We must decide whether prices listed in a wholesale coin price guide contain sufficient originality to merit the protection of the copyright laws.

I

Kenneth Rapes operates a coin business, Western Reserve Numismatics, in Ohio. In response to many inquiries he received regarding the price of coins, Rapes developed “The Fair Market Coin Pricer,” which listed on his internet web page the retail prices of many coins. In order to generate the prices he listed, Rapes used a computer program he developed to create retail prices from wholesale prices. The exact process is unclear, but Rapes acknowledges using appellee CDN, Inc.’s wholesale price lists.

CDN publishes the Coin Dealer Newsletter, a weekly report of wholesale prices for collectible United States coins, as well as the Coin Dealer Newsletter Monthly Supplement and the CDN Quarterly. The Newsletter, or “Greysheet” as it is known in the industry, includes prices for virtually all collectible coins and is used extensively by dealers. In December 1996, CDN discovered the existence of Rapes’ internet site and list of current retail prices. CDN filed a complaint on February 21, 1997 in the U.S. District Court for the Central District of California, alleging that Rapes infringed CDN’s copyrights by using CDN’s wholesale prices as a baseline to arrive at retail prices. The complaint asked the court to determine that Rapes infringed its copyright and to enjoin Rapes from future infringement.

Rapes responded that although the subject works contained some original copyrightable subject matter, he did not copy any of it. Rapes also asserted various affirmative defenses including license, unclean hands, and estoppel. On December 17, 1997, the parties executed a “Stipulation to Waive Trial in Lieu of Case Dispos-itive Cross-Motions for Summary Judgment.” (“Stipulation”) The Stipulation provided that “the dispositive issue in this copyright infringement case is whether the prices listed in plaintiff’s copyrighted wholesale coin price guides comprise copyrightable subject matter under Section 102 of the 1976 Copyright Act ( 17 U.S.C. § 102 ).” The parties agreed that the “issue of eopyrightability may effectively be presented to the Court by cross-motions for summary judgment which, once argued and ruled upon, will dispose of the case in its entirety.”

In accordance with the stipulation, the parties filed cross-motions for summary judgment, which the district court heard on February 2, 1998. After reciting the parties’ stipulation that the issue of copy-rightability was dispositive of the case, the court ruled that CDN’s “prices are original creations, not uncopyrightable facts.” By order entered February 9, 1998, the court granted CDN’s motion for summary judgment and denied that of Rapes. The court enjoined Rapes from infringing CDN’s copyright.

Rapes timely appealed.

II

As an initial matter it is important to clarify the scope of this appeal. To make out a claim for copyright infringement, a plaintiff must show: (1) ownership of a valid copyright and (2) copying by the defendant of protectable elements of the work. See Smith v. Jackson, 84 F.3d 1213, 1218 (9th Cir.1996); Harper & Row Publishers, Inc. v. Nation Enters., 471 U.S. 539, 548 , 105 S.Ct. 2218 , 85 L.Ed.2d 588 (1985). Although CDN’s original complaint alleged infringement, the parties in their stipulation agreed that the dispositive issue in this infringement case was whether the prices are copyrightable subject matter. By entering into this stipulation, Rapes effectively admitted to having copied CDN’s work.

Nevertheless, Rapes attempts to raise several issues in his appeal beyond that of eopyrightability. This he cannot do for he is bound by the stipulation. Because stipulations serve both judicial economy and the convenience of the parties, courts will enforce them absent indications of involuntary or uninformed consent. See United States v. McGregor, 529 F.2d 928, 931 (9th Cir.1976). No claim that the stipulation should not be enforced has been made here. Thus the stipulation bars any litigation over copying, the second prong of an infringement action.

The stipulation also prevents Rapes from raising on appeal the affirmative defenses&emdash;license, unclean hands, and estoppel-originally raised in his answer to CDN’s complaint. An appellate court will not consider issues not properly raised before the district court. See Crawford v. Lungren, 96 F.3d 380 , 389 n. 6 (9th Cir. 1996). The “ ‘withdrawal of an objection is tantamount to a waiver of an issue for appeal.’ ” Slaven v. American Trading Transp. Co., Inc., 146 F.3d 1066 , 1069 (9th Cir.1998) (quoting United States v. Manante, 44 F.3d 1407 , 1419 n. 18 (9th Cir. 1995)). In Slaven, the appellant first raised several objections to a settlement agreement. See id. at 1069. It then unconditionally signed a stipulation agreeing to the proposed settlement. See id. When the appellant tried to object to the settlement on appeal, the court held that it had waived its right to challenge the agreement by signing the stipulation. See id. Likewise, by stipulating that the sole issue in this case is the copyrightability of the prices, Rapes waived the affirmative defenses he initially asserted and the issue of whether he copied CDN’s prices. Thus the sole issue in this appeal, and the only one presented to the district court for decision, is whether the prices are copyrightable.

