Effects of Real Estate Tax Rate Changes
on Market Values;
and a Method of Computing Economic Rent
Mitchell S. Lurio
[Reprinted from the Henry George News,
September, 1961]
Here is an approach that can be developed easily and accurately by
researchers in this field. The economic rent of a city can be
estimated in a matter of minutes; and by extension, the same formula
will reveal the economic rent of the country. We need such estimates
if we wish to demonstrate that economic rent is sufficient for the
properly limited functions of government. Following is an example
indicating methods and results.
A small apartment house was purchased recently for, say, $150,000,
all cash. (Actually the price paid was $163,000; $18,000 cash, subject
to a first mortgage of $105,000 for 15 years at 6 per cent per annum,
and a second mortgage of $40,000 for 8 years at 6 per cent per annum.
This second mortgage may have a market value of approximately $27,000,
that is, its immediate cash value if offered for sale by the present
holder is $13,000 less than its face value, which is at a discount of
32.5 per cent for 8 years, or a little more than 4 per cent per annum
discount).
The assessed value of this property is $15,000 for the land and
$75,000 for the building, or a total of $90,000. At the same ratio of
building to land, namely 5 to 1, we may use a figure of $25,000 for
the market value of the land and a figure of $125,000 for the market
value of the building, making the total of $150,000.
The total assessed value of $90,000 is 60 per cent of the total
market value of the property. The present tax rate of 5 per cent on
assessed value of $90,000 is equivalent to 60 per cent of 5 per cent
or 3 per cent on the market value of $150,000.
Assume that after all expenses: maintenance, fuel, electricity,
water, insurance, repairs, janitorial services, vacancies, commissions
for getting new tenants, legal and accounting expenses, taxes other
than real estate taxes, and depreciation, there is left, out of the
gross income, the sum of $18,000. This is the amount available for the
real estate tax and the net income to the owner. Since the real estate
tax is 5 per cent of the assessed value of $90,000 or in terms of
market value, 3 per cent of $150,000, which is $4,500, the balance of
$13< 500 is the owner's net income and is equal to 9 per cent of an
investment of $150,000.
Thus we may write that the amount available for real estate tax and
net return to the owner is (.03 + .09) ($125,000 + $25,000) = $18,000.
If the tax rate goes up 12% per cent (from 5 per cent to 62% per
cent) this is equivalent to 60 per cent of 624 per cent or 4 per cent
of the market value. The 62/3 per cent rate is on the assessed value
of $90,000 and produces a tax of $6,000, which is the same as taking 4
per cent of $150,000, the full market value.
After the tax rate increase, assuming other things equal or
unchanged, there is still $18,000 available for real estate tax and
owner's net income. We must deduct 4 per cent of $150,000 or $6,000
from $18,000, leaving $12,000 for the owner. This is 8 per cent per
annum on the investment of $150,000.
Let us assume, from the original actual sale which gave the new owner
a 9 per cent. yield, that 9 per. cent is the rate of return expected
by prospective purchasers. (This figure will change at various times
and places and for different types of tenancies and some good
approximation of it can be made by men in the field.) After the tax
rate increase, the property is no longer worth $150,000, for, at that
price, the purchaser could expect only an 8 per cent yield. Neither
the gross income of the property nor its assessed value, changes
quickly, although as will be seen, changes will come about. On the
basis of a 9 per cent yield, the new market value is $138,462. Proof:
new real estate tax is 4 per cent of $138,462 or $5,538. The total
available for real estate taxes and owner's income is assumed to be
unchanged at $18,000. Deducting $5,538 from $18,000 leaves $12,462.
This is 9 per cent of the new market value of $138,462.
The drop in the market value from $150,000 to $138,462 or $11,538 may
be distributed in any number of ways against the building and against
the land. This is a question in which a prospective purchaser is not
interested. As far as he is concerned, the total value of the property
has fallen to $13&,462 and that is the price he can pay for the
yield he is looking for.
For our purposes, however, it is worthwhile to consider the
consequences if the drop in market value is ascribed to the building
alone, or to the land alone, or distributed between the two. This
distribution would usually be in the same proportions as original
building value to land value, namely, in our example, 5 to 1. On this
basis, the building would be valued at $115,385 and the land at
$23,077, making a total of $138,462. The building drop of $9,615 is
five times the land drop of $1,923, the two together making up the
total drop in market value of $11,538.
