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Rents Vs House Price Long Term

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I know this has been done to death, but I tried doing another (trivial and invalid) longer term comparison of ownership vs rents. Again disregarding maintenance etc. Just for fun :P

There seems to be a lot of comparisons of rent vs the current price. Just taking into account interest only payment for this year vs rent. That seems wrong since the sum that interest is payed on is fixed. So using time value of money the later payments are considerably cheaper than the close payments. In contrast to rent which increases each year. I chose a fixed rate interest only mortgage for comparison. Any repayments could be invested at the interest rate...

I made some big big assumptions. BOE keep CPI at 2% on average. Rates are constant! House price and rent price inflation matched (housing shortage) and run at double CPI throughout. As an example property I chose one nearby that I'm thinking of renting. Rent: £1000/month. Last sold price £350,000. 3 bed end of terrace with garage. I also assumed no capital gains tax, no difference in interest on savings vs mortgage cost and no tax on savings.

Using this program and being "in it for the long term" - 25 years in this case, as long as I can fix. The numbers I think should compared are discounted cost (total interest - equity) vs discounted total rent. The discounted ones are in brackets.

At 5% things look about equal - perhaps £50,000 overvalued.

After 25 years - total rent:499750(255325) cost:-145542(321113) total interest:437500(246644) equity:583042(-74469)

At 4% houses look £70,000 too cheap - should be worth £420,000

After 25 years - total rent:499750(288461) cost:-233042(218709) total interest:350000(218709) equity:583042(1.16415321826935e-10)

At 6% we're about £200,000 overvalued - should be worth £150,000

After 25 years - total rent:499750(227318) cost:-58042(401052) total interest:525000(268450) equity:583042(-132602)

At 7% the house is £250000 overvalued - should be worth £100,000

After 25 years - total rent:499750(203528) cost:29457(463600) total interest:612500(285512) equity:583042(-178087)

At 8% (long term average) it looks like the house should worth about £20,000?!

After 25 years - total rent:499750(183222) cost:116957(512652) total interest:700000(298893) equity:583042(-213759)

I've come to the understand why I'm a software engineer and not a modeler of house prices. Because its hard to do right and there are gazillions of factors to consider. Perhaps this just means I should fix at any cost if rates hit 4% again:-)

Mark

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Code follows for anyone interested. What did I get fundamentally wrong here given these assumptions.

#!/usr/bin/perl -wuse strict;my $interest = 0.04;  #Long term averagemy $inflation = 0.02; #boe target (includes rent)my $rentpi = 0.04;    #Housing in demand, so rent and hpi runs at double rest of inflationmy $housepi = 0.04;my $starthouseprice = 350000;my $currenthouseprice = $starthouseprice;my $startrent = 1000*12;my $currentrent = $startrent;my $totalrent = 0;my $discountedtotalrent = 0;my $totalinterest = 0;my $discountedtotalinterest = 0;my $years = 25;foreach (1..$years){$totalinterest += $starthouseprice*$interest;$discountedtotalinterest += ($starthouseprice*$interest)/((1+$interest)**$_);$totalrent += $currentrent;$discountedtotalrent += $currentrent/((1+$interest)**$_);print "Year $_: rent:$totalrent interest:$totalinterest\n";$currentrent *= (1+$rentpi);$currenthouseprice *= (1+$housepi);}my $equity = ($currenthouseprice-$starthouseprice);my $x = (1+$interest)**$years;my $discountedequity = ($currenthouseprice/((1+$interest)**$years))-$starthouseprice;my $cost = $totalinterest-$equity;my $discountedcost = $discountedtotalinterest-$discountedequity;print "After $years years - total rent:$totalrent($discountedtotalrent) cost:$cost($discountedcost) total interest:$totalinterest($discountedtotalinterest) equity:$equity($discountedequity)\n";

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