Ill

The Constitution gives Congress the power “To promote the Progress of Science ... by securing for limited Times to Authors ... the exclusive Right to their ... Writings.” U.S. Const, art. 1, § 8, cl. 8. Accordingly, Congress has granted copyright protection to “original works of authorship,” 17 U.S.C. § 102 (a), as well as “compilations.” Id. at § 103(a). The copyright in a compilation “extends only to the material contributed by the author of such work, as distinguished from the preexisting material employed in the work....” Id. at § 103(b).

Discoverable facts, like ideas, are not copyrightable. But compilations of facts are copyrightable even where the underlying facts are not. See Feist Publications, Inc. v. Rural Tel. Serv. Co., 499 U.S. 340, 344 , 111 S.Ct. 1282 , 113 L.Ed.2d 358 (1991). The distinction between facts and non-facts, and between discovery and creation, lies at the heart of this case. The essential ingredient present in creations, but absent in facts, is originality, “the sine qua non of copyright.” Id. at 345 , 111 S.Ct. 1282 . Subject matter created by and original to the author merits copyright protection. Items not original to the author, i.e., not the product of his creativity, are facts and not copyrightable. In Feist, the issue was whether white page listings of telephone numbers qualified for copyright protection as compilations. The Court held that they did not. In order to warrant protection, compilations and other works must contain a minimal amount of originality or creativity. See id. at 361 , 111 S.Ct. 1282 . The white page listings, which included everyone within a geographical area and were arranged alphabetically, did not. See id. at 362-63 , 111 S.Ct. 1282 . Thus they could be copied in their entirety despite the time and effort spent to compile them.

Appellant’s attempt to equate the phone number listings in Feist with CDN’s price lists does not withstand close scrutiny. First, Rapes conflates two separate arguments: (1) that the listing, selection, and inclusion of prices is not original enough to merit protection; and (2) that the prices themselves are not original creations. Whether CDN’s selection and arrangement of the price lists is sufficiently original to merit protection is not at issue here. CDN does not allege that Rapes copied the entire lists, as the alleged in-fringer had in Feist. Rather, the issue in this case is whether the prices themselves are sufficiently original as compilations to sustain a copyright. Thus Rapes’ argument that the selection is obvious or dictated by industry standards is irrelevant.

Although the requirement of originality is a constitutional one inherent in the grant to Congress of the power to promote science and the useful arts, the required level of originality is “minimal.” Feist, 499 U.S. at 358 , 111 S.Ct. 1282 . The telephone listings did not qualify because they fell into the “narrow category of works in which the creative spark is utterly lacking or so trivial as to be virtually nonexistent.” Id. at 359 , 111 S.Ct. 1282 . The numbers themselves were given by the phone company. Their selection (or rather universal inclusion) and arrangement in alphabetical order were too obvious to be original. Nevertheless, “the requisite level of creativity is extremely low; even a slight amount will suffice. The vast majority of works make the grade quite easily, as they possess some creative spark, ‘no matter how crude, humble or obvious’ it might be.” Feist, 499 U.S. at 345 , 111 S.Ct. 1282 (quoting 1 M. Nimmer & D. Nimmer, Copyright § 1.08[C][1] (1990)). This spark glows in CDN’s prices, which are compilations of data chosen and weighed with creativity and judgment.

Here, the district court, explicitly referencing Feist , held that the prices in CDN’s guides are not facts, they are “wholly the product of [CDN’s] creativity. The evidence indicates that the plaintiff uses its considerable expertise and judgment to determine how a multitude of variable factors impact upon available bid and ask price data. And it is this creative process which ultimately gives rise to the Plaintiffs ‘best guess’ as to what the current ‘bid’ and ‘ask’ prices should be. As such, the Court finds that these prices were created, not discovered.” District Court Order Granting Summary Judgment, February 5,1998.

