del.Ch. LEXIS 146, *199.
     
      
      . We use the term "other financial inputs” to refer to the inputs challenged by Cinerama on appeal excluding the discount rate and corporate debt. We consider the merits of Cinerama’s critique of the Court of Chancery’s discount rate and corporate debt figure infra at Part III.
     
      
      . M.G. B(incorporation v. Le Beau, 737 A.2d 513, 526 (Del. 1999) (citing Rapid-American Corp. v. Harris, 603 A.2d 796, 802 (Del. 1992); In re Appraisal of Shell Oil Co., 607 A.2d 1213, 1219 (Del. 1992)).
     
      
      . Id. (citing Rapid-American Corp., 603 A.2d at 802).
     
      
      . Id. (citing Alabama By-Products, 588 A.2d at 259).
     
      
      . In re Appraisal of Shell Oil Co., 607 A.2d at 1219.
     
      
      . Bell v. Kirby Lumber Corp., 413 A.2d 137, 142 (Del. 1980) (quoting In re Delaware Racing Ass'n, 213 A.2d 203, 207-08 (Del.1965)).
     
      
      . Rapid-American Corp., 603 A.2d at 802.
     
      
      . Id. (citing Kahn v. Household Acquisition Corp., 591 A.2d 166, 175 (Del.1991); Alabama By-Products, 588 A.2d at 258-59; Cavalier Oil v. Harnett, 564 A.2d 1137, 1146 (Del.1989)).
     
      
      . Hudak v. Procek, 806 A.2d 140, 151 n. 28 (Del.2002).
     
      
      . Alabama By-Products, 588 A.2d at 259.
     
      
      . Cavalier, 564 A.2d at 1146 (citing Baríes v. Herzberg, 206 A.2d 507, 509 (Del. 1965)).
     
      
      . Levitt v. Bouvier, 287 A.2d 671, 673 (Del. 1972).
     
      
      . Alphamed Inc. v. B. Braun Medical, Inc., 367 F.3d 1280, 1285 (11th Cir.2004) (citing Field v. Mans, 157 F.3d 35, 40 (1st Cir.1998)) (providing that an appellate court reviews de novo a trial court’s application of the law of the case doctrine).
     
      
      
        .Levitt v. Bouvier, 287 A.2d 671, 673 (Del. 1972).
     
      
      . The CY 1983 Plan was a financial forecast for each of Technicolor’s operating entities. The CY 1983 Plan was completed after MAF had begun to assume operational control over Technicolor and was found by the Court of Chancery to be the "most suitable” forecast for determining the fair value of Technicolor as of the merger date. See Technicolor, 2003 WL 23700218, at *7, 2003 Del.Ch. LEXIS 146, at *26.
     
      
      . Insurance Corp. of Am. v. Barker, 628 A.2d 38, 40 (Del.1993) (citing Bankers Trust Co. v. Bethlehem Steel Corp., 761 F.2d 943, 949 (3d Cir.1985) (citations omitted)).
     
      
      . Piambino v. Bailey, 757 F.2d 1112, 1119 (11th Cir.1985) (citations omitted).
     
      
      . Barker, 628 A.2d at 40 (citing Delgrosso v. Spang & Co., 903 F.2d 234, 240 (3d Cir.), cert. denied, 498 U.S. 967, 111 S.Ct. 428, 112 L.Ed.2d 412 (1990)).
     
      
      
        .Id. (citing Piambino, 757 F.2d at 1119 (citations omitted); Gegenheimer v. Galan, 920 F.2d 307, 309 (5th Cir.1991); Nguyen v. United States, 792 F.2d 1500, 1502 (9th Cir.1986); Bankers Trust Co., 761 F.2d at 950 (citations omitted)).
     
      
      . Id.
      
     
      
      . See id. (citations omitted). See also Arizona v. California, 460 U.S. 605, 618, 103 S.Ct. 1382, 75 L.Ed.2d 318 (1983) (providing that when a court decides upon a rule of law that decision should continue to govern the same issues in subsequent stages of the same litigation).
     
      
      . Gannett Co., Inc. v. Kanaga, 750 A.2d 1174, 1181 (Del.2000).
     
      
      . Id.
      
     
      
      . Barker, 628 A.2d at 41 (quoting Bankers Trust Co., 761 F.2d at 950).
     
      
      . Hamilton v. State, 831 A.2d 881, 887 (Del. 2003) (citing Brittingham v. State, 705 A.2d 577, 579 (Del. 1998); Zim v. VLI Corp., 681 A.2d 1050, 1062 n. 7 (Del. 1996)).
     
      
      . Id. at 887.
     
      
      . Cinerama, Inc. v. Technicolor, Inc., 1999 WL 135242, at *3, 1999 Del.Ch. LEXIS 32, at *8.
     
      
      . Id.
      
     
      
      . Technicolor, 2003 WL 23700218, at *43, 2003 Del.Ch. LEXIS 146, at *179.
     
      
      . Technicolor, 1990 WL 161084, at *29.
     
      
      . Cede & Co. v. Technicolor, Inc., 758 A.2d 485 (Del.2000).
     
