
23 F.Supp.2d 741 (1998)
John P. QUINN, Plaintiff,
v.
CITY OF DETROIT, Defendant.
No. Civ.A 96-40291.
United States District Court, E.D. Michigan, Southern Division.
September 29, 1998.
*742 Jerry R. Swift, Eames Wilcox, Detroit, MI, for plaintiff.
Marjory G. Basile, Miller, Canfield, Detroit, MI, for defendant.

MEMORANDUM OPINION AND ORDER
GADOLA, District Judge.
On August 9, 1996, John P. Quinn ("Quinn") filed the above-entitled action *743 against the City of Detroit ("the City") seeking monetary damages for the City's alleged infringement of his copyright to a computer program entitled Litigation Management System/Claims Management System ("LMS"). On December 12, 1997, this Court issued a memorandum opinion and order denying defendant's motion for summary judgment and granting plaintiff's motion for partial summary judgment, specifically holding that the City of Detroit does not own the copyright pursuant to the work made for hire provisions of the Copyright Act of 1976. A bench trial in the above-entitled was held during the week of September 7, 1998.
This Opinion represents the Court's findings of fact and conclusions of law with respect to all issues. These findings of fact and conclusions of law result from a careful consideration of all of the evidence and the documentary and demonstrative exhibits in light of the pertinent law and the Court's observation of the witnesses and its evaluation of their demeanor, qualifications and credibility. Every finding of fact that may be construed to incorporate a conclusion of law is hereby adopted as a conclusion of law. Every conclusion of law that may be construed to incorporate a finding of fact is hereby adopted as a finding of fact. The sub-headings used herein are for convenience only. If a finding of fact or conclusion of law is pertinent to any determination other than that indicated by the heading under which it appears, it is deemed adopted as a finding of fact or conclusion of law applicable to such other determination or determinations as may be appropriate.

I. STIPULATED FACTS
The facts recited immediately below reflect those stipulated by the parties prior to trial, and as expressed in the joint pre-trial order:
1. In 1985, Quinn was hired as a staff attorney by the Law Department for the City of Detroit.
2. Quinn became Supervising Assistant Corporation Counsel on or about January 15, 1991.
3. In this capacity, Quinn was responsible for managing the cases assigned to him personally, as well as the cases assigned to the 8 to 10 attorneys he supervised.
4. After being promoted to supervisor, Quinn decided to develop a computerized litigation management system for use in the Law Department.
5. Quinn decided to use an off-the-shelf fourth generation application development tool called "Professional File."
6. Quinn purchased his own copy of "Professional File" and installed this store-bought software on his home computer and educated himself about it.
7. Using the "application manager" contained in "Professional File" Quinn designed a computer application which he dubbed, "Litigation Management System/Claims Management System" (hereinafter "LMS" or "LMS program").
8. LMS is a menu-driven case management system which stores and processes information relating to litigation and claims.
9. The LMS program cannot function and does not run without "Professional File."
10. After creating LMS, sometime in 1992, Quinn installed the LMS program onto the Law Department's computer network, without seeking permission beforehand. Thereafter, Quinn used LMS to track deadlines and perform other functions necessary to manage litigation.
11. After installing it, Quinn continued to refine and develop the LMS program.
12. Eventually, the majority of the employees in the litigation section, as well as personnel in other sections of the Law Department, began using LMS to assist them in the performance of their duties. As a consequence, these employees came to rely on the LMS program.
13. Sometime after installing the program onto the Law Department's network, Quinn incorporated into LMS a screen that notified its users of his ownership of LMS.
14. During 1995, however, the Law Department began asserting a proprietary interest in LMS, notwithstanding Quinn's claim of ownership in the same.
15. Prior to November 20, 1995, the Law Department attempted to make alterations to LMS, without obtaining Quinn's permission.
*744 16. On or about November 20, 1995, Plaintiff wrote a memorandum to Phyllis James, Corporation Counsel for the City, withdrawing his permission for the City's use of LMS and instructing the City to promptly inform all of its employees that they must immediately discontinue use of LMS.
17. However, the City explicitly claimed ownership in LMS and continued to use the LMS program after the November 20, 1995 memorandum, including making backup copies.
18. Moreover, the City forbade Quinn from making further changes to LMS and suspended him for attempting to do so.
19. In 1995, Quinn retained an attorney, William J. Schramm, to register LMS in his own name with the United States Copyright Office.
20. A certificate of registration was issued to Quinn for LMS, effective February 14, 1996.
21. The law department's alleged infringement of Quinn's ownership interest in LMS commenced before, but continued after, the effective date of his Certificate of Registration.
22. On August 9, 1996, plaintiff filed the instant action against the City claiming that the City had infringed his copyright by making unauthorized copies of LMS and continuing to use it after Quinn purportedly withdrew his permission to use the LMS program.
23. On September 9, 1997, plaintiff filed a motion for partial summary judgment as to his ownership of LMS, which this Court granted in a memorandum opinion and order dated December 11, 1997.
24. Quinn still used LMS at work on his personally owned computer and allows people under his supervision to use the same.

