Upon written request by the legislative body of a newly incorporated city, the board of supervisors shall cause the county auditor to prepare, without cost, a statement of the value of the assessable property in the disincorporated city and the value of that property now contained in the incorporated city. If the statement shows that at least two-thirds of the assessed value of all assessable property formerly contained within the disincorporated city is contained within the boundaries of the newly incorporated city, the board of supervisors shall fix the relative proportion by an order entered in the minutes, and the newly incorporated city is liable for that proportion of the debts and liabilities of the disincorporated city.