PER CURIAM.

A jury found defendant St. Clair County liable to plaintiffs for $20,500 in damages. The jury also found third-party defendant DiLegge Construction Company liable to St. Clair County for $1,500 in damages. St. Clair County appeals as of right.

St. Clair County (defendant) contracted with third-party defendants for a sewer project which was to pass under plaintiffs' land. Initially, however, plaintiffs refused to sign a right-of-way agreement provided by defendant because of difficulties experienced several years before in restoring their land after defendant had installed a water line. Eventually, plaintiffs signed the agreement but only after typing in additional provisions regarding restoration of their property. Included among those provisions was the following one regarding liquidated damages:

"Should the restoration of the property exceed 90 days after the work is first done on description 1106 installing the sewer, the owner shall have the option of either contracting to have the property restored himself at the County's expense or penalize the County $25.00 per day for each day over the 90 days that the work has not been completed to the owner's satisfaction."

Defendant's agent recorded the agreement but defendant failed to comply with the time limit. After numerous letters and calls to defendant (which resulted in little action), plaintiffs effectuated restoration of their property 820 days after the 90-day limit had passed. After initial pleadings were filed in the trial court, defendant moved for summary judgment, GCR 1963, 117.2(3), seeking a ruling that there was no contract between plaintiffs and defendant or, in the alternative, that the liquidated damages provision was invalid as a penalty. However, the trial court found that a contract existed and that the liquidated damages provision was valid and enforceable. Even though plaintiffs had not moved for summary judgment, such action was clearly within the trial court's power. GCR 1963, 117.3. Thereafter, at the trial, the jury was instructed that there was a valid and enforceable contract, including the liquidated damages provision. The jury was left to determine whether the contract had been breached and, if so, the amount of damages. On appeal, defendant claims that the trial court committed reversible error by finding, as a matter of law, that (1) a contract existed between plaintiffs and defendant and (2) the liquidated damages clause was valid and enforceable.

Initially, it should be noted that the affidavits of defendant's right-of-way agent and director of public works, submitted for the first time on appeal, cannot be used to enlarge the appellate record and will be disregarded. Philips Industries, Inc v Smith, 90 Mich. App. 237, 249-250; 282 N.W.2d 788 (1979).

As for the existence of a contract, although defendant admitted the existence of the easement, it neither admitted nor denied that it agreed to all of the provisions added by plaintiffs. However, it is clear that defendant admitted that it agreed to the liquidated damages provisions. Thus, it cannot now claim that that provision was not part of the agreement. Beals v Walker, 98 Mich. App. 214, 233-234; 296 N.W.2d 828 (1980), lv gtd 411 Mich. 900 (1981).

When the terms of an agreement are disputed, it is the duty of the trier of fact to determine them. Smith v Saginaw Savings Loan Ass'n, 94 Mich. App. 263, 273; 288 N.W.2d 613 (1979). Although plaintiffs signed the right-of-way agreement as grantors, no one representing defendant signed on its behalf as grantees. Indeed, there is no space on the form for any representative of the grantee to sign, other than as a witness or as a notary. Defendant's filing of the agreement, however, most likely amounted to an acceptance of plaintiff's conditions. Nevertheless, this is a factual determination that should have been submitted to the jury.

Moreover, the scope of the right-of-way agent's actual authority is a question of fact. Caldwell v Cleveland-Cliffs Iron Co, 111 Mich. App. 721, 732; 315 N.W.2d 186 (1981). Similarly, an agent's apparent authority is a question of fact "to be determined from all the surrounding facts and circumstances". Smith, supra, 271-272. Consequently, the trial court committed error requiring reversal by finding, as a matter of law, that a contract existed between plaintiffs and defendant.

As for the liquidated damages provision, even though defendant admitted that it was part of the agreement, the trial court recognized that it had the duty to determine whether the clause was a valid and enforceable one for stipulated damages, or was invalid as a penalty. This determination is a question of law and there is no need for an inquiry into the intent of the parties. Wilkinson v Lanterman, 314 Mich. 568, 574-575; 22 N.W.2d 827 (1946). Rather, only the writing itself need be examined. However, if the amount stipulated is valid but damages in the event of breach are uncertain or difficult to ascertain, then it must be determined whether the parties intended to fix the amount of damages, based upon the writing, subject matter and situation of the parties. Curran v Williams, 352 Mich. 278, 286-287; 89 N.W.2d 602 (1958). This is also a question of law.