We agree. CDN’s process to arrive at wholesale prices begins with examining the major coin publications to find relevant retail price information. CDN then reviews this data to retain only that information it considers to be the most accurate and important. Prices for each grade of coin are determined with attention to whether the coin is graded by a professional service (and which one). CDN also reviews the online networks for the bid and ask prices posted by dealers. It extrapolates from the reported prices to arrive at estimates for prices for unreported coin types and grades. CDN also considers the impact of public auctions and private sales, and analyzes the effect of the economy and foreign policies on the price of coins. As the district court found, CDN does not republish data from another source or apply a set formula or rule to generate prices. The prices CDN creates are compilations of data that represent its best estimate of the value of the coins.

That this process takes much time and effort is wholly irrelevant to whether the end product of this work is copyrightable. See Feist, 499 U.S. at 349 , 111 S.Ct. 1282 . The Supreme Court in Feist expressly rejected the “sweat of the brow” theory of copyright which would protect subject matter that was expensive and time-consuming to gather. See id. at 352-56 , 111 S.Ct. 1282 . “[C]opyright rewards originality, not effort.” Id. at 364 , 111 S.Ct. 1282 . Thus if CDN did nothing more than discover and report the prices paid by dealers in transactions throughout the country, the prices would not be copyrightable. But it did much more than this. The prices listed are not mere listings of actual prices paid; rather, they are CDN’s best estimate of the fair value of that coin. To arrive at this estimate, CDN employs the process described above that satisfies the “minimal degree of creativity” demanded by the Constitution for copyright protection. Id. at 345 , 111 S.Ct. 1282 . This is not a process that is “so mechanical or routine as to require no creativity whatsoever.” Id. at 362 , 111 S.Ct. 1282 . As this court has stated, consistent with Feist , the requisite level of creativity is “extremely low.” Urantia Foundation v. Maaherra, 114 F.3d 955, 959 (9th Cir.1997) (holding that the arrangement of divine revelations met the level of creativity required for copyright); see also Los Angeles News Serv. v. Tullo, 973 F.2d 791 (9th Cir.1992) (holding that raw news videotape is original and copyrightable).

Our holding that the prices are copyrightable is consistent with that of the Second Circuit in CCC Info. Servs., Inc. v. Maclean Hunter Mkt. Reports, 44 F.3d 61 (2d Cir.1994). Maclean Hunter published the Red Book, a list of car values for various regions of the United States. The Red Book listed the editors’ projections of the value of different kinds of used ears for six weeks after publication. CCC Information Systems had used these values in compiling its computer databases. Mac-lean Hunter sued for infringement, and the district court found that the values were facts and as such were not copyrightable. The Second Circuit reversed. The court held that the valuations were not “preexisting facts that had merely been discovered by the Red Book editors,” but instead “represented predictions by the Red Book editors of future prices estimated to cover specified geographic regions.” CCC, 44 F.Sd at 67. Like CDN’s prices, the prices in the Red Book granted copyright protection by the Second Circuit, are “based not only on a multitude of data sources, but also on professional judgment and expertise.” Id.

Kapes attempts to distinguish CCC by arguing that the prices in the Red Book were projections of future values, while the prices in the Greysheet are estimates of present value. But the distinction between present and future values is not important to this case. What is important is the fact that both Maclean and CDN arrive at the prices they list through a process that involves using their judgment to distill and extrapolate from factual data. It is simply not a process through which they discover a preexisting historical fact, but rather a process by which they create a price which, in their best judgment, represents the value of an item as closely as possible. If CDN merely listed historical facts of actual transactions, the guides would be long, cumbersome, and of little use to anyone. Dealers looking through such data would have to use their own judgment and expertise to estimate the value of a coin. What CDN has done is use its own judgment and expertise in arriving at that value for the dealers. This process imbues the prices listed with sufficient creativity and originality to make them copyrightable.

