The City of Clarksville owns electric, water, and waste water utility systems and operates those utilities through the Clarksville Light and Water Commission. CL&W impounds water, produces potable water, and transmits and distributes the water to retail customers inside and outside its city limits. In addition, Clarksville sells treated water at wholesale rates to six other nearby water utility distribution systems. Those six water distribution systems, in turn, provide water to retail customers located in their respective territories. The six water distribution systems that purchase water wholesale are the six appellants, East Johnson County Water Association, Horse-head Water Users Association, Ludwig Water Users Association, and the Cities of Lamar, Coal Hill, and Hartman. Clarks*417ville increased the rate it charges the six distribution systems for water. The sale of water to the six appellants is governed by contracts that, in the material part, provide any “increase or decrease in rates shall be based on a demonstrable increase or decrease in the costs of performance hereunder.” (Emphasis supplied.) This case primarily involves a dispute over whether Clarksville has demonstrated an increase in the costs of performance sufficient to justify a rate increase to $1.56 per thousand gallons of water.
Since the date the contracts were initially signed Clarksville has made various improvements to its water system, and, in both 1985 and 1988, increased the rates it charged the six appellants. The 1988 wholesale rates resulted in an average charge of 78 cents per thousand gallons. In 1989, Clarksville commissioned a rate study to determine the cost of water after additional improvements were constructed. The improvements were to be made with the proceeds of a proposed 1990 bond issue. After the study, in February 1990, Clarksville enacted an ordinance that raised the rates for all customers effective April 15, 1990. This new rate structure resulted in an average wholesale price to the six appellants of $1.56 per thousand gallons of water. The six appellants refused to pay this higher rate and, instead, continued to pay the previous rate of $.78 per thousand gallons.
Clarksville filed suits in circuit court against the six appellants and sought monetary judgments for the difference in the rate paid and the rate charged for water supplied after the effective date of the ordinance and, in addition, sought a declaratory judgment that the ordinance setting rates was valid. Appellants counterclaimed for alleged breaches of the contracts, and three of the appellants sought a modification of provisions in their contracts that limited the quantity of water to be supplied.
The cases were consolidated and tried to the court. The trial court’s letter opinion found that Clarksville had met the burden of showing a demonstrable increase in the cost of performance of $1.56 per thousand gallons. Consequently, the trial court gave monetary judgments against the six appellants for the difference between the old and new rates. However, the trial court did not give a declaratory judgment on the validity of the ordinance. The six appellants appeal, and Clarksville cross-appeals. We affirm *418the monetary judgment on direct appeal and reverse, in part, on Clarksville’s cross-appeal.
The first assignment of error by the six appellants is that the trial court erred in using the “reasonableness” standard provided in Ark. Code Ann. § 14-234-110(b)(1) (1987) to approve the rate increase. The cited statute provides that “[w]ater may be supplied to nonresident consumers at such rates as the legislative body of the municipality may deem just and reasonable.” We recently interpreted this statute in a case involving Fayetteville providing wholesale water to the Mount Olive Water Association, and we affirmed the trial court’s determination that increased rates were “just and reasonable” under the provisions of the statute. Mt. Olive Water Ass’n v. City of Fayetteville, 313 Ark. 606, 856 S.W.2d 864 (1993). However, in that case, the contract provided that Fayetteville “in its sole discretion has the right to increase or decrease the rates and charges,” and, therefore, the statutory reasonableness standard was the only standard governing the rate increase. The case at bar has the contractual standard that any “increase or decrease in rates shall be based on a demonstrable increase or decrease in the costs of performance hereunder.” Clarksville did not argue that the statutory reasonableness standard governed and does not make such an argument in this appeal. It is evident from the trial judge’s letter opinion that he was well aware the contract provisions governed because, in material parts, the letter provides:
This first issue we are concerned with is whether the increase in water rates by Clarksville is based on a demonstrable increase in the cost of production.
... I conclude that Clarksville has met the burden of showing a demonstrable increase in the cost of production.
I now consider the amount. The decision on the amount is not predicated on the credibility of witnesses since I feel they were all very knowledgeable and thorough. It is based more on what the Court considers the more proper methodology. . . .
Stated another way, I am convinced the methodology and figures produced by Clarksville are more realistic than *419those of the defendants. . . .
I am not going to recite all the evidence that supports Clarksville’s contention that its cost of production has increased, except to say I feel it is ample to sustain the contention a raise is justified and the average rate of $ 1.56 per thousand gallons is reasonable.
In sum, it is evident that the trial judge used the language of the contract as the standard for the rate increase, and did not use the “reasonableness” standard of the cited statute.