II. FINDINGS OF FACT
The Court makes the following additional findings of fact:
1. Quinn created LMS outside the scope of his employment as an attorney for the City of Detroit.
2. Quinn did independently create "original expressions" of ideas and concepts when he used Professional File as a programing tool and created the source code of the various "executable" files and "data" files contained in LMS.
3. LMS is a data base program.
4. On June 28, 1995, it appeared to Quinn that despite his notification of ownership through incorporating an "about" screen into the LMS program (see Stipulated Fact 13, supra), the City was assuming that it owned LMS. In a memorandum on that same date, Quinn reminded the City in writing of his ownership of LMS. See Plaintiff's Exhibit 5.
5. In a meeting on or about July 1, 1995, with Phyllis James, Corporation Counsel for the City of Detroit, and Terri Renshaw, Deputy Corporation Counsel, Quinn discussed the apparent conflict concerning ownership of LMS and urged the City to promptly complete its then ongoing search for another case management system, as LMS was not going to be available to the Law Department indefinitely.
6. In mid-September of 1995, Brenda Miller, Division Chief of the Litigation Division for the City of Detroit, instructed Quinn to add functions to the LMS applications used by the senior legal secretaries. Quinn responded by adding the functions, but also by protecting them with passwords. He informed Miller that he would not permit actual use of the added functions until the City purchased a license. See Defendant's Exhibits C and D.
7. On October 23, 1995, Quinn was directed to provide specified access to LMS for Ann Daniels, Miller's secretary. Quinn refused this request. See Defendant's Exhibits D and E.
8. On October 25, 1995, the directive to provide access for Daniels was again given by Brenda Miller, accompanied by a threat of discharge. See Defendant's Exhibit E (¶ 2).
9. Immediately thereafter Quinn blocked access to LMS department-wide by placing passwords on LMS. See Defendant's Exhibit E (¶ 3).
10. On October 26, 1995, Miller gave Quinn a written directive to provide the LMS passwords to Miller, accompanied by a threat *745 of discharge. See Defendant's Exhibit E (¶ 4).
11. On October 26, 1995, Quinn met with Miller and Renshaw. At that meeting, Miller's directive was rescinded. See Defendant's Exhibit F. An agreement was reached whereby Quinn would restore access to LMS throughout the department and the City would take no action inconsistent with Quinn's claim of ownership.
12. Within two days after the meeting, the City hired Jurist Systems to modify LMS without Quinn's permission or knowledge. Jurist Systems in fact did modify LMS to allow Ann Daniels access.
13. Upon discovering that unauthorized changes had been made in LMS, Quinn removed the changes.
14. Quinn was ordered on November 15, 1995, in a memorandum from James, to restore the changes that had been made by Jurist Systems, to refrain from making any changes in LMS without express approval from his superiors, and to not limit the Law Department's access or operation of the system. Further, James threatened dismissal and legal action, including damages, for violation of her directive. See Defendant's Exhibit H.
15. On November 20, 1995, Quinn withdrew permission for the City to use LMS and demanded that all employees be informed that they must immediately discontinue use of LMS. See Defendant's Exhibit I (letter from Quinn to Phyllis A. James). Furthermore, Quinn demanded that the City delete LMS from the City's computer system. See id. Quinn also offered to discuss a license for the use of LMS. See id.
16. During the 1995 Christmas holiday season, Quinn made changes to LMS which had been requested by James the previous July.
17. The City took the position that the changes violated the directives of November 15, 1995, and Quinn was thereafter suspended for one week without pay.
18. Quinn filed a grievance in response his suspension. The City on February 26, 1996 explicitly claimed ownership of LMS. See Plaintiff's Exhibit 7, n. 1.
19. Quinn admitted at trial that he is only claiming infringement after November 20, 1995, the date of his letter to Phyllis A. James, Corporation Counsel for the City.
20. The City used and copied LMS after November 20, 1995, after Quinn denied them permission to do so and continued to use and copy LMS after February 14, 1996, the effective date of his Certificate of Registration for LMS, until April 1996.
21. Quinn still uses LMS in the Law Department and allows the attorneys he supervises to use LMS.
22. Quinn has never tried to market or commercialize LMS.
23. Quinn admits that after his November 20, 1995 letter, certain members of the Law Department used LMS with his knowledge and assistance and that he encouraged such use. For example, Allen Charlton and Lesley Knapp testified that use of LMS was with Quinn's knowledge and consent.
24. Late in 1995, the City retained a consultant, Jurist Systems, Inc., to develop a new data management system for use in tracking cases and providing information about reserves on cases. That system was subsequently installed after the Law Department moved to a new building in April of 1996. The new data base system was developed using Microsoft Access which is a commercially available application development program. The cost of developing this new data base manager was $3,500.00. The City Law Department continues to use the newly developed data base manager. In addition, Law Department personnel have developed other means for managing cases. For example, Brenda Miller testified that she developed a Word Perfect spreadsheet to record information on new cases handled by the Law Department.
25. The only evidence offered by Quinn in support of damages is the testimony of Joseph Toland, a computer programmer retained by Quinn as an expert witness. Toland testified that the cost to develop a system allegedly comparable to LMS is $125,000.00.
26. Toland's estimate is based on developing a data base management system which *746 did not use Professional File as a development tool. In performing his work, Mr. Toland admitted that he did not have a full understanding of how LMS operated and that he did not study the needs of the City Law Department.
27. Quinn did not present any testimony regarding the potential cost to the City of obtaining a license to use LMS.
28. Toland's calculation of damages does not attempt to apportion the cost of creating a comparable system to the actual asserted length of unauthorized use made of LMS by the City.
29. Toland testified that the so-called "comparable" data management system would be created with C + +, a sophisticated third generation programming language, and not using Professional File, an easy to use fourth generation development tool.
30. The City did not engage in any selling or marketing activities with respect to LMS and did not earn any profit from its use of LMS.
31. Toland admitted that he never used Professional File.
32. Toland admitted that he is not familiar with software applications for use by lawyers and that he has no experience in developing case management systems. Toland also testified that he did not know the type of data tracked by LMS or the types of reports generated by LMS.
33. Toland admitted that the $125,000 development cost is not the fair market value for LMS.
34. Toland admitted that the $125,000 development cost does not bear any relationship to the period of purported infringement by the City.
35. Toland admitted that he did not compare LMS to other litigation management systems.
36. Toland admitted that he did not consider any other cost alternatives to replacing LMS or the cost of other systems.
37. Plaintiff's claims for statutory damages and attorney's fees have been dismissed by stipulation.

