Before being granted a permit, each person shall deposit with the City Auditor an amount of money sufficient to cover the cost of any work which the city may be required to do in connection with backfilling, restoration of pavement or other work. Upon completion of the work for which a permit was issued and acceptance thereof by the Director of Service, the Auditor shall refund to the applicant any amount of this deposit not required to cover the cost of work done by the city. In the event that the deposit shall not have been sufficient to cover the cost of the work, the applicant shall pay such additional amount as is required to cover the city’s cost.