The auditor shall then calculate the proportion that the assessed value, on the preceding lien date of the property annexed or incorporated bears to the total assessed value, as of that day, of all the property in the district from which the annexation or incorporation was made. He shall prepare a claim in favor of the city, to be allowed by the board of supervisors and paid by warrant on the treasurer, for that part of the unencumbered funds of the district which bears the same proportion to the whole of such unencumbered funds as the assessed value of the property annexed or incorporated bears to the total assessed value of all the property in the district from which the annexation or incorporation was made.