II. CONCLUSIONS OF LAW

A. ELEMENTS OF INFRINGEMENT
1. To prevail on a copyright infringement claim, a plaintiff must prove both ownership of a valid copyright and copying of constituent elements of the work that are original. Feist Publications v. Rural Telephone Service Co., 499 U.S. 340, 361, 111 S.Ct. 1282, 113 L.Ed.2d 358 (1991). Plaintiff has the burden of proving both elements of his prima facie case.

(i) VALIDITY OF QUINN'S COPYRIGHT
2. Quinn must prove that he owns a valid copyright in LMS. See id.; see also Durham Industries, Inc. v. Tomy Corp., 630 F.2d 905, 908 (2d Cir.1980). The issuance of the certificate of registration for LMS establishes a prima facie case that LMS contains copyrightable subject matter. See 17 U.S.C. § 410(c).

a. REBUTTABLE PRESUMPTION OF VALIDITY
3. The prima facie presumption of copyright validity that accompanies a registration certificate is rebuttable. See HiTech Video Productions, Inc. v. Capital Cities/ABC, Inc., 58 F.3d 1093, 1095 (6th Cir. 1995); Masquerade Novelty, Inc. v. Unique Industries, Inc., 912 F.2d 663, 668 (3d Cir. 1990). Defendant may rebut the presumption by presenting evidence casting doubt on the validity of the copyright. If defendant makes a sufficient showing, then the presumption dissolves and the burden shifts back to plaintiff. Nintendo of America, Inc. v. Elcon Industries, Inc., 564 F.Supp. 937, 943 (E.D.Mich.1982); Durham, 630 F.2d at 908.

