This paper explores a housing market with an existing tenant in each house and where the existing tenants initially rent their houses. The idea is to identify equilibrium prices for the housing market given the prerequisite that a tenant can buy any house on the housing market, including the one that he is currently possessing, or continue renting the house he is currently occupying. The main contribution is the identification of an individually rational, equilibrium selecting, and group non-manipulable price mechanism in a restricted preference domain that contains almost all preference profiles. In this restricted domain, the identified mechanism is the minimum price equilibrium selecting mechanism that transfers the maximum number of ownerships to the existing tenants. We also relate the theoretical model and the main findings to the U.K. Housing Act 1980 whose main objective is to transfer ownerships of houses to existing tenants.