Consider the assumption that the entire loss in market value
($11,538) is borne by the site, an assumption based on the fact that
the bricks and mortar of the buildings are exactly the same the day
before as the day after the tax rate increase. On this assumption,
each increment in tax rate further reduces the land value, until it
goes to zero. Calculation shows that at a tax rate equivalent to 5.4
per cent of the market value, the land value becomes exactly zero.
Proof: (.054 + .09) ($125,000) = $18,000 available for real estate tax
and owner's income.
In the case of a new building, this means that a builder, seeking to
put up an identical building on a similar adjacent site cannot afford
to pay more than zero for the land if he expects to earn from the
building a net income of 9 per cent on his investment.
There is a difficult problem when old buildings are considered  the
problem of replacement value, always a thorny one for appraisers.
From one point of view, the old building should be considered as
having the same value before and after the tax rise. On this
assumption, there is a result which appears illogical. In our example,
we ascribed the $11,538 loss to the land, reducing its theoretical
market value to $13,462. But if the same calculation is performed on
an adjoining, identical site, improved with a smaller or a larger
building, the resulting value of the land is different in each case,
being smaller for the larger building site and larger for the smaller
building site.
It can be argued that because the old building is already attached to
the land, its value may vary inversely depending upon the value of the
building upon it.
It can also be pointed out that there must be some ideal ratio of
proper building for a given site that would yield the largest net
income to the owner and that it is upon this ratio that the land value
should be determined. This method gives as a residual the value of the
building.
There is another assumption that can logically be made. That
assumption is that the increased tax on the building (caused by an
increased tax rate, other things being equal) can be passed on to the
tenants and that the increased tax on the land value (caused by the
same increased tax rate) cannot be passed and must be lost by the
owner  that is, his net income is reduced by the increased tax on
the land value only.
On this assumption, additional increments to the tax rate lower the
value of the site but in such a way as to approach but never reach
zero. Then it turns out that regardless of the size of the building in
relation to identical sites, the resulting lowered land values are
identical.
In figures, for our example, the amount available for the real estate
tax and owner's net income is assumed to be increased by the extra tax
on the building alone. If the new rate is 1 per cent higher than the
old rate (based on market value) the gross income of the building is
assumed to increase by .01 ($125,000) or by $1,250. This added on to
the $18,000 previously available gives the new amount available as
$19,250.
The new rate of 4 per cent plus the 9 per cent rate on the owner's
investment applied to the sum of the building and land value is
therefore equal to $19,250. The building value is assumed constant at
$125,000. The land value falls to such a point as to satisfy the
equation. That value is $23,077, for (.04 plus .09) ($125,000 plus
$23,077) is equal to $19,250.
If the same calculation is performed on an identical site, on which
the building is worth $100,000 or $200,000 or any other figure
(assuming sufficient income to make 14 per cent of the total market
value available for taxes and yield to owner), the land value remains
constant at $23,077.
Determination of Economic Rent
More important and of inestimable value in research along these lines
is the following method of determining the economic rent of land. To
go back to our original example: a 3 per cent tax on $150,000 =
$4,500, or the amount paid in real estate taxes. If the selling price
of the site were reduced to zero by reason of an increased tax
thereon, while the tax on the building were removed, the owner should
get 9 per cent of the building value only, or $11,250. Since he was
getting $18,000 as available for tax and owner's income, the
difference $18,000  $1l,250 or $6,750 is the economic rent for the
land.
For if the city collected $6,750 on the land, it would leave to the
owner $11,250 equal only to his expected return of 9 per cent of
$125,000.
For a given property, producing a 9 per cent yield to the owner, this
method of calculation is apparently independent of building to land
ratio. But if an adjoining property on which there is a $100,000
building also yields 9 per cent to the owner, the lot being also
valued at $25,000, the amount available for taxes and yield is (.03
plus .09) ($100,000 plus $25,000) or $15,000 Deducting 9 per cent of
$100,000 leaves $6,000 as the rental value of the land, as compared
with $6,750 for an identical lot in the previous example.
The correct rental value can be defined as the maximum rental figure
as determined by the best building on a given site which is the one
that yields the maximum net income.
It is interesting that if total loss is ascribed to the lot, the
market value of building being unchanged, and the economic rent is
sought after a change in tax rate, we get the same economic rent for
the site and the same yield of 9 per cent on the same building.
This is merely an introduction to methods that may he developed by
those engaged in real estate studies.
