The presence of leverage means that appreciation still favors you. Assume you buy a $100k house, with a 30 year mortgage at a 6% interest rate and a 20% down payment. You then buy an equivalent house.
Over the course of those 5 years, you will spend $28.77k in principle and interest, reducing your loan balance from $80k to $74.44k
At 0% appreciation, you sell, giving you $25.56k in equity, then buy another $100k house at 20% down leaving you with $5.5k in cash.
At 2% appreciation, you sell, giving you $35.96k in equity, then buy another $110.4k house at 20% down leaving you with $13.88k in cash.
At 4% appreciation, you sell, giving you $47.22k in equity, then buy another $121.66k house at 20% down leaving you with $23.00k in cash.
At 6% interest, the difference between the 80k loan and 97.328k loan is $103.89 a month, or about $1.25k a year. Set asside $6.23k from your surplus to cover the marginal P&I cost for 5 years and you are left with $16.77k cash. Subtracting the $5.5k of equity you woupd have had at 0% appreciation, and a 4% appreciation rate netted you $11.27k over just 5 years.
Given your 20k initial investment, that is a net return of 56.35%. Which is an annualized return if 9.35%.
Your math may well be correct but I can't follow it without a spreadsheet, so let's do a simpler example with two different appreciation scenarios.
Scenario A: I buy a $100k house with $50k down and a $50k mortgage. House prices don't change. I sell the house, then buy another $100k house. I'm still at $50k in equity and I still owe the bank $50k.
Scenario B: same as scenario A, but this time, all home prices double, including mine. I sell for $200k and now have $150k, which I use to buy another $200k house. I now have $150k equity, but I still owe the bank $50k.
In Scenario B I'm better off than someone who didn't buy the house before prices went up -- a fact that should surprise no one -- but I'm not necessarily better off than I would have been if prices hadn't doubled at all. I still owe the bank $50k in both scenarios. The housing price appreciation hasn't actually helped my finances unless I sell the house or use it as collateral for loans, neither of which I am interested in doing. Because I own the house to live in it, not to use it for financial engineering or speculation.
The appreciation presumably does not include all the money you spent just maintaining the house, or all the fees involved in both buying and selling. And the costs don't include remodeling the new house so that it's got the things you liked about the old one, or the cost of moving. I'm not arguing home ownership is a bad investment, it's been a good one for me. But every time I look into the actual cost of trading up houses, the calculation gets really complicated, and doesn't look as cut and dry as it did on the back of the envelope.
Over the course of those 5 years, you will spend $28.77k in principle and interest, reducing your loan balance from $80k to $74.44k
At 0% appreciation, you sell, giving you $25.56k in equity, then buy another $100k house at 20% down leaving you with $5.5k in cash.
At 2% appreciation, you sell, giving you $35.96k in equity, then buy another $110.4k house at 20% down leaving you with $13.88k in cash.
At 4% appreciation, you sell, giving you $47.22k in equity, then buy another $121.66k house at 20% down leaving you with $23.00k in cash.
At 6% interest, the difference between the 80k loan and 97.328k loan is $103.89 a month, or about $1.25k a year. Set asside $6.23k from your surplus to cover the marginal P&I cost for 5 years and you are left with $16.77k cash. Subtracting the $5.5k of equity you woupd have had at 0% appreciation, and a 4% appreciation rate netted you $11.27k over just 5 years.
Given your 20k initial investment, that is a net return of 56.35%. Which is an annualized return if 9.35%.