(1) ORIGINALITY
4. The presumption of validity can be overcome by a showing by defendant that the copyrighted work does not meet the requirement of originality. North Coast Indus. v. Jason Maxwell, Inc., 972 F.2d 1031, 1033 (9th Cir.1992). For a valid copyright to exist, the copyrighted work must be an original work of authorship. See 17 U.S.C. § 102. Copyright protection only extends to those *747 components of a work that are original to the author. See Feist, 499 U.S. at 348, 111 S.Ct. 1282.
5. LMS is a derivative work under the statutory definition, because Professional File is the underlying work through which LMS was created. 17 U.S.C. § 101. Quinn admitted in his copyright application that LMS is a derivative work based on Professional File. See Plaintiff's Exhibit 1. The copyright protection extended to a derivative work only extends to the new material contributed by the author, not to preexisting material that was derived from the underlying work. 17 U.S.C. § 103(b). Consequently, for a derivative work to be copyrightable, the new material must be independently copyrightable.
6. Defendant argues that LMS lacks the requisite originality to be copyrightable. For the following reasons, this Court disagrees and concludes that the "new" material (the "source code") created by Quinn and constituting the LMS program does meet the originality requirement. Discussing the issue of originality, the Supreme Court in Feist Publications, Inc. v. Rural Tel. Serv. Co., 499 U.S. 340, 111 S.Ct. 1282, 113 L.Ed.2d 358 (1991), stated that
[t]he sine qua non of copyright is originality. To qualify for copyright protection, a work must be original to the author. [See Harper & Row, Publishers, Inc. v. Nation Enterprises, 471 U.S. 539, 547-549, 105 S.Ct. 2218, 85 L.Ed.2d 588 (1985)]. Original, as the term is used in copyright, means only that the work was independently created by the author (as opposed to copied from other works), and that it possesses at least some minimal degree of creativity. 1 M. Nimmer & D. Nimmer, Copyright §§ 2.01[A], [B] (1990) (hereinafter Nimmer). To be sure, 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. Id., § 1.08[C][1]. Originality does not signify novelty; a work may be original even though it closely resembles other works so long as the similarity is fortuitous, not the result of copying.
499 U.S. at 345, 111 S.Ct. 1282. The Court further discussed the originality requirement, specifically with respect to a "factual compilation" or database, as is the LMS program. Such works may be deemed "original" when "the choices as to selection and arrangement ... are made independently by the compiler and entail a minimal degree of creativity." Id. at 348, 111 S.Ct. 1282. The Court continued, "[t]hus, even a directory that contains absolutely no protectible written expression, only facts, meets the constitutional minimum for copyright protection if it features an original selection or arrangement." Id. (citing Harper & Row, 471 U.S. at 547, 105 S.Ct. 2218; accord Nimmer § 3.03.)
In the instant case, LMS does possess the "creative spark" necessary for a finding of originality. As the Feist Court commented and as quoted above, "the requisite level of creativity is extremely low; even a slight amount will suffice." Feist, 499 U.S. at 345, 111 S.Ct. 1282. Quinn created a computer program using a set of instructions (so-called "source code") which innovatively handled previously unresolved problems faced by the employees of the City Law Department. The fact that the syntax of the source code was dictated by Professional File does not detract from a finding of originality. Defendant's argument that LMS cannot be considered an independent program and thus must be unoriginal is without merit.
Pursuant to Section 101 of the Copyright Act, a "computer program" is defined as "a set of statements or instructions to be used directly or indirectly in a computer in order to bring about a certain result." 17 U.S.C. § 101. This very broad definition encompasses Quinn's creation because he authored a set of statements or instructions, admittedly using the syntax and symbols dictated by Professional File, ordering these statements or instructions in such a way as to produce certain outcomes. Examples of some of the functions which resulted are included in the following list: automatically setting deadlines for certain events, tracking attorneys' time, printing reports, calculating reserves, automatically assigning case numbers, and automatically checking to see if another law suit had been filed by the same plaintiff's attorney. Finally, it is well-settled that "a computer *748 program, whether in object code or source code, is a `literary work' and is protected from unauthorized copying, whether from its object or source code version." Apple Computer, Inc. v. Franklin Computer Corp., 714 F.2d 1240, 1249 (3d Cir.1983).
8. The Court does not base its ruling that Quinn's copyright is valid on the so-called "sweat of the brow" doctrine. Feist, 499 U.S. at 354, 111 S.Ct. 1282; CMM Cable Rep, Inc. v. Ocean Coast Properties, Inc., 97 F.3d 1504, 1521 (1st Cir.1996). The amount of effort put into the creation of a work is not a factor that should be considered in determining whether a work is original. "Copyright rewards originality, not effort." Feist, 499 U.S. at 364, 111 S.Ct. 1282. Regardless of how many hours Quinn spent creating LMS, the amount of time spent is irrelevant to the inquiry of whether LMS is an original work. Only the nature of the contributions to LMS is important, and, as discussed above, his contributions are original.

(2) PROTECTABLE ELEMENTS
9. The presumption of validity may also be overcome by a showing by defendant that the copyrighted work does not contain protectable elements. Copyright protection only extends to the expression of ideas, not to the ideas themselves. Engineering Dynamics, Inc. v. Structural Software, Inc., 26 F.3d 1335, 1344 (5th Cir.1994). "In no case does copyright protection ... extend to any idea, procedure, process, system, method of operation, concept, principle, or discovery." 17 U.S.C. § 102. Assuming arguendo that LMS meets the originality requirement, defendant argues that there are no original aspects of LMS that are protectable.
Plaintiff has admitted that he is not seeking copyright protection of the underlying data which LMS manipulated; that data is owned by the City. Nor does plaintiff claim any ownership interest in Professional File itself. Rather, plaintiff contends that the "source code" which he authored is protectable, representing "new" elements which deserve protection under the Copyright Act. Defendant argues that "expressions that are standard, stock or common to a particular subject matter or are dictated by external factors" are not protectable. Engineering Dynamics, 26 F.3d at 1344. Defendant further maintains that standard techniques found in every data management system also are not protectable. Harbor Software, Inc. v. Applied Systems, Inc., 925 F.Supp. 1042, 1051 (S.D.N.Y.1996).
Defendant's arguments would be persuasive if it were true that LMS were the same as any other database program. But, in fact, LMS contained other functions which the previous system (the CLIS or City Law Information System) simply did not have the capability of performing. Given this factor, it cannot be said, as defendant maintains, that LMS merely contained "standard techniques found in every data management system." While ideas themselves are not copyrightable, expressions of those ideas certainly are.[1] The LMS program deserves copyright protection, at least with respect to those aspects of the program authored by Quinn.

