I wrote out my thought totally incorrectly there. What I meant to say was add up all costs associated with owning the home, add in the opportunity cost of the down payment,* and subtract the rent I would receive from roommates. Then compare that to the cost of renting a room.

Also, the way I' thinking of opportunity cost is this: Say over the ten year period I would expect to be in this arrangement, a $40,000 down payment could become 78,686 compounded at 7% (in an index fund) vs $53,756 at 3% (as an investment in a house that keeps up with inflation). so that difference is about $25,000 or $2,500/year. Is this a correct way to think about this?

Sorry if these are dumb questions, I've always been a happy renter, but recently started to consider buying.