Present Value of shelter -- part 2

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Here is part two of a post that aims to evaluate housing as an investment ... where owners are expecting to earn an annual return (rent) as well as capital gains due to appreciating property values upon final sale.

in part 1 - I laid the groundwork as to the basic premise which would be used to evaluate the prices of real-estate.

recall -- that basically, the most a rational investor would be willing to pay for an investment is the present value of the income stream of the investment, with all future income being discounted by a corresponding equivalently risked market return. for a re-hash as to what this looks like, part 1 can be found here.

In this, we have to lay some basic assumptions out first.

• housing in Victoria, BC (the CRD) has had an average growth rate of 5.07% per year from 2005 to 2016 based on the Canadian Real Estate Associations Housing Price Index (CREA HPI) which can be found here.
• (For those familiar with the rule of 72 -- this estimates that if this continues, the price of housing will double approximately every 14.2 years.
• Rent prices between 2015 and 2016 in the CRD increased on average by 5.77% although this does differ from a min of 4.9% for a 1 bedroom and up to a 6.8% increase for a 3+ bedroom, as determined by CMHC which can be found here. 
• Recognizing that between 2015 and 2016 there was an influx of people into the CRD pushing up prices, coupled with not being able to have access to a longer time frame of rental prices, I have arbitrarily adjusted the annual growth rate of rental prices down to 4.5% from 5.77% as I feel this 5.77% is not representative of normal rental activity.
• Second, BC tenancy act allows landlords to increase rent at 2% above inflation ... given a targeted inflation rate of 2%, this further seems to fit this assumption
• For reference: Expected return over the last 61 years from an aggressive to a conservative portfolio is as follows: data obtained from here.
• Aggressive portfolio (80% equity, 20% bond): 10.9% per year.
• Moderate portfolio (60% equity, 40% bond): 9.8% per year.
• Conservative portfolio (20% equity, 80% bond): 8.11% per year.

Recall we want to compare our payments from this investment in real-estate versus an equivalently risked investment -- Based on a preliminary search, the consensus seems to be that real-estate is less risky than equities, but riskier than bonds (due to potential maintenance problems, non-payment, periods of vacancy etc.). Thus perhaps around 9% similar to our Moderate portfolio may be good grounds to compare real-estate to (we will, in fact, calculate for an array of interest rates).

Presently we have the following price and rental situation in greater Victoria (CRD):

If we (as investors) were to assume that our annual house price was to continue to increase at 5.07% per year and that our annualized rental payment could be expected in to increase at 4% per year into the for seeable future, then we should expect the following present values if we hold on to the property for 30 years, collecting rent, and then willing to sell it for its market price.

Where if we sum up the present value of the future income streams over 30 years (discounting by the respective interest rates) we see that at the current market price -- If the interest rate is 7% then all real-estate regardless of unit type is a great buy! alternatively, as we move up to an 8% interest rate, one bedroom and three plus bedroom units are over priced. Finally, as we move up to a 9% interest rate, all units are over priced.  

Now perhaps investors are not actually looking to purchase real estate to invest in for a 30 year time period, so perhaps that is too long to consider. Thus, let's graphically look at the present value of each unit based off of its income streams over a 0,1,5,10,15,20,25 and 30 year time period. keep in mind that over a time period of zero, we have the current price of the unit. 

As this would be a bit too cumbersome to display in tables, we have graphs:

Updated: As was kindly pointed out to me, the previous graphs in this post were very misleading - the nature of a line graph seemed to show how the price of real-estate was expected to change over the next 30 years when this was not the case. the graph instead is demonstrating what the present value of real-estate is based on the period of time you hold it for as an investment.

At a 7% prevailing interest rate, all unit types are currently for sale for cheaper than their present value for all holding period.

As we move to an 8% prevailing rate, three or more bedrooms and one bedroom units initially have higher present values (for short holding periods) but quickly decrease.

 Finally, as we look at a 9% prevailing rate, we see rapidly falling present values for all holding periods greater than 1 year -- indicating that all unit types would be overpriced relative to their present value of future income.

As stated at the beginning, real estate as a risk class is considered less risky than equities, but riskier than bonds -- I arbitrarily assumed a rate of 9% based off of historical portfolio returns. It shouldn't however, be a surprise to learn that in recent years we have been in a lower interest rate environment, thus it is under this rationale that I have included a range of prevailing rates. To finish off, for reference, I will include one lower rate of 6% and the corresponding present values.

The takeaway? depending on our view of the prevailing interest rate on a similarly risky investment, current real-estate in the CRD could continue to increase, or could already be over-priced.

Of course -- all of this is extremely sensitive to our assumptions - especially the growth of real-estate and rental prices into the future ... if either of these begins to slow, then we have a very different story!

What are your thoughts -- should real estate be viewed as an investment? or strictly as a means to provide shelter? Feel free to comment below.

Thank you to Francis and Joel for your comments leading to this revision!