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What is this thing?
This is a calculator to help you compare the financial implications of buying
versus renting a home. You have two scenarios, where by default in the left one
you get a mortgage and buy a house, and in the right one you pay rent and invest
the available capital in stocks instead. The plots and the Final values section
show predictions for how these two scenarios might play out over time.
Below are many different parameters you can tune. Hover on the little question
marks to get more information about each one.
The calculator assumes UK taxation and uses UK concepts such as leaseholds and
ISAs. Some of the default values are based on London numbers, such as historical
house price growth in London. You can change those values though. Changing the
taxation system would require editing the code.
The outcomes depend massively on future inflation, salary growth, house price
growth, rent growth, and the growth of the value of any stock portfolio. These are
all modelled probabilistically, and the value for each of these is assumed to be
log-normal distributed. You can set the mean and scale. The probabilistic nature of
the simulation is why the plots at the top have error bars. The midline is the
median, the limits are the 20th and 80th percentiles.
The logic of the simulation is roughly as follows: Each year
- Random sample from a normal distribution that year's inflation rate.
- Random sample all the other growth numbers, such as salary, house price, and
stock portfolio growth, and add inflation to the these values.
- Add annual salary to your cash balance, and then subtract from the balance
rent/mortgage payments/running costs. Decrease the mortgage balance appropriately.
- If there is cash left over, invest all of it in the stock portfolio. Primarily
put it in an ISA, but if you've maxed out your ISA allowance, put the rest in a
stock portfolio that is subject to capital gains tax.
- Conversely if you have a negative cash balance, sell stocks to cover it.
If you don't have enough to sell, you go bankrupt. This means all
values such as cash, stock, salary, rent, etc. are set to zero, and the
simulation effectively ends.
- Increase your salary, rent, house value, and stock portfolio value by the
random values sampled.
- Go to the next year and repeat.
You may also optionally overpay your mortgage before investing surplus cash in
stocks, but by default this is turned off.
By default the output values shown at the top are corrected for inflation, i.e.
they are expressed in today's money. You can change this setting at the bottom.
Do remember that buying a home is not only a financial decision, but affects your
life in many ways. This calculator only tries to capture the investment aspect.
Some caveats, things I'm not happy with in this calculator, that you should be
aware of:
- The default standard deviation for house price growth is probably too low.
I've estimated it by looking at how much variation there is year-to-year in
the price of the average house in London. But that's very different from
how much variation there may be in the price of a single house. I'm not
sure how to best estimate the latter though.
- The default values for rent growth and salary growth distributions are pure
guesses, I have no particular reason for them.
- I have no idea if the assumption that the random variables are all normal
distributed is realistic.
- The calculator doesn't really do variable mortgage rates. That's because it
doesn't model central bank interest rate development in any way. There's
probably some connection one could make there to inflation, but this would
get quite deep into macroeconomics. So currently you can just set the
mortgage rate you expect, and that's it.
- Bankruptcies are handled a bit awkwardly. Currently if you ever come to a
situation where your yearly incomings can't cover the outgoings, all your
wealth, stock, salary, rent etc. are set to zero. This effectively
terminates the simulation. This may skew the distributions at the end of
the simulation in unexpected ways.
- The default values I've set for ground rent, service charges, and
maintenance costs aren't based on more than a quick online search.
- The time step of the simulation is a full year. Having monthly time steps
would be more accurate.
- The capital gains tax calculator assumes you are in the >50k tax bracket.
This calculator is free software and its source code is here: github.com/mhauru/buyvsrent
No one involved in making this calculator has any relevant qualifications, and
nothing here is financial advice.