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Valuation of Residential Property: Why the Property Market is Overvalued

		I want to live in Auckland. At least I think I do. \
	I want to live in Auckland. I might try Otahu[hu]. \
					- Kevin Black

People buy houses. There is an opportunity cost to buying houses, and that
is renting them. However, most people chose to buy houses, in the hope of
capital gain, and as a proxy for some form of super fund. This paper, a
corollary to the hugely successful Valuing Growth Assets, looks at houses
as growth assets and attempts to value them. In a particular case we see
that housing prices are vastly overpriced. While the housing market is the
housing market, determined by supply and demand, this price may not fairly
reflect the opportunity cost of investments in other areas. Hence the wise
investor would seek to rent, until the housing bubble burst.

Initial Considerations

In [1], we looked at the Benjamin Graham model for valuing growth assets,
viz., assets with the possibility of capital gain. This equation is:
						Market Price for house
		Price per earnings ratio	 =
-----------------------------------------------
					    	     Rental Income

					= 8.5 + 2 times Rental Growth %

We modify this equation to bring it more into line with value valuations
for Rental Growth =0. LHS;

					=1/ (10 year bond rate + 1%) + 2 x Rental Growth %

That is, the risk free rate for owning a long term (10 year asset) is
simply the PE ratio of bonds with an extra percentage point added to
indicate that property is more risky than NZ government debt (we would add
on 2% for considerations of shares, in line with the long term performance
of the US asset markets over the last fifty years).Now this is 	

					= 11.5 + 2 x Rental Growth

Rental Growth

Great, but what is the rental growth for a given property ? The market will
decide, surely, on the basis of what tenants, and all homeowners are
tenants as a result of the opportunity cost of potentially renting, rather
than owning their house. This is true, but I am valuing the house as a
result of long term asset appreciation, rather than comparing, say, this
year with last year. Note that I am making an assumption here. I am
assuming that it is Rental Growth which drives asset growth over the long
term. Effectively this means that, in the long term, house prices walk in
lockstep with rentals, i.e.:

		house prices		house prices
		-----------------  	  = 	-----------------
		house rentals		house rentals
			       now			       ten years time

Now you may ask, why do I do this ? The reason is that I am assuming that,
in the long term, the housing market is in equilibrium. I cannot say
anything about house rentals as a proportion of house prices in the future
apart from the idea that, if they were more, people would buy property, and
if they were less, they would sell property, to lock in the higher returns
available in the future.
So, my value of rental growth I plug into the Benjamin Graham equation is
the long run growth in house rentals for the here and now, not some
question of average asset increases over the last five years (which are of
the order of 15%). One of the reasons for this assumption is that 15%
increases in asset prices cannot happen "forever" without corresponding 15%
increases in rentals "forever", otherwise the value of the house divided by
the rental would tend to zero. Landlords make money out of capital
appreciation, but they do rely to some extent on the ongoing rental income
stream which is growing (but not, at say 15%).

The Lifecycle Hypothesis

How can we measure this rental growth. It will vary from area to area,
depending on the market; what supply and demand are like for rental
accommodation. This is true, but this may also fluctuate wildly, and we are
really interested in the growth in rentals for the long term. What can we
say ?
One of the things that we can say is that we do not want rentals as a
proportion of income to wildly increase. i.e.
	
		rental outgoings
		------------------------ to approach one.
		         wages

This would happen for tenants who spent all of their money on rent. We also
don't want

		rental outgoings
		---------------------- to approach zero.
		        wages	

We're going to make an equilibrium assumption, and assume that, over one's
working life, this ratio is constant. Richer people buy more expensive
houses, and poorer ones cheaper ones in less gaudy locations, true, but, on
average, the population has a good idea of what proportion of their income,
over their entire life, they want to spend on housing. Admittedly, this
lifecycle hypothesis is open to attack. Keynesians, for example, would
argue that one might do things like live in a house forever, and that this
ratio is really only dependent on the choice somewhere near the start of
work. However, we assume that the housing market is an efficient one, and
even if the house is never sold until it hits the estate, the potential to
sell is always there, and so the ratio is determined by rational
expectations over the entire working life.
Making this simplifying assumption therefore, we see that:

