# The Mathematics of House Prices

I was talking and thinking about affordability of housing a couple of days ago and that same day saw a series of interactions on Twitter which included this one. I thought I’d play around with the mathematics of a simple example of housing.

Let’s hypothesise that the average affordable one-bedroom home price should be a maximum of £150 per square foot of living space. Assuming an average, reasonably-sized one-bedroom home comprises 600 square feet of total living space, the price of this home would be £90,000. In 2009, the UK average weekly pay was £489 or around £25,000 per annum. Assuming a homeowner could save up enough for a 10% deposit and pay the stamp duty and transaction costs (conveyancing, survey), they would need a mortgage of at least £81,000. This loan represents 3.2x the average salary and assuming a total interest rate of 6%, a 25-year mortgage, the monthly payments would be one third of the homeowner’s net monthly salary. Based on prudent borrowing principles and affordability, this is just about manageable and housing costs should certainly not cost more than one third of someone’s net salary.

The last time the price of an average flat was less than £90,000 was in August 2000.

More recently, the average flat or maisonette (using data over the last 12 months) has been priced at £153,000 or £255 psf. House prices are increasing again since the low in March 2009 when the average cost was £141,000. The last time the average house price was at this level was March 2004. For those who are able to buy their homes, they continue to buy and house prices are on the rise again.

In London it is even more accentuated with average salaries around £33,000 and average flat prices around £295,000 – that’s 9 times the average salary. And assuming a 600 square foot flat, a cost of £492 psf, more than 3 times the hypothesised affordable flat.

So, what’s behind these house prices? The rule of thumb on residential developments is one third land cost, one third development cost, one third profit. If such a ratio were to be maintained, each of these elements must be reduced by a third which requires a complete re-basing of land values, materials, labour, and remuneration.

Having spoken to architects about the average development cost, this ranges between £150 psf to £200 psf (not including professional fees and financing costs). The price of the hypothesised affordable house is in one way based on the development cost alone. To bring the price of buying a house back to affordable levels, one way which would have the greatest impact would be to remove the cost of the land and the profit element from the purchase price paid by a home-buyer. Community land trusts, housing elements of development trusts, co-operative housing, and other not-for-private-profit housing initiatives aim to achieve this. Land values are locked in, owned in perpetuity by a trust.

Let’s stretch the imagination. Imagine a place where the price of all land did not increase over time. Where capital appreciation in the value of property came only from improving property or possibly changes in its use. Is this possible? What would the economics of such a place look like? A community land trust would fit right at home in such a place.

(The data for average salaries was taken from the Office of National Statistics and average home prices are for maisonettes and flats taken from the House Price Index tool on the Land Registry website. There is a margin of error due to the use of averages and incomplete information, but such margin of error is not so big as to counter the pattern and trends of house prices and average earnings.)