As the cost of rental housing shoots up across the country, so has the need for affordable housing. Yet most new apartment buildings are geared to the higher end of the market; building and operating affordable housing, many developers argue, isn't profitable.

Seattle builder Spectrum Development Solutions is testing the conventional wisdom. With help from Canada-based financial partner Gracorp Capital Advisors, Spectrum is spending nearly $70 million to construct three apartment buildings in the First Hill section near Seattle's...