Present Value of shelter -- part 1

Here comes another post about the housing market in BC as the news keeps peaking my interest along different avenues of this topic.

This time I began to wonder if maybe the driving demand for housing is not at all for shelter -- but what if the primary consumers of real-estate saw real-estate as an investment. That is, a place to park their capital in order to earn a decent return.

This idea was spurred by a recent article the tyee, an independent online newspaper written by Geoff Dembicki which can be found here.

I'm not sure I fully agree with all the conclusions made in the article, but just the same it made me think. If real-estate is primarily seen as an investment, then we could realistically obtain a price for real-estate based on the expected returns to be had over time.

First, this will be long enough to describe the methodology, the basic concept by which we will attempt to measure the present value of housing. Thus for this post, part 1, I will strictly be discussing one way to determine the price of an investment, while in a follow-up post I will apply this method to the housing market to explore the effects.

The way I normally teach this premise is to introduce the idea of some magic machine that you can buy and put in your house. This machine then regularly creates money, such that it generates $1000 a year. Now this machine is only capable of doing this for two years, then runs out of its magic. Despite the loss of the magic, the machine is still worth $5,000 for the scrap metals and parts - thus it can still be sold after it stops producing your money.

Based off of this -- I ask, "What is the absolute most you are willing to pay for this machine?" typically the answer is $7000 ($1000 from each year and the $5000 you sell the machine for) The rationale being that if you paid $7000 for this machine, you neither made or lost money -- thus it would be the most you would be willing to pay.

Well, the problem with this answer is - If I offered $7000 today or $7000 in 2 years - which would you take? Most rational individuals would take the $7000 today because they to a degree discount the future.

Alternatively, they know that even if they have no need for the money today, but might in 2 years time, if they take the $7000 today and invest it at a market rate of return they will have more than $7000 in two years.

In this same way, the $1000 we earn from the machine at the end of year 1 is less than $1000 today, and the $5000 we sell the machine for at the end of the two years is less than $5000 today. Thus we need to discount these values based on the market interest rate.

Thus we say the present value (maximum we are willing to pay) for this machine would be equal to:

Thus in each year, we discount the payment (and the final sale price) by the equivalent interest rate we could have earned, had we instead bought an equivalent risk-adjusted item in the market.

Thus if we assume a similar case would have held an interest rate of 5% we have the following maximum willingness to pay for this magic machine:

Thus the absolute most you would be willing to pay for this machine is $6394.56 as this is the amount that if you had today, would yield $7000 in over 2 years time at the given interest rate.

In this sense - If the current price of this machine is anything less than $6394.56 then you buy this machine without hesitation because it will be making some positive amount of money for you.

That is, to put it a different way -- $7000 in two years is worth $6394.56 to you today ... thus if you could pay $6200 in order to get this machine, you have instantly made $194.56.

In a follow up post I will take this basic premise an apply it to the real-estate market.