		rate of growth in rentals	=	rate of growth in wages

So, for the entire housing stock over the entire country (one critique of
this is that it is dependent on the number of people entering or leaving
the workforce: we match dwellings with wage/salary earners using the
Pigeonhole principle), we see that:

		rate of growth in rentals 	= 	nominal wage growth

We have various figures for the nominal wage/salary growth for the country
over the last five years, and they have been of the order of 0-2%. However,
we will actually assume, as an equilibrium assumption, that:

		rate of growth in rentals	=	rate of inflation + real GDP growth

Over the long run, the percentage of wages as a proportion of the nominal
GDP will remain constant as an equilibrium  assumption. Various people have
various different prescriptions for what this should be, dependent on how
we want to reward labour as compared to capital, but, over time, this
should remain constant, else there will be wage inflation/deflation leading
to price inflation/poverty slash inequity if this goes on forever.

I will make the bold assumption that, over the next ten years, real GDP
growth will average at 3.5%. This is because the US economy, vastly less
efficient than our own, is capable of growing at circa 2.5% by my
estimates. Even though I have made a number of simplifying assumptions,
this is probably the one most open to attack. I will also assume that, by
the Coalition's estimates, the average for inflation is 1.5% pa for the
next ten years.

So: 		rate of growth in rentals	= 	5%

Note that this is reasonably in line with the current nominal wage increase
over the last year of 4.5%, corresponding well with the nominal GDP growth
of 4.9%, so for this year, the approximation is a good one.
This however will vary from housing market to housing market, because this
figure will vary dependent on the wage growth of the people concerned. Some
people live in poor neighborhoods, and even though they might be rich
themselves, their rental growth is largely determined by that of their
neighbors, and in the current environment, poor people have less chance of
high wage increases than rich people. While we will look at this later, I
will not necessarily relax this assumption for any given housing market,
where we may estimate the nominal wage growth directly, but I will point
out that this cannot go on forever, or else there will be a revolution;
democrats critique "dollar-votes" with "people-votes".

Plugging it in

So, PE ratio for housing = 11.5 + 2 x 5 = 21.5

As a rough, rule of thumb estimate we could round this to twenty. This
would tell us that we expect the house price to be one thousand times the
weekly rental value.

The average house price in New Zealand is $149,000. Our estimate is that
the PE is 21.5 (you'd be pretty lucky to get this with shares). The rental
income for a year is

	 ~ (1 x 0.05+2 x 0.3 + 4.4 x 0.45)/ 0.75  	x 	$39 x 52= 3.5 x $2028
		^^^^^^^^^^^^				^^^^^^^^^^^
	average number of occupants per house		rental income

	= 3.5 x 2028 = $7098 average rental per house pa

This gives a housing valuation of 21.5 x $7098 = $152,600. This is not much
greater than the average house price of $149,000. However, it does rely on
people "getting a good deal", and while all of us like to get a good deal,
there are not many feminist law lecturers going around. I am notoriously
bad at buying good assets.

This may be good value, but does it make sense ?

Lots of people say that you can earn big money while you sleep because of
the implied 12% asset growth of the price of houses. This may be true, but
remember there are those mortgage payments to pay off.

	12% gain  - 10% interest over the cycle is 2% gain a year or about $5000

While this is better than a kick in the pants, remember your cashflows are
negative, viz.:

	4.6% = 1/21.5 as a percent  minus 10% is negative 5.4% or some $13,000

While it is true that it has been suggested to me that I should cover my
friends mortgage payments when they were away in Minnesota, it is also true
that I laughed when I put the phone down. I will not pay $220 a week per
head for a flat ! You will only get this capital gain on retirement.

Lets apply our above estimate. Using the Gordon Growth Model [1], we see
that

	RRR	=	rental income %	+     growth in rental %
		=	       4.6%		+	5%
		=	9.6%

Hence, to merely break even, mortgage interest rates have to be less than
9.6% over the cycle for you to make money. Else there is negative
opportunity cost to owning the house; you should be renting. Mortgage
interest rates will only decrease to these levels as people learn to buy
other growth assets and diversify away from housing. Demand for borrowing
will decrease; the spreads banks are willing to lend at are more
competitive; money is lent into other, more productive (houses do not
"make" anything) areas of the economy. So, even though houses are fairly
priced, you do not make any money from owning them. You make money from
paying them off. However the RRR of housing compares poorly with say that
of a diversified bundle of international shares, for which returns of
14-15% are actuarially possible. On the other hand, it compares favorably
with bonds; this should come as no surprise, as bonds are less risky than
property.