(3) LIMITATIONS OF COPYRIGHT ABILITY OF A DERIVATIVE WORK
10. Creation of a derivative work is one of the exclusive rights of the copyright owner. *749 17 U.S.C. § 106. Therefore, the author of a derivative work must have permission from the author of the underlying work in order to create a derivative work. Quinn was implicitly authorized through the purchase of Professional File, as well as explicitly through the Professional File Owner's Manual, to create, use, and disseminate applications made with Professional File. See Defendant's Exhibit R, Chapter 18.
11. Copyright in a derivative work does not extend to any part of the work in which preexisting protected material was used without authorization from the owner of the preexisting material. 17 U.S.C. § 103(a).
12. Defendant argues that Quinn does not possess a valid copyright to LMS because he exceeded the scope of authorization to create and use a derivative work by copyrighting his application. However, this Court holds that Quinn did not exceed his authorization by copyrighting LMS. The case cited by defendant, Gracen v. Bradford Exchange, 698 F.2d 300, 303 (7th Cir.1983), is inapposite. In that case, an artist had made a painting of Dorothy from the movie "The Wizard of Oz," pursuant to a contract to produce a series of collectors' plates. See id. at 301-02. MGM produced and copyrighted the original movie in 1939, and the copyright was still in effect at the time of the case. See id. at 301. The Seventh Circuit held that the artist's painting was not an original derivative work within the meaning of the Copyright Act. See id. at 305. This holding was based on an assessment by the court that the artist's painting was not different enough in appearance from Judy Garland's Dorothy, i.e., the character in the movie. See id. The Seventh Circuit never dealt with the issue of whether the plaintiff had exceeded the scope of her authority by attempting to copyright her painting. See id.
It is true that Quinn did not explicitly receive authorization from the owner of Professional File to copyright applications made therefrom. But, this fact does not automatically prove that Quinn exceeded his authorization by seeking copyright protection for those applications.

2. UNAUTHORIZED USE OR COPYING
14. In order to prevail on a copyright infringement claim, plaintiff must also prove that defendant copied the protected work. See Feist, 499 U.S. at 361, 111 S.Ct. 1282. The term "copy" is used to designate any of the copyright owner's exclusive rights as described in the Copyright Act. S.O.S., Inc. v. Payday, Inc., 886 F.2d 1081, 1085 n. 3 (9th Cir.1989).
15. If Defendant had a license to make a particular use of a copyrighted work, defendant cannot have committed infringement. Peer International Corp. v. Pausa Records, Inc., 909 F.2d 1332, 1338 (9th Cir.1990). If it is established that a license existed for the use of LMS, the only question is whether the City exceeded the scope of that license. See Graham v. James, 144 F.3d 229, 1997 WL 894500, *5 (2d Cir.1998). The burden is on Quinn to demonstrate that the City's use exceeded the scope of its implied license. See Bourne v. Walt Disney Co., 68 F.3d 621, 631 (2d Cir.1995), cert. denied 517 U .S. 1240, 116 S.Ct. 1890, 135 L.Ed.2d 184 (1996); S.O.S., 886 F.2d at 1085.
16. Quinn granted an implied license to the City to use LMS. Non-exclusive licenses may be implied from conduct. See Graham, 144 F.3d at 235; Johnson v. Jones, 885 F.Supp. 1008, 1013 (E.D.Mich.1995); Silva v. MacLaine, 697 F.Supp. 1423, 1430 (E.D.Mich.1988). Quinn's conduct of installing LMS on the computers in the Law Department and allowing the Law Department employees to use it granted the City an implied license by conduct. See e.g., Graham, 144 F.3d at 235. Moreover, Quinn's November 20, 1995, memorandum revoking permission for the City to use LMS demonstrates that the City was using LMS under an implied license. Since the City possessed a license to use LMS, Plaintiff cannot prevail on its claim of infringement. Moreover, Quinn testified that he knew that Law Department personnel continued to use LMS after November 20, 1995, and that he also encouraged such use. Thus, the license extended beyond his November 20, 1995 letter.
17. Quinn stipulated in the final pre-trial order that the majority of attorneys in the *750 Law Department and a number of employees in other departments used LMS and came to rely on it. The City had been using LMS for years. Ceasing use of LMS could not be done immediately upon notice of revocation of permission. The City required a period of time to make the transition to another data management system. Without a period of time to transfer to a new system, the City would have been left helpless, with no way to update cases or access information in the manner necessary to properly monitor cases.
18. Accordingly, the City's license to use LMS included a reasonable period of time to transfer its data from LMS to a new system in the case of a revocation of the license by Quinn. Otherwise, the license would have been useless to the City. This is the only use of LMS made by the City. Thus, the City did not exceed the scope of its license to use LMS. As Quinn testified, he knew it would take the City time to find an alternative to LMS.
19. Furthermore, the City of Detroit was entitled to reasonable notice before termination of the implied license/contract to use LMS. See Paw Paw Wine Distrib., Inc. v. Joseph E. Seagram & Sons, Inc., ___ F.Supp.2d ___ [1998 WL 486961], No. G84-911 CA, 1987 U.S.Dist. Lexis 15348, at *13 (W.D.Mich. Dec. 8, 1987); Aaron E. Levine and Co., Inc. v. Calkraft Paper Co., 429 F.Supp. 1039, 1049 (E.D.Mich.1976) (holding that Michigan requires reasonable notice for termination of at-will distributorship agreements). Michigan courts have imposed the reasonable notice requirement so that a distributor will not suffer serious hardship by a sudden, immediate termination of the agreement. See Paw Paw, 1987 U.S. Dist. Lexis 15348, at *13. The same rationale applies to the facts of the instant case. The rule should be extended to apply to any agreement where hardship would result if sudden, immediate termination occurred.
20. Since Quinn could not immediately terminate the implied license without reasonable notice, the City's continued use of LMS for a reasonable period of time after the notice of termination does not constitute infringement.