IV

In his defense, Kapes argues that a price is an idea of the value of the product, which can be expressed only using a number. Thus the idea and the expression merge and neither qualifies for copyright protection. This is the doctrine of merger. The argument springs from a venerable principle of copyright law. See Mazer v. Stein, 347 U.S. 201, 217 , 74 S.Ct. 460 , 98 L.Ed. 630 (1954) (Copyright “protection is given only to the expression of the idea-not the idea itself.”). Ideas, like facts, are not entitled to copyright. See 17 U.S.C. § 102 (b); Baker v. Selden, 101 U.S. 99 , 25 L.Ed. 841 (1879). In order to protect the free exchange of ideas, courts have long held that when expression is essential to conveying the idea, expression will also be unprotected. “When the ‘idea’ and its ‘expression’ are thus inseparable, copying the ‘expression’ will not be barred, since protecting the ‘expression’ in such circumstances would confer a monopoly of the ‘idea’ upon the copyright owner free of the conditions and limitations imposed by the patent law.” Herbert Rosenthal Jeiv-elry Corp. v. Kalpakian, 446 F.2d 738, 742 (9th Cir.1971). But accepting the principle in all cases, including on these facts, would eviscerate the protection of the copyright law. Cf. CCC, 44 F.3d at 70 (noting that every compilation represents an idea, which in order to be conveyed accurately must be conveyed only by its expression).

Conceptually, the problem arises because the “critical distinction between ‘idea’ and ‘expression’ is difficult to draw. As Judge [Learned] Hand candidly wrote, ‘Obviously, no principle can be stated as to when an imitator has gone beyond copying the “idea,” and has borrowed its “expression.” ’ ” See Rosenthal, 446 F.2d at 742 (quoting Peter Pan Fabrics, Inc. v. Martin Weiner Corp., 274 F.2d 487, 489 (2d Cir. I960)). We have endorsed Judge Hand’s abstractions formulation laid out in Nichols v. Universal Pictures Corp., 45 F.2d 119, 121 (2d Cir.1930). See Rosenthal, 446 F.2d at 742 . The formulation recognizes that every work can be described at varying levels of abstraction, and the higher the level of abstraction copied, the less likely this taking will be infringement of a copyright.

As Judge Hand noted, the difference between idea and expression is one of degree. This circuit has held that “[t]he guiding consideration in drawing the line is the preservation of the balance between competition and protection reflected in the patent and copyright laws.” Rosenthal, 446 F.2d at 742 . In this case, the prices fall on the expression side of the line. CDN does not, nor could it, claim protection for its idea of creating a wholesale price guide, but it can use the copyright laws to protect its idea of what those prices are. See id. at 742 (denying protection to the idea of creating a jeweled bee pin where there was no indication that the alleged infringer had copied the pin in question). Drawing this line preserves the balance between competition and protection: it allows CDN’s competitors to create their own price guides and thus furthers competition, but protects CDN’s creation, thus giving it an incentive to create such a guide. See Mazer, 347 U.S. at 219 , 74 S.Ct. 460 (“The economic philosophy behind the clause empowering Congress to grant patents and copyrights is the conviction that encouragement of individual effort by personal gain is the best way to advance public welfare through the talents of authors and inventors.... ”). The doctrine of merger does not bar copyright protection in this case.

V

A

Kapes raises the defense of copyright estoppel, arguing that because CDN represented its prices in its promotional literature as facts, it is estopped from arguing that they are non facts entitled to protection. Like the district court, we do not consider this argument because Kapes did not raise the issue properly below and waived it when he stipulated that the only issue in this case was the copyrightability of the prices. “It is well-established that an appellate court will not consider issues that were not properly raised before the district court.” Slaven, 146 F.3d at 1069.

B

Finally, Kapes argues that CDN lacks equity for lack of diligence because it did not use the appropriate legal regime (license) to protect its material. Kapes cites several cases in which companies protected their uncopyrighted works through license and claims that CDN could have done so here. But Kapes cites no authority to support the proposition that CDN is not entitled to an injunction because it attempted to use copyright as opposed to contract to protect its work. In fact, the argument makes little sense. Either CDN was correct in claiming copyright and is entitled to the injunction the district court ordered, or CDN’s material is not copyrightable and the injunction should be dissolved. If copyright protection were not warranted, then CDN would not be entitled to an injunction regardless of whether it inappropriately claimed copyrightability.

VI

For the foregoing reasons, we affirm the district court’s holding that the prices in the guides contain sufficient originality to sustain copyright protection.

AFFIRMED.

. We review the district court's determination that the prices are sufficiently original to merit copyright protection de novo. See Los An-geles News Serv. v. Tullo, 973 F.2d 791 , 793 (9th Cir. 1992).