In several sub-arguments under this same assignment of error the appellants contend that even if the trial court attempted to use the “cost of performance” standard, it erred by using “reasonableness” standards of methodology. These sub-arguments concern various costs that the trial court allowed in determining the cost of performance. The facts leading to the sub-arguments are summarized as follows. Clarksville introduced the testimony of James Ulmer, the consulting engineer who conducted the rate study. He testified a “cash basis” rate analysis reflected a cost of $2.49 per one thousand gallons of water, and that a “utility method” of determining the cost of production, which would include a 1.5 times interest earning ratio, reflected a cost of $2.00. Clarksville also introduced the testimony of Stephen Merchant, an economist with experience in utility rate matters, who testified that Clarksville had to meet the debt service requirements imposed by the public bond markets in order to obtain financing for its waterworks improvements. The trial court found Clarksville’s figures to be “realistic” and ruled that the rate set in the ordinance, $1.56 per one thousand gallons, was based on an increase in the cost of performance.
The six appellants do not dispute that a cash basis rate study would accurately reflect the cost of performance, but rather they contend that the trial court erred in refusing to exclude certain costs from the cash basis analysis, and, because it did not exclude those cash costs, the trial court in effect reverted to a reasonableness standard. They contend the trial court, as a matter of law, should have excluded a number of such cash costs.
The six appellants’ first sub-argument is that the trial court erred in allowing Clarksville to accrue too much expense *420through funded depreciation. Clarksville’s expert witnesses testified that the rate of depreciation should be even more rapid than the rate used because new federal and state standards for water purity often made waterworks equipment obsolete years before it actually wears out. On the other hand, appellants’ witnesses testified that a longer useful life should have been assigned to various assets. This was a matter of credibility of witnesses, and was a matter for the trial court to weigh. Clearly, it was not an error of law in the methodology used.
Appellants’ second sub-argument about methodology is that the trial court erred in allowing Clarksville to include in “general and administrative expenses” an expense item that CL& W pays to Clarksville. The expense item is 5 percent of gross income. A contract must be interpreted in accordance with the law in' force and effect at the time of the contract formation. McArthur v. Smallwood, 225 Ark. 328, 281 S.W.2d 428 (1955). The statutes governing municipal waterworks that were in effect at the time these contracts were made are presumed to be a part of the contracts and, at the least, provide guidance in interpreting the contracts. At the time these contracts were entered, section 14-234-114 of the Arkansas Code Annotated of 1987 was in effect, and it provides that municipal water systems are authorized to pay a sum equal to 5 percent of gross income to the municipality in “lieu of taxes, in return for police, fire, and health protection . . . and other services furnished the waterworks system by the municipality.” Thus, the expense item was a valid expense in the lawful cost of performance of the contracts.
Appellants’ next sub-argument is that the trial court erred in allowing a part of $127,648 per year “debt service coverage” for the revenue bonds issued by Clarksville. This figure amounts to 130 percent of the amount necessary to pay the current principal and interest. Testimony described this as the amount deemed necessary in the bond trust indenture for the city “to provide sufficient revenue to pay the bonds and to provide a cushion or coverage or additional security for the bond holders.” The cushion was also referred to as a sinking fund. There was no testimony to indicate that this cushion or additional security will go to anything other than the retirement of the revenue bonds. Again, the contract must be interpreted in accordance with the law in force at the time of the making of the contract. Section 14-*421234-214 of the Arkansas Code Annotated of 1987 provides that rates for resident and nonresident customers of a municipal waterworks system must be adequate to pay the principal and interest on all revenue bonds and to make such payments into a revenue bond sinking fund as may be provided by a bond trust indenture. In addition, a witness qualified in the field of municipal bonds testified that this debt service requirement was imposed by the commercial market of public bonds and further testified that if Clarksville did not agree to the sinking fund, it could not compete in that market for funds at a reasonable rate. Accordingly, the trial court did not err as a matter of law in holding that the debt service coverage was a valid expense in the cost of performance of the contract.