B. DAMAGES

1. ACTUAL DAMAGES
21. Under Section 504(b) of the Copyright Act, "actual damages" may be recoverable by a plaintiff. 17 U.S.C. § 504(b). While the Copyright Act does not define "actual damages," courts generally have characterized actual damages as the loss suffered by a plaintiff. The primary method courts have chosen for calculating actual damages consists of equating actual damages of a plaintiff with the amount by which the market value of the copyrighted work has been injured or destroyed due to the infringement. See In Design v. K-Mart Apparel Corp., 13 F.3d 559, 563 (2d Cir.1994); Manufacturers Technologies, Inc. v. Cams, Inc., 728 F.Supp. 75, 80 (D.Conn.1989). Most commonly under this measure of damages, a prevailing plaintiff receives as actual damages the profits that plaintiff would have earned from the infringed work but for defendant's infringement. See, e.g., Cams, 728 F.Supp. at 80; Business Trends Analysts, Inc. v. Freedonia Grp., Inc., 700 F.Supp. 1213, 1232 (S.D.N.Y. 1988), aff'd in part and rev'd in part on other grounds, 887 F.2d 399 (2d Cir.1989).
22. There is no allegation or proof that the alleged unauthorized use by the City of Detroit harmed Quinn's ability to market and earn profits from LMS. Additionally, the value of the program to Quinn was not diminished by any unauthorized use by the City of Detroit, as it has not affected the overall marketability of LMS. Quinn's only proposed calculation of damages is the amount it allegedly would have cost the City of Detroit to create a so-called comparable data management system. This method of calculating damages is not recognized under the Copyright Act.
23. Some courts have developed an alternative method for calculating actual damages to protect a plaintiff in situations where an infringement results in neither a profit to the infringer nor a quantifiable loss to the owner. In such cases, courts apply the "value of use" theory, which is essentially an implied license theory. See Steven Greenberg Photography v. Matt Garrett's of Brockton, 816 F.Supp. 46, 49 (D.Mass.1992); see also 4 Melville B. *751 Nimmer & David Nimmer, Nimmer on Copyright § 14-02[A] (1995). The value of use is equal to what a willing buyer would have been reasonably required to pay to a willing seller for the plaintiff's work or, in other words, what the cost of a license for use of the work would have been. Sid & Marty Krofft Television Productions, Inc. v. McDonald's Corp., 562 F.2d 1157, 1174 (9th Cir.1977). Quinn, however, cannot recover under an implied license theory because he presented no evidence of the cost of a license for the City to use LMS.
24. Quinn claims that he should be entitled to recover what it would have cost the City to purchase a system comparable to LMS. Plaintiff relies on Deltak, Inc. v. Advanced Systems, Inc., 767 F.2d 357 (7th Cir. 1985). Deltak, according to Quinn, stands for the proposition that a copyright owner may recover an infringer's "avoided" costs.
25. Quinn, however, has presented no evidence that the City would have spent $125,000 on a case management system. To the contrary, the only evidence offered at trial of the cost of replacing LMS was the testimony of Brenda Miller. Ms. Miller testified that the City was charged $3,500.00 for a new system.
26. Furthermore, the rationale of Deltak has been criticized by other courts and by Nimmer. See 4 Melville B. Nimmer & David Nimmer, Nimmer on Copyright, § 14.02[A]. The Second Circuit, in Business Trends Analysts, Inc. v. Freedonia Group, Inc., 887 F.2d 399 (2d Cir.1989), stated that the copyright statutes provided an adequate remedy to a copyright owner in the absence of actual damages or profit to the infringer and that the definition of damages should not be expanded.
27. In the case at bar, the Deltak rationale should be rejected especially in the absence of any proofs of savings to the City from using LMS or evidence that the City would have purchased a comparable system. Such an award would be based on sheer speculation.
28. In addition, to recover actual damages Quinn must prove the existence of a causal connection between the City's alleged infringement and some loss of anticipated revenue. Jarvis v. A & M Records, 827 F.Supp. 282, 293 (D.N.J.1993). The plaintiff must show that the infringement was the cause-in-fact of its loss by showing with reasonable probability that "but for" the defendant's infringement, the plaintiff would not have suffered the loss. See Data General Corporation v. Grumman Systems Support Corp., 36 F.3d 1147, 1171 (1st Cir.1994); see also Robert R. Jones Associates, Inc. v. Nino Homes, 858 F.2d 274, 280-81 (6th Cir.1988). "Actual damages are only available where there is a causal connection between the infringement and the copyright owner's losses." Banff Ltd. v. Express, Inc., 921 F.Supp. 1065, 1068 (S.D.N.Y.1995). Quinn has not demonstrated the necessary connection between the alleged actions of the Defendant and the damages requested. In particular, Quinn cannot show that his alleged loss resulted from the de minimis period of alleged infringement by the City. Quinn's own expert witness, Joseph Toland, admitted that there was no relationship between his $125,000 development cost and the period of infringement.
29. Plaintiff's damage theory is also inconsistent with the facts of this case. Plaintiff claims that the City should pay the full creation cost of LMS as if the City owned it. This conflicts with plaintiff's assertion and this Court's previous holding that plaintiff is the owner of LMS. See memorandum opinion and order denying defendant's motion for summary judgment and granting plaintiff's motion for partial summary judgment, issued December 12, 1997. Defendant should not be required to pay for the alleged full value of LMS when it did not appropriate the application or destroy LMS's value in any way.
30. Further, the City's use of LMS after the November 20th purported revocation letter was de minimis. Plaintiff's damage theory seeking to recover for the full cost of a so-called comparable system ignores the limited use made by the City of LMS after November 20, 1995. Since the useful life of a data base management system extends over many years, and in this instance the City had Quinn's permission to use LMS for most of that time period, Quinn's recoverable damages would be limited to the time period *752 between revocation of permission and cessation of use. Quinn's failure to present a damage calculation resulting from the City's use of LMS over only the few months of claimed infringement undermines his damage claim.
31. Plaintiff's theory that he should be entitled to recover the cost of developing a comparable system is also flawed because the so-called comparable system would have been created using a much more sophisticated programming language, C + +, used by professional programmers. The allegedly comparable system would not have been created using the commercially available and much more user-friendly "Professional File." Moreover, plaintiff's expert, in developing his cost estimate, admittedly did not have a full understanding of the features and functions of LMS. For all the preceding reasons, his cost estimate is unduly speculative and inappropriate to the facts of the instant case.
32. Plaintiff in a copyright action cannot recover damages that are unduly speculative. Johnson v. Jones, 149 F.3d 494, 1998 WL 404033, at *14-15 (6th Cir.1998).