"It is a well-settled rule in this State that the parties to a contract can agree and stipulate in advance as to the amount to be paid in compensation for loss or injury which may result in the event of a breach of the agreement. Such a stipulation is enforceable, particularly where the damages which would result from a breach are uncertain and difficult to ascertain at time contract is executed. If the amount stipulated is reasonable with relation to the possible injury suffered, the courts will sustain such a stipulation.

"The purpose in permitting a stipulation of damages as compensation is to render certain and definite that which appears to be uncertain and not easily proven. The courts recognize that the parties, particularly at the time of execution of the instrument, are in as good a position as anyone to arrive at a fair amount of damages for a subsequent breach. In the event they are not unconscionable or excessive courts will not disturb it. Just compensation for the injuries sustained is the principle at which the law attempts to arrive. Courts will not permit parties to stipulate unreasonable sums as damages, and where such an attempt is made have held them penalties and therefore void and unenforceable." Curran, supra, p 282.

Furthermore, use of the words "penalty" or "forfeit" do not necessarily imply a penalty. Ross v Loescher, 152 Mich. 386, 398; 116 N.W. 193 (1908); Western Gas Construction Co v Dowagiac Gas Fuel Co, 146 Mich. 119, 120; 109 N.W. 29 (1906); Lamson v City of Marshall, 133 Mich. 250, 262-263; 95 N.W. 78 (1903). Rather,

"it will still be held to be stipulated damages, if, from the whole contract, the subject matter, and situation of the parties, it can be gathered that such was their intention. And in proportion as the difficulty of ascertaining the actual damage by proof is greater or less, where this difficulty grows out of the nature of such damages, in the like proportion is the presumption more or less strong that the parties intended to fix the amount." Jaquith v Hudson, 5 Mich. 123, 138 (1858).

Of course, use of the terms "liquidated" or "stipulated" damages does not necessarily mean that the clause is valid and not a penalty. Nichols v Seaks, 296 Mich. 154, 161-162; 295 N.W. 596 (1941). We also observe that liquidated or stipulated damages at a daily rate are commonly provided for and permitted when work or services contracted for are not completed on time. Hall v Gargaro, 310 Mich. 693; 17 N.W.2d 795 (1945) ($10 per day); Ross, supra ($20 per day); Western Gas, supra ($25 per day). Such clauses are also permissible when local governments contract for public works projects. Lamson, supra ($10 per day); Ann Arbor Asphalt Construction Co v City of Howell, 226 Mich. 647; 198 N.W. 195 (1924) ($20 per day).

"It is permissible, in cases where damage by delay is impossible of actual ascertainment by reference to any pecuniary standard, to stipulate the damage in advance, and, if reasonable, agreed damages for delay may be recovered by a municipality." Wisconsin Bridge Iron Co v City of Alpena, 238 Mich. 164, 168; 213 N.W. 93 (1927).

Damages due to delay in completion are typically uncertain as to amount and difficult to ascertain. Ann Arbor Asphalt, supra, p 652; Western Gas, supra, p 121.

In this case, it is clear that at the time the agreement was made, $25 per day represented a reasonable amount for any delay in restoration of the property beyond 90 days after work commenced. Also, undoubtedly, damages due to any delay were necessarily uncertain as to amount and difficult to ascertain. Moreover, it cannot be said that the parties did not intend to fix the amount of damages. Finally, if governmental entities are permitted to recover liquidated damages for delays in the completion of public works contracts, private citizens should also be allowed such a recovery. Accordingly, we hold that the trial court did not err in finding, as a matter of law, that the liquidated damages provision was valid and enforceable.

We applaud the plaintiffs' foresight in providing for this arrangement. We are gratified by the prospect that at least one set of victims of an unresponsive bureaucracy may not go uncompensated for their troubles.

We affirm the trial court's determination that the liquidated damages clause was valid. We reverse the trial court's finding that a valid contract existed and remand for a new trial limited solely to that issue.

Affirmed in part and reversed in part. No costs, neither party having prevailed in full. We do not retain jurisdiction.