Appellants’ final sub-argument is that the trial court erred in the computation of the allowable interest expense on the bonds. Their argument is valid in part, but it does not cause us to reverse. At some time in 1990, Clarksville received the money in exchange for the revenue bonds it issued. The improvement projects were not completed at the time, and so it was not necessary for Clarksville to expend all of the money at that time. As a result, Clarksville had a period of time that it was able to invest these funds, perhaps in United States Treasury obligations, and receive interest in return. One witness testified that Clarksville invested the money it obtained from issuing the bonds and, in return, received $362,000 in interest before it had to use the money to pay the contractors and suppliers. This interest received by Clarksville was not deducted from the cost of the interest it expended on the outstanding revenue bonds. The trial court allowed all of the interest Clarksville expended on the revenue bonds, but did not offset that with the interest it received. To this extent the trial court’s ruling was in error. However, we do not reverse because of it. According to the exhibit abstracted on this issue, Clarksville claimed in 1991 an expense of $ 127,646 for debt service coverage on the 1990 bonds. According to the exhibit, if the interest received from Clarksville’s investment of the bond funds were offset against this amount, the allowable expense for debt service coverage for that year would have been only $33,432. However, according to appellants’ witness, this difference in interest would have only reduced the cost of water by 39 cents per thousand gallons. Clarksville’s cash rate analysis showed a cost of *422$2.49 per thousand gallons of water, and even if the trial court had deducted the 39 cents, Clarksville’s proof was still sufficient to show that the rate of $1.56 was justified under the contracts as equal to or less than the cost of performance. In addition, this offsetting interest income to Clarksville was a one- year phenomenon. It had not occurred when the ordinance setting the rate was enacted, it will not occur again, and it did not and will not reduce the cost of performance in any year other than the year it was received.
In summary, we hold that the trial court did not err in the methodology it used in finding that the rate of $1.56 per one thousand gallons of water is justified under the contract. This holding is confirmed in a practical way. The 1990 capital improvements cost approximately $10,000,000, and the six appellants, through the rate increase, will pay 8'/: percent of those overall capital costs, but will use 29 percent to 33 percent of the water produced by the system.
Appellants’ second assignment of error involves the quantity provisions of the contracts with three of the six appellants, the Horsehead Water Users Association, the Ludwig Water Users Association, and the City of Hartman. Each of these long term contracts provide that Clarksville will make available potable water in “such capacity as may be required by the Purchaser not to exceed_gallons per month.” In the contract with appellant Horsehead the blank is filled in with the figure 5.4 million. It is undisputed that when the contract was executed, in 1978, Clarksville had a duty to make up to 5.4 million gallons of potable water available to appellant Horsehead. The contracts with Ludwig and Hartman contain the same provision, with a different number of gallons specified. The CL&W, which operates the utility, has recently sold an amount of water to each of the three appellants that is in excess of the figures contained in the original contracts. The three appellants contended below that the original contracts were modified by the conduct of the parties and their course of performance under the contract. The trial court ruled against the contention, and the three separate appellants assign the ruling as error. The ruling of the trial court was correct.
The contracts are between the City of Clarksville and the three separate appellants. Section 14-234-108 of the Arkansas *423Code Annotated of 1987 provides that these contracts must be between the city owning the producing system and the city or association purchasing the water. It must be authorized by city ordinances, or if one of the purchasers is an association then by resolution, and the contract “shall be signed by the mayor of each contracting municipality and by the chairman of the board of each contracting improvement district.” Ark. Code Ann. § 14-234-108 (1987). These contracts were with Clarksville, and not with CL&W, the entity that operates the utility for Clarksville. The City of Clarksville has not delegated any legislative powers to CL&W. See Adams v. Bryant, 236 Ark. 859, 370 S.W.2d 432 (1963). Thus, it is the City rather than CL&W that has the authority to enter into or modify the contracts, and the conduct of CL&W in supplying water in excess of the amounts specified did not have the effect of modifying the contract.
Appellants alternatively contend that, even if CL&W did not have the authority to modify the contracts, the trial court’s ruling was still in error because Clarksville ratified the modification. Ratification of a contract must be by the principal or by an authorized agent. City of Greenbrier v. Cotton, 293 Ark. 264, 737 S.W.2d 444 (1987). There was no evidence to indicate that Clarksville authorized CL&W, or any of its employees, to modify these contracts.
Another alternative argument propounded by appellants is that Clarksville is estopped to deny the modification. Estoppel may be applied against a city, but its application will be rare indeed. In Miller v. City of Lake City, 302 Ark. 267, 789 S.W.2d 440 (1990), we stated that a city cannot be estopped by the unauthorized act of one of its officers. There was no evidence that Clarksville authorized any employee to modify the contracts. As a result, even if one of the CL&W employees stated that the three appellants could have water in excess of the amount provided in the contracts, the City would not be estopped from enforcing the quantity provision of the contract. We affirm the ruling of the trial court on the alternative arguments.
Appellant Horsehead Water Users Association separately makes the third assignment of error which involves an alleged modification of the term, or length, of its contract. On January 25, 1978, Clarksville and Horsehead entered into a contract for a *424term of ten years. Horsehead received a loan for the construction of its system from the Farmers Home Administration. Before the Farmers Home Administration would loan the money, it requested that Horsehead seek to have the term of the contract extended from ten to twenty years. Subsequently, the superintendent of Horsehead went to the executive officer of CL&W, Otis Cude, and suggested the requested change. At some time later the “ten” in the contract was lined out and “twenty” was handwritten in its place. Beside the handwriting were the initials O.R.C., which are Otis Cude’s initials. The trial court ruled this was not a valid modification of the contract. Separate appellant Horsehead assigns the ruling as error.
