I'd be interested in the throughout then, instead of annual snapshot figures. If the average homelessness is say 5 weeks /1.2 months roughly, then you may be servicing 10x as many homeless people or 160 thousand, for 20k each.

With servicing meaning: short term housing for the duration of the homelessness, medical care, counselling, labour force training and placement, employer and landlord subsidies for the first six months of employment/housing contract etc.