Relationship between incomes, maximum mortgage loans, and purchase prices in the CRD

My recent post on housing in BC, looking at the rates of household formation and new residential construction (can be found here) got me thinking - Based off of incomes, what is the maximum price which a household could afford when buying their residence?

In order to calculate this maximum, we need to know a few things.

1. What is a household's gross income?
2. What are the qualification criteria for a mortgage?

Well first, to address households gross income. Such data is not publically available at a household level. Instead what is available are mean and median household incomes, as well as incomes by household according to set income brackets.

For example, In the Greater Victoria Area (CRD), from the 2011 and 2006 census:

• 2006 Median household income: $61,553 and Mean household income: $76,711
• 2011 Median household income: $67,041 and Mean household income: $78,583

giving us an annual growth rate of Median and Mean Incomes equal to

• Median household income growth rate: 1.72% per year
• Mean household income growth rate: 0.48% per year

If we make the assumption that these growth rates are roughly constant, then we get:

• 2016 median household income: $73,008
• 2016 mean household income: $80,487

Then if we refer to the CRD gap analysis conducted in August 2015 which breaks the CRD population into different sized groups based on incomes. primarily the findings are:

Armed now with an estimated 2016 mean and median, as well as a bit of distributional information as to what percentage of the population fits into each category, I can now generate a simulated distribution of household income to approximate the above information.

Doing so we get a simulated income distribution of the CRD with:

• Simulated Median household  income: $71,527
• Simulated Mean household income: $80,704
• Simulated Min household income: $0.2
• Simulated Max household income: $1,551,000
• Simulated Standard Deviation of household income: $61,692

which gives us an estimated income distribution for 2016 which looks like:

Next let's move to determine what is the maximum mortgage amount each household could qualify for, given their income.

To do so we need to make some general assumptions.

1. Property taxes are constant at 0.8% of property value.
2. The cost of heating one's home when averaged over the year is $100/mo.
3. after considering the monthly payment for heat, property tax, and the mortgage, all other monthly debt payments account for less than 7% of a household's gross income. 
4. The interest rate at which a household is qualified at is the 5 year fixed rate as posted by the Bank of Canada -- 4.64% as of the time I am writing.

These assumptions are needed due to the qualification requirements which are (simplified for this):

• no more than 35% of gross income will be spent on Mortgage, Property taxes, heat.
• hence the need for assumptions 1, 2 and 4.
• no more than 42% of gross income will be spent on total debts. 
• hence the need for assumption 3, as well as the others.

Recall we are looking at calculating the maximum mortgage or loan amount each household would qualify for given their income and the above assumptions. This does not mean the maximum purchase price they could afford as we have made no assumptions about the buyer's equity and down payment -- thus if we were to assume that buyers have only the minimum down payment available, then maximum mortgage amount would be expected to be similar to the maximum purchase price. 

Note: currently the Median price in the CRD is $645,000 while the Mean price is: $752,509

With these assumptions, we can calculate the maximum mortgage payment for each household, then if we work backward, figure out the maximum mortgage amount each household could afford. This can be seen below:

If we interpret this graphic we see that the average maximum mortgage (loan) amount is in the realm of $365,919 while the median maximum is at $321,128. 

Comparing these maximum mortgage amounts to the average and median purchase prices we are currently seeing in the CRD we have a large discrepancy. The big issue here is that clearly, not all households can afford to own, those who make up the bottom of the income distribution simply do not have the means to achieve home ownership. Thus, following the lead of the CRD gap analysis previously referenced, let's assume that only those households earning $80,000 a year or more are able to afford to buy a house. 

If we invoke this assumption, then we get a truncated distribution of maximum mortgage amounts, and a revised higher mean and median maximum mortgage, which can be seen below:

By eliminating the bottom part of our income distribution by assuming they are not able to participate in the housing market, we obtain a new, higher mean and median max mortgaged amount. Still, there seems to be a gap between these values and those of the mean and median purchase prices. for reference:

• Median max mortgage $551,991 Vs Median purchase price $645,000.
• Mean max mortgage $596,135 Vs Mean purchase price $752,509.

Based off of this we can begin to infer that: 

1. Households are making massive down payments allowing them to reach purchase prices much higher than their maximum qualified mortgage amount.
2. Given the recent inflation of house prices in the CRD, $80,000 a year is no longer representative of the threshold household income required to enter the housing market. 
3. We may not be able to actually make inferential statements by comparing the maximum mortgage amounts and present purchase prices.

My last question becomes. If it is true that $80,000 is no longer the threshold household income to enter the housing market, which level of household income would yield a maximum mean and median mortgage amount similar to present housing prices?

The answer to that is a threshold household income equal to $125,000 yielding:

• Median max mortgage $678,200 Vs Median purchase price $645,000.
• Mean max mortgage $755,800 Vs Mean purchase price $752,509.

That is at this price, only the top 19.78% of households (roughly 1/5) could reasonably be expected to be able to participate in the housing market in the CRD.

What are your thoughts? feel free the comment below!