Sauder Housing Predictions

In a previous post I outlined basic theory behind net present value (NPV) calculations as it pertains to real estate and related it to a working paper (PDF) published by Dr. Somerville and Kitson Swann at the Sauder School of Business at UBC. I have read a few online discussions popping up recently regarding this paper, brought on I am sure in part by Dr. Somerville’s many recent quotations in the local media.

The paper claims that Vancouver’s house prices would need to drop 11%, from a benchmark of $754,500, to return to “equilibrium”: $680,000. If we look into the methodology used in the paper, the cost of capital elements such as tax, depreciation, and maintenance are determined by a percentage of current house value. This is fine however, should the house value change, we must re-adjust the figures as I will now do.

The cost of capital was calculated to be, as percentages of the original price: maintenance and insurance 0.5%, depreciation 1.07%, and tax 0.5%. All of course are fixed costs that will not vary significantly with changes in land value so nominally these values are $3773, $8073, and $3773 respectively. Note the $8073 number for depreciation is way too high and should be around $2500-3000 but for now let’s leave it as is.

The REBGV just released their statistics showing the new benchmark price in Vancouver is about $696,000 so let’s re-calculate the cost of capital, assuming as before a 5.4% annual capital appreciation (which I will deal with in a bit). The new percentages are: maintenance and insurance 0.54%, depreciation 1.16%, and taxes 0.54%. The new equilibrium cost of capital is 4.27%.

Uh oh. Now we need to re-calculate a new equilibrium price with the new cost of capital. Plugging in the numbers we get a new “equilibrium” value of $652,000. That is a drop of -13.5% from the paper’s benchmark price and a further -6.3% from today’s market price. If we perpetually plug in the new “equilibrium” prices into the formula, as we now must given prices are dropping fast, the new “equilibrium” converges at $602,000. Put another way, the true “equilibrium” price, given the property’s nominal costs and expected capital appreciation, is -13.5% below today’s benchmark price and -20% below the number used in Somerville et al’s paper.

It unfortunately does not stop there. I must take exception with the purported 5.4% annual appreciation numbers cited as the long term expected average appreciation in Vancouver. While this may have been true in the past there are at least three good reasons to believe this level of appreciation is far too optimistic.

The first way that prices appreciate is by rising incomes however Vancouver’s real incomes are flat. This means that in terms of long-term affordability, dwelling prices cannot increase much faster than incomes are rising, roughly at the rate of inflation. There is little in the short term to believe that incomes will be rising faster than inflation; in aggregate with falling employment and a looming recession the opposite is far more likely to happen in the medium term.

The second way prices appreciate is by densification; that is, the anticipation of using a piece of land to produce higher future incomes. Here there is a good argument that some property prices can appreciate faster than incomes are rising if they have not fully densified yet. However some quick deduction can show that there is a limit as to how fast average densification can occur: the population growth rate (around 1.2% in Vancouver area). From a practical perspective the actual densification will occur less because new land (farmland and forest) is being turned into residential dwellings, easing the maximum densification potential.

The third, and the most striking, way prices appreciate is through a waning of inflation expectations that has resulted in perpetually lower mortgage rates over the past generation and this has, through a perpetually decreasing cost of capital, caused unusually high capital appreciation. We are at a point where inflation expectations are unlikely to decrease much more. The best scenario is for mortgage rates to stay flat; the worst is for them to increase.

Taken all three together, the maximum nominal appreciation I would expect from Vancouver detached housing going forward is around 2.5-3% annually. Condos, due to the fact there is little possibility of densifying further, will likely appreciate at inflation, say, 2%.

Coming full circle, using my newly expected capital appreciation estimates, we can further adjust the cost of capital up by 2.4% and re-calculate “equilibrium” value. Astonishingly the new price drops to $270,000. Note this is too low, mostly because the depreciation number used in the paper is too aggressive. Using a more realistic annual building depreciation of $2500 we can re-calculate “equilibrium” at approximately $400,000. You can make other assumptions – perhaps a lower mortgage rate – and arrive at equilibrium a bit higher, however it will be difficult to justify anything but a significantly reduced outlook for the long-term appreciation of property prices compared to Somerville et al’s estimates.

Edit: Commenters here and in other places in the local RE blogosphere have raised questions about depreciation as a line item in a DCF (discounted cash flows) calculation. While I agree depreciation is not a cash flow, in this case depreciation represents an expected decrease in future cash flows below headline estimates. In terms of the formula's framework, for what it is, depreciation does account for decreased future cash flows but is not explicit enough to really know what Somerville is modelling. Read the comments for an alternate approach.

Also the "densification premium" awarded to detached properties is further reduced when one accounts for capital costs associated with making land more productive. More bad news.