So, at the moment, you should rent, and invest money in other assets with
larger rates of return than housing, with a little money aside in bonds and
cash for emergencies.

Note

	In any given housing market, as opposed to the New Zealand average market,
there may be inefficiencies. Prices for houses may be sticky ("my neighbor
sold his house for $500,000 and now you say that, because growth has
leveled off, I won't get nearly that much ? Bugger you !"). However, much
more likely is the fallacy of composition idea. What happens when the local
freezing works/J C Penny cataloguer closes down laying off half the town ?
They will all have to move. What has effectively happened is that the real
wage has dropped dramatically. All this means however is that past
performance does not guarantee future returns. Your house may have value
more than or less than what it is sold at; this is why we consider any
asset to be "mispriced" if it's valuation using some rational model is much
lower than its market price.

Considerations of a particular housing market

	I know quite a lot about the student flat market in Mt. Eden. Mt. Eden is
well known as the swing seat in FPP elections which will determine whether
National or Labour win the election, and, as Auckland areas go, it is
somewhat diverse, providing an excellent model of the Auckland housing
market as a whole.

I went up and looked at the Realtors locally. The average house price
seemed about $450,000. However, there are two things to be noted:

1.Anecdotaly, the average house is crossing at $350,000
2.The average house requires $100,000 of maintenance to see it through the
next ten years. It should be noted that I have assumed, too, that ongoing
maintenance costs are zero. This should be taken off the rental income.

Hence the houses are effectively priced at circa $450,000.

	The inhabitants of the seat are generally, however, high earnings growth
individuals. My friends estimate that wage growth is of the order of 8%
nominal. This leads to an estimate of 27.5 for the PE ratio of rental to
asset value. This is a Waste Management (Kewl growth share) PE, but a real
estate agent would defend it on the grounds of that wonderful ratcheted 8%
growth in rental pa. Such large possibility for capital gain, as well as a
rather reasonable rental of 3.6%. You may have to put in a lot of cashflow
to defend the mortgage(because the rentals are not large in comparison to
the value of the property) but certainly the rate of return is looking good
at 11.6% >> 9.6%.

This gives us a value of 	27.5 x $100 x 52 x 3.5 = $500,000, as a value,
which compares favorably with the $450g price above.

This seems quite expensive for a house, and the area is somewhat la-de-da,
but it's those high growth in rentals of 8% which are driving this market.
However, I have snack in an assumption which might not be too valid.

The assumption is that people will pay $100 per week on average to live in
Mt. Eden.

This is a very interesting assumption, as last year people were only
prepared to pay $72 per week to live in Mt. Eden. We are seeing rental
increases of the order of 38%. However, people do want to live in Mt. Eden.
They are clearly willing to pay $100 per week, a $28 rent increase this
year, for the privilege. 

Personally I find this unlikely. Demand for housing has taped off as the
flow of white rednecks moving away from Howick closer into the city
decreases with smaller Asian immigrant flows. While the nominal wage is
likely to puck up by 1%, next year, this will affect the multiplier PE
ratio, and not the rent. Grunging out a $72 pw rent and assuming a slightly
greater rate of nominal wage increase, we get:

Value of average house = 29.5 x $72 x 52 x 32.5 = $360,000

So, any attempt to buy a house with $100,000 of maintenance requirements at
last years prices will mean that the house is mis-priced at more than
$260,000. Which is half the advertised price. You are free to buy the house
if you desire, but there are two problems.

1. The rent may not ratchet into the foreseeable future, which is what we
require for such high PE ratios. Basically, any attempt to over-price the
rent will lead to your tenants moving out during the next recession, with
rent decreases required to attract new ones.

2. You are buying a house at 172% of its value. As the only reasonable
assumption, we will assume that in 25 years time, when you pay off the
mortgage completely, the house is fairly priced i.e. value = net sales
price.

