Any irrigation district, city, town, or other water user or users whose lands are irrigated by water carried in works transferred by the United States to a board of control, are hereby authorized to enter into contract with another irrigation district whose lands are irrigated by water carried in the same canal to operate and maintain the main canal and other works known as transferred works, and to pay such district in a lump sum its pro rata proportion of the cost of maintenance and operation of such transferred works: PROVIDED, That the amount said pro rata proportion may be estimated and such estimated amount paid at the beginning of any year, and at the end of the year the board shall after determining the true pro rata amount of such user's cost, require such user to pay the balance, if any, of said true pro rata amount.