Do Cap Rates (and ROI) Improve over Time with Inflation?

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E.g. You buy a $100k house that has cap rate of 10%, so $10k cash flow.

Since you adjust 3% per year for inflation, after 15 years your income is doubled to $20k, yet the asset price is still only $100K, so now you have a cap rate of 20%. In 30 years it doubles again.

Considering alternatives for other investments where the ROI is fixed, this would make real estate seem a lot more lucrative.

What am I doing wrong here?

Typically I would look at a metric like cap rate at a specific point in time. Using your example with 3% inflation it is presumable that the house is now worth $200,000. Note that this is not appreciation, it is just your hard asset retaining it's value while the money is only worth half of what it used to be.

Say you then did a tax and cost free exchange of a carbon copy house across the street. When you valued that new transaction would you say the house was a $100k house and has a 20% cap rate? Not generally. 

Also, it is likely that all of your other associated costs with the property have doubled too, other than the financing. It is a great advantage to be paying off a long term fixed rate loan after 10 or 20 years of inflation and rent increases.

Another way to look at it is this. Say you paid all cash for the house, and the income was just enough to pay for your car lease.  Assuming even, across the board inflation, in 20 years or 100 years, that house is still only going to be just enough to pay for a car lease.

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