      
      . 1990 WL 161084, *24-*25, 1990 Del.Ch. LEXIS 259, *82.
     
      
      . Id.
      
     
      
      . 2003 WL 23700218, *40-*41, 2003 Del.Ch. LEXIS 146, *170.
     
      
      . We take this opportunity to reconcile the result here with this Court’s prior holdings in this case. We will first address our holding in Technicolor TV, where this Court required the Court of Chancery to value Technicolor under the Perelman Plan as of the merger date rather than valuing Technicolor under the Kamerman Plan. Technicolor V, 758 A.2d at 489 (citing Technicolor TV, 684 A.2d at 299). In that case we held that the Court of Chancery excluded from its valuation calculus the “value added to the going concern by the 'majority acquiror,’ "including the value "created by substituting new management” and “redeploying assets.” Technicolor IV, 684 A.2d at 298-99. Our holding today finds that Perelman's Technicolor was worth $6.81 more than Kamerman’s Technicolor. This is consistent with our prior holding that the Court of Chancery's "undervalued” determination of a $4.43 differential should not be deemed the law of the case. Id.
      
      We next reconcile this result in light of our decision affirming the Court of Chancery’s judgment in favor of the defendants in the personal liability action. This Court affirmed the Court of Chancery’s finding that the $23 deal price was the highest price reasonably available because it was supported by substantial record evidence. Technicolor III, 663 A.2d at 1177. This decision simply meant that $23 was a fair price for Perelman to pay in October 1982 for a company then operating under the Kamerman Plan. The Court of Chancery held in 1990 that the Perelman Plan actually increased the value of the company between October 29, 1982 (the date the Technicolor Board agreed to MAF's acquisition proposal) and January 24, 1983 (the date the merger was accomplished) by $4.43 per share, but that the minority shareholders were not entitled to receive that increase. Cede & Co. v. Technicolor, 1990 WL 161084, at *T9-*20, 1990 Del.Ch. LEXIS 259, at *66. We reversed that determination and held that any increase as of the date of the merger had to be paid to the dissenting shareholders on that date. Technicolor TV, 684 A.2d at 298-99. Our decision today accepting the valuation by the Court of Chancery under the Perelman Plan at the new trial, but with the law of the case discount rate and corporate debt, simply determines that the increase that the minority shareholders were adjudged to be due under Technicolor TV was $6.81 per share rather than $4.43 per share.
     
      
      . Del. Code Ann. tit. 8, § 262(i) (2005).
     
      
      . In re Appraisal of Shell Oil Co., 607 A.2d at 1221.
     
      
      . Id.
      
     
      
      . Alphamed, 367 F.3d at 1285 (citing Field, 157 F.3d at 40).
     
      
      . Technicolor, 2003 WL 23700218, at *4-*5, 2003 Del.Ch. LEXIS 146, at *16.
     
      
      . Id. at *45, 2003 Del.Ch. LEXIS at *185.
     
      
      . Cf. Wheeler v. John Deere Co., 935 F.2d 1090, 1097 (10th Cir.1991) (holding that when a case is completely reversed on its merits post-judgment interest is properly commenced on the date of the remand judgment); Ashland Oil, Inc. v. Phillips Petroleum Co., 607 F.2d 335, 336 (10th Cir.1979), cert, denied, 446 U.S. 936, 100 S.Ct. 2153, 64 L.Ed.2d 788 (1980) (holding that post-judgment interest accrues from the date of the second judgment where the case was remanded for development of additional facts); Riha v. International Tel. & Tel. Corp., 533 F.2d 1053, 1054 (8th Cir.1976) ("A judgment vacated on appeal is of no further force and effect”); Fisher Props., Inc. v. Arden-Mayfair, Inc., 115 Wash.2d 364, 798 P.2d 799, 805 (1990) (providing that post-judgment interest runs from the date of the new judgment where the original judgment has been reversed); Printed Terry Finishing Co. v. City of Lebanon, 264 Pa.Super. 192, 399 A.2d 732 (1979) (finding that interest did not run from the date of the original verdict when the original case was reversed where communication between appellee’s attorney and a juror cast suspicion upon the integrity of the original jury verdict in its entirety); Maynard v. Maynard, 251 S.W.2d 454 (Ky.Ct.App.1952) (holding that the denial of interest on the wife's cash award was proper because the award did not bear interest until reduced to final judgment which was not done until the case was remanded to the trial court); Stewart v. Storm's Shoes, Inc., 426 A.2d 839, 841 (Del. 1981) (affirming the Superior Court’s determination to accrue interest from entry of the judgment following the acceptance of a remittitur); Handler Const., Inc. v. CoreStates Bank, N.A., 633 A.2d 356, 359 (Del.1993) (quoting Angelli v. Sherway, 560 A.2d 1028, 1034 n. 2 (Del.1989)) ("The authority to enter a judgment nunc pro tunc, which is applied to acts allowed to be done after the time they should have been done, with retroactive effect, is ‘limited to corrections of clerical errors or ministerial defects to the end that the original intention of the Court will be implemented.’ ”).
     