## Monday, 14 April 2014

### I thought the Chinese were supposed to be good at maths...

From Numbeo.com (a rather handy website, as it happens, it even converts figures to your home currency):

Property prices in Shanghai

Index

Price to Income Ratio: 27.86
Monthly mortgage payments as Percentage of Income: 249.60%
Gross Rental Yield (City Centre): 3.16%
Gross Rental Yield (Outside of Centre): 3.64%

Rent Per Month Range
Apartment (1 bedroom) in City Centre - £573.61
Apartment (1 bedroom) Outside of Centre - £314.13
Apartment (3 bedrooms) in City Centre - £1,385.60
Apartment (3 bedrooms) Outside of Centre - £771.69

Price per Square Meter to Buy Apartment in City Centre - £4,565.91
Price per Square Meter to Buy Apartment Outside of Centre - £2,194.05

Salaries And Financing
Average Monthly Disposable Salary (After Tax) - £606.57
Mortgage Interest Rate in Percentages (%), Yearly - 6.52%

So to be able to even afford to rent one-bed flat in the city centre or a three-bed flat in the 'suburbs' you need two earners, fair enough.

This is when it gets weirder and weirder...

Price to Income Ratio is the basic measure for apartment purchase affordability. It is the ratio of median apartment prices to median familial disposable income, expressed as years of income. Our formula assumes and uses:
◦net disposable family income, as defined as 1.5 * the average net salary
◦that the average apartment has 90 square meters
◦its price per square meter is the average price of square meter in city center and outside of city center

Mortgage as Percentage of Income is a the ratio of the actual monthly cost of the mortgage to take-home family income. Average monthly salary is used to estimate family income. It assumes 100% mortgage is taken on 20 years for the house(or apt) of 90 square meters which price per square meter is the average of price in city center and outside of city center.

So a flat costs 27.86 x 1.5 x £606.57 = £253,000, or possibly (£4,565.91 + £2,194)/2 x 90 = £304,200, let's call it £280,000.

The simple average of the four rents is £760 a month, which is a gross yield of 3.3%, which is very much on the low side.

£280,000 on a 100% 20-year repayment mortgage at 6.52% interest = £2,121 per month, or £606.57 x 1.5 x 249.6% = £2,270, call it £2,200 mortgage repayments.

Given that the average of the four rents is £760 a month, why would anybody take out a mortgage costing £2,200 a month?

If we knock off one-third of rental income for a landlord's costs and taxes and assume that he finances the annual loss at the same interest rate as the original mortgage, rents and flat prices would have to increase by 4.6% a year compound for the next twenty years for him to even get his money back, and even if all that happened, the rental yield in twenty years' time would only be 2%.