Parties are free to modify a contract between them, but it is essential that both parties agree to the modification and its terms. Leonard v. Downing, 246 Ark. 397, 438 S.W.2d 327 (1969). Here, there is no evidence that one of the parties, Clarksville, approved the modification, and there was no evidence that Cude was authorized to act for the City. Consequently, the trial court’s ruling was correct.
The foregoing three assignments of error are all of the points advanced by the appellants. None of the points require reversal, and, accordingly, we affirm on direct appeal.
Clarksville, on cross-appeal, makes four assignments of error. The first of these is that the trial court erred in refusing to enforce an implied declaratory judgment in Clarksville’s favor. The argument is meritorious. Clarksville filed suit for the money due under the new rate and, in addition, asked for a judgment declaring the validity of the municipal ordinance setting the rate at $1.56 per thousand gallons of water. The trial court, by granting the money judgment at the rate set in the ordinance, impliedly declared the ordinance valid. However, the trial court declined to formally enter such a declaratory judgment. The result is that Clarksville has a money judgment to the date of the trial. The six appellants filed a supersedeas bond for this amount. However, since the date of trial the appellants have been paying at the rate of only 78 cents per thousand gallons of water, not at the rate of $1.56, and, under the trial court’s ruling, Clarksville will have to continue to file suits to collect the additional deficiencies that will accrue. The ruling was in error. We reverse *425on this point of cross-appeal and remand for the trial court to enter and to enforce a declaratory judgment.
Clarksville’s second assignment of error involves the trial court’s refusal to award prejudgment interest. Again, the assignment has merit. In Atlanta Exploration, Inc. v. Ethyl Corp., 301 Ark. 331, 784 S.W.2d 150 (1990), we wrote that the test for awarding prejudgment interest is:
whether a method exists for fixing an exact value on the cause of action at the time of the occurrence of the event which gives rise to the cause of action. If such a method exists, prejudgment interest should be allowed, because one who has the use of another’s money should be justly required to pay interest from the time it lawfully should have been paid. Where prejudgment interest is collectible at all, the injured party is always entitled to it as a matter of law.
Id. at 339, 784 S.W.2d at 153-54 (citationsomitted). Clarksville met this test, and prejudgment interest should have been allowed. We reverse and remand on this point of cross-appeal.
Clarksville’s third assignment, which involves separate cross-appellee City of Hartman, is also meritorious. Clarksville and Hartman entered into a forty-year water supply agreement on February 23,1968. In one part of this case, Clarksville moved for a partial summary judgment declaring that the forty-year term was void as a matter of law. The trial court denied the motion for partial summary judgment and later ruled that the forty-year term was valid.
Section 14-234-108 (b)(2) of the Arkansas Code Annotated of 1987, which has been in effect since 1949, authorizes municipalities to sell water to other municipalities and provides that the “contract may be for a term of not exceeding twenty (20) years.” The Cities of Clarksville and Hartman had no authority to into a contract that was contrary to the general laws of the state. Morrilton v. Comes, 75 Ark. 458, 87 S.W.2d 1024 (1905). A contract by a city that is contrary to the general law of the state is void. Id. Cross-appellee Hartman does not deny the foregoing law, but rather contends that federal law preempts state law because the Farmers Home Administration loaned *426money to Hartman to build its system. We need not decide whether federal law preempted state law at any time because the Farmers Home Administration is no longer involved in financing the Hartman system. It has sold the notes without recourse, and no authority is cited that federal law would preempt state law in such an event.
Clarksville’s final assignment on cross-appeal is that the trial court erred in refusing to award it a 10 percent penalty against all six cross-appellees in accordance with the 1985 city ordinance that increased the rates. The provision in the ordinance is penal in nature and must be strictly construed, and a trial court will be granted a reasonable amount of discretion in denying or allowing such penalties depending on the circumstances. Lamar Bath House, Inc. v. City of Hot Springs, 229 Ark. 214, 315 S.W.2d 884 (1958). The trial court did not abuse its discretion under the circumstances of this case. The contract, which initially determined the rates, did not provide for a penalty. The contract provided for modification of the rates through city ordinance when the cost of performance increased or decreased. The validity of the ordinance was dependent proof of cost of performance of the contract. We need not decide whether a penalty could lawfully be subsequently added to the cost of performance, because; even if it might be, the trial court did not abuse its discretion in refusing to penalize the appellants for raising a valid justiciable question. In sum, on cross-appeal, we reverse and remand in part, and affirm in part.
Affirmed on direct appeal; reversed and remanded in part and affirmed in part on cross-appeal.
Glaze, J., concurs on direct appeal.