The expenses associated with moving in to a property typically include first months rent, security deposit, utility deposits and moving expenses. By requiring a full first month's rent no matter what day they move in, you are ensuring the ability for a tenant to make payment. It's similiar to the principle of putting more money down to qualify for a mortgage. The prorated amount is paid the second month. If all the monies are not collected up front, there is a higher chance of the tenant falling behind on payment.
