Valuing the Housing Cooperative Conversion Option

Since the 1990s, both private and municipal owners of multifamily rentalproperties in Sweden have sold a large number of their properties to hous-ing cooperatives established by the property's tenants. One motivationfor the large increase in so called housing cooperative conversions is thatthe practice of rent regulation causes actual rents to be lower than market-clearing rent levels, especially in attractive areas in larger cities. By sell-ing the property to a housing cooperative, the property owner can takeadvantage of the positive price di®erence between the price of housing co-operative dwellings, which are determined by demand and supply, and thevalue of the property based on the assumption that the rents will continueto be lower than market rents.In this paper we use a real options approach to derive a closed-formvaluation formula for the option an owner of an income producing multi-family property has to sell it to a housing cooperative. In traditionaloption valuation models, the date when the option matures is known inadvance. However, it is common that the property owner does not knowin advance when the tenants (through the housing cooperative) will buythe property. In this paper we let the expected time to maturity, which isthe day when the tenants purchases the property from their landlord, tobe a random variable. The numerical examples suggest that the value ofthe conversion option increases as expected time to conversion increases,as well as when the volatility of the price of housing cooperative proper-ties increase. The real options approach suggested in this paper may beespecially useful to explicitly conceptualize the problem of valuing a rentalproperty with embedded options to switch it to another type of property.