As of the first of the month, both insurance and payroll will be handled by the same department.
By the time starting at the first of the month, both insurance and payroll will be handled by the same department.
As of the first of the month, both insurance and payroll will be handled by the same department.
By the time starting at the first of the month, both insurance and payroll will be handled by the same department.
The idiom "as of" is appropriate for discussing a starting date for something. The structure "by the time starting at" is needlessly wordy and awkward, and would not be preferred by the GMAT.