2. PROFITS OF INFRINGER
33. A plaintiff who prevails on an infringement claim can recover profits of the infringer earned from the infringement. See 17 U.S.C. § 504. The City of Detroit earned no profits from its alleged infringement since it did not engage in the marketing or sale of LMS. Therefore, there are no profits of the City of Detroit for Quinn to recover.

3. DEVELOPMENT EXPENSES OF PLAINTIFF
34. The expenses incurred by a plaintiff in developing the work which has been infringed are not recoverable in an infringement action, unless they qualify as "unrecovered costs." Softel, Inc. v. Dragon Medical and Scientific Commun.'s Ltd., 891 F.Supp. 935, 941 (S.D.N.Y.1995), cert. denied, ___ U.S. ___, 118 S.Ct. 1300, 140 L.Ed.2d 466 (1998). Quinn has had an opportunity, and continues to have an opportunity, to recover any development expenses. Furthermore, Quinn has offered no proof of his development costs. Therefore, Quinn cannot recover any claimed development expenses.

4. STATUTORY DAMAGES
35. Plaintiff has stipulated to an order dismissing his claim for statutory damages.

5. COSTS AND ATTORNEY'S FEES
36. Plaintiff has stipulated to an order dismissing his claim for attorney's fees.
37. Pursuant to Section 505 of the Copyright Act, a court, in its discretion, may allow the recovery of full costs and attorney fees "by or against any party other than the United States or an officer thereof." 17 U.S.C. § 505. Some the factors a court should consider in exercising its discretion include: "the degree of success obtained ... frivolousness; motivation; objective unreasonableness (both in the factual and legal arguments in the case); and the need in particular circumstances to advance considerations of compensation and deterrence." Jackson v. Axton, 25 F.3d 884, 890 (9th Cir.1994) (citing Fogerty v. Fantasy, Inc., 510 U.S. 517, 114 S.Ct. 1023, 1033 n. 19, 127 L.Ed.2d 455 (1994)). The Ninth Circuit in Jackson v. Axton commented that "[c]ourts should keep in mind the purposes of the Copyright Act (to promote creativity for the public good) and apply the factors in an evenhanded manner to prevailing plaintiffs and prevailing defendants alike." Id.
Applying the Jackson factors, this Court finds that imposition of costs and attorneys fees as authorized by 17 U.S.C. § 505 is not warranted. Plaintiff's action was not frivolous, given this Court's finding that the copyright in LMS is valid. Furthermore, the purposes of the Copyright Act, "to promote creativity for the public good," are better served when plaintiffs are not unduly penalized for bringing potentially successful infringement claims, even if such claims are ultimately unsuccessful.