This is 2.2% off your required rate of return pa, even though you do intend
holding it for a very long time. 

Hence the Mt. Eden housing market is overpriced dramatically. People may be
prepared to lose another 2.2% of their house value pa, or $11,000 per year,
for a while, but it is unlikely that this will be sustained. Hence house
prices are very likely to fall in the next five years, as at the end of
five years the value will still only be:

				$260,000 x (1+0.08)^5 = $380,000   <<   $450,000
	
or in seven years		$260,000 x (1+0.08)^7 = $445,000    ~    $450,000

In other words, by buying now you are foregoing the opportunity of buying
at any time in the next seven years when the price per rental will probably
be cheaper, AND you are foregoing capital gain for all that time (because
you bought an expensive asset, you are effectively only receiving the
rental income of 3.6% on the property as a gain, because your capital gains
are paying off the surplus to value of the house).

So I would not buy a house in the Mt. Eden area as a money-making
proposition. While it is hard to make money on residential real estate in
general, there is a very good chance of losing a large sum of money in a
forced sale (unemployment, death), and the asset is very poor as an
investment on a time scale of seven years.

Normative Comments in considerations of purchasing houses

Clearly one should buy a house where there exists a large possibility of
capital gain. By Ben Graham, the rental percent will be smaller, so you
have to come up with more cash, but you at least have the chance to make a
capital gain out of leveraged property. Note that it is easy to show that
the function:

	Total gain on property = rental + rental growth = function ( rental growth
 )

is monotonically increasing with respect to rental growth, viz.:

Total gain on property % = 100/(11.5+2 x rental growth) + rental growth %

		d Total Gain on property %			-200
Hence 	-----------------------------------     =
-----------------------------------------     +     1
		         d rental growth %		(11.5 + 2 x rental growth)2

Which is always effectively greater than zero (for very low values of
ratcheted rental growth this is actually negative, but such nominal rates
are at 1.3% or less, below the average rate of inflation estimated, and
assume negative real growth in a particular area for a very long period of
time), meaning the total gain is always increasing as a function of rental
growth. 

But because of our simplifying assumptions that rental growth moves in line
with wage/salary growth over the lifecycle, it is clear (due to the
meritocratic nature of modern society) that such houses will exist in rich
neighborhoods.
However, as we noted, this cannot go on forever. Society moves as a
pendulum, and there is no reason to believe that the poor will not
experience large wage growth compared to the rich at some time in the
future. Hence, at that time, precipitated by ,say, an Alliance government,
or the generation of a capital rich, labour poor society as New Zealand
(and the world) moves into the 21st Century, with large numbers of the
retired, the savvy traveler will look to pick up housing in poorer areas to
take advantage of the increased wage growth. These houses will be very
cheap, having been bludgeoned by decades of poor rental growth, and a large
possibility of capital gain will ensue. We're about ten years too early for
such a hypothesis, in my view, but the wise will be ready for the technical
breakdown in capital growth rates when they occur.
For the trader, the above analysis also indicates the potential for trading
gains on property with the change of government. While under, say, a Labour
government, it is unlikely that the well-off will experience wage growth
less than the poor, the gap will close as aggregate demand is pumped,
generating capital gains in houses in poorer areas as the PE multiplier
increases, and capital losses in richer areas as the large ratchet effects
decrease.

One of the calculations we might like to make is the estimated break even
point for capital losses.

10% 	= rental income + rental growth
			= 100/(11.5+2 x rental growth) + rental growth %

Thus: 	10 x (11.5 + 2 x rental growth) =100 + rental growth x (11.5 + 2 x
rental growth)

		115 + 20 x rental growth = 100 + 11.5 x rental growth + 2 x rental
growth2

		0 = -15 - 8.5 x rental growth +2 x rental growth2

A quadratic, yielding rental growth = 5.6% just to break even.

		 - Paul Taylor
- Famo Triangle Enterprises

Bibliography

1. 	Valuing Growth Assets , paper, informal circulation, Paul Taylor
2. 	The Intelligent Investor, Graham, Benjamin
3. 	Key Statistics, Department of Statistics New Zealand
4. 	Consumer Prices, Department of Statistics New Zealand
5. 	Statistics Yearbook 1995, Department of Statistics New Zealand