## Monday, November 03, 2008

### 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.

buff_butler said...

(slow clap)... awsome article :P

patriotz said...

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.

Note also that a significant amount of existing commercial and industrial land is being reused for residential, which further reduces the densification potential for existing residential.

Change of use for such land is also more politically feasible, which pushes the densification of existing residential farther into the future and reduces present value.

Panda said...

This is a wonderful article. I particularly enjoyed the part where you explain the premium for densification in such simple terms. Thanks.

M- said...

Great explanation of Somerville's report. I think the most dishonest thing in the report was failing to run it iteratively, until the home price value converged or stabilized; the single-run result is hugely misleading.

jesse said...

I do believe Somerville is genuinely bearish on real estate -- the fact he is using a form of fundamental analysis is a good start. I opine he will be surprised by how much prices will undershoot his estimates. I recall him being quoted that

"Markets tend to overreact in the other direction,"

apparently in direct rebuttal to questions of why price estimates have fallen below his original estimates. If markets were to "overreact" past my estimates there would be absolutely screaming deals though it's worth noting it is not explicitly required that markets undershoot.

patriotz said...

I do believe Somerville is genuinely bearish on real estate

He was bullish until prices started falling. He's about as useful as a weather forecaster who always predicts the same weather tomorrow as today.

VancouverGuy said...

Depreciation should not be taken into account in a cashflow calculation at all. Instead of using a perpetuity calculation, you should just shut the calculation off at some point.

You can take into account growth in rent instead of growth in housing prices to be more accurate. You can then take into account the actual differential between equity and debt costs of capital to be even more accurate.

Regardless, I agree with your conclusion that Tsur was way off.

VancouverGuy said...

I am going to be at UBC tomorrow presenting to a finance class. I am going to throw in a slide on the local markets and tear that paper to shreds in the process.