C. AFFIRMATIVE DEFENSES

1. ESTOPPEL
38. Quinn is estopped from pursuing his infringement action against the City because he gave the City permission to continue using LMS. The four elements for the estoppel defense in copyright infringement *753 cases are: (1) plaintiff knew about defendant's infringing conduct; (2) plaintiff must intend that his conduct be acted on or must act in a way that the party asserting the estoppel had a right to believe it was so intended; (3) defendant must be ignorant of the true facts; and (4) defendant must rely on plaintiff's conduct to its detriment. Hampton v. Paramount Pictures Corp., 279 F.2d 100 (9th Cir.), cert. denied 364 U.S. 882, 81 S.Ct. 170, 5 L.Ed.2d 103 (1960).
39. It is also well-settled that a plaintiff may be estopped from asserting his rights under a copyright if he has aided the defendant in infringing or otherwise induced it to infringe or has committed covert acts such as "holding out ... by silence or inaction." Nimmer § 13.07, at 13-134. "The plaintiff's acquiescence in the defendant's infringing acts may, if continued for a sufficient period of time and if manifested by overt acts, result in an abandonment of copyright." Id. at 13-135. In such a case, the estoppel "destroys the right asserted" and will be a defense for all acts occurring after the acquiescence. Id.
40. In the instant case, as early as 1992, the City relied on Quinn's permission to use LMS, and as a result, the majority of employees in the Law Department and some in other departments transferred and stored all the data regarding their cases to LMS. The City came to rely on its use of LMS and abandoned CLIS, its prior data management system. At trial, both Knapp and Charlton admitted that while there was continuing use of LMS after November 20, 1995, Quinn authorized or consented to such use and helped Charlton, for example, use LMS. Therefore, long before the November 20, 1995 letter, Quinn was estopped from withdrawing his consent because of the City's reliance and Quinn's permission to use LMS.

SUMMARY OF CONCLUSIONS OF LAW
For the reasons set forth above, this Court finds that:
1. Quinn does have a valid copyright in LMS. Defendant has not rebutted the presumption of copyrightable subject matter accompanying the copyright registration.
2. Even though there are copyrightable elements to LMS, the City's continued use of LMS after November 20, 1995 did not infringe Quinn's copyright in LMS.
3. The City had permission to continue using LMS for a reasonable period of time after Quinn's revocation of his prior consent to use LMS.
4. Quinn was estopped from withdrawing his consent to use LMS.
5. Quinn has failed to establish recoverable damages under the Copyright Act.
6. Defendant is not entitled to recover its reasonable costs and attorney fees as the prevailing party in this case.

ORDER
NOW, THEREFORE, IT IS HEREBY ORDERED that plaintiff is not entitled to damages under the Copyright Act, 17 U.S.C. § 101, et. seq., for any alleged infringement of his copyright in the LMS program.
IT IS FURTHER ORDERED that defendant is not entitled to recover its reasonable costs and attorney fees as the prevailing party in this case.
SO ORDERED.

JUDGMENT
This action came on for trial before the Court, Honorable Paul V. Gadola, District Judge, presiding, and the issues having been duly tried and a decision having been duly rendered,
It is hereby ORDERED and ADJUDGED that the plaintiff, John P. Quinn, take nothing and that the action be dismissed on the merits.
It is further ORDERED that the defendant is not entitled to recover its reasonable costs and attorney fees as the prevailing party in this case.
It is further ORDERED that the clerk serve a copy of this judgment by United States mail on the counsel for the plaintiff and on the counsel for the defendant.
NOTES
[1]  Defendant argues that algorithms are unprotectable because they constitute ideas. Since, as defendant alleges, Quinn's instructions to the computer (the source code) are "algorithms," they deserve no protection. See 4 Melville B. Nimmer & David Nimmer, Nimmer on Copyright § 13.03[F][1] (1997) (quoting A. Aho, J. Hopcraft & D. Ullman, Data Structures and Algorithms 2 (1983)). However, if the Court were to accept this argument, it would lead future courts down a conceptual slippery slope. Under such a theory, the code underlying any computer program could be deemed "merely algorithms" and thus undeserving of any protection under the Copyright Act. Clearly this is not what Congress intended. See 17 U.S.C. § 101 (defining "computer program" as "a set of statements or instructions to be used directly or indirectly in a computer in order to bring about a certain result"). As the Third Circuit stated in Apple Computer,

the category of "literary works", one of the seven copyrightable categories, is not confined to literature in the nature of Hemingway's For Whom the Bell Tolls. The definition of "literary works" in section 101 [17 U.S.C. § 101] includes expression not only in words but also "numbers, or other ... numerical symbols or indicia", thereby expanding the common usage of "literary works."
Apple Computer, 714 F.2d at 1249.
