Deferring Land Tax until Death

Dr Colin Rose

I. Introduction

• First, it allows one to assess the impact of the residential land tax in a single quantifiable figure under any scenario. This makes it an ideal tool for evaluating the effect of policy (i.e. what happens if we change the tax rate, or the threshold, or the inflation rate, or if real interest rates rise, or ...).

• Second, not only does this measure apply to those who do defer their land tax, but it also applies to those who do not (or cannot) defer.
  
  • for those who do defer, the 'death tax' calculation tells us how much they will have to pay at death;
    
  • for those who cannot defer, the 'death tax' calculation provides an estimate of how much land tax they will have paid by the time they die. This is an 'estimate' because the actual cost to those who cannot defer is in fact about 10% larger than the figures shown here.
    [ see footnote 1 ]
    

Example 1:	For land already above the threshold.
Example 2:	For land currently below the threshold.
Example 3:	What happens if the threshold is lowered ?
Example 4:	Bracket creep: what tax will the next generation pay ?

Section III derives the general mathematical solution that is used to answer these questions. A coda follows.

II. Examples

The Carr Government's land tax framework implicitly assumes that land prices grow at the rate of inflation; that is, that land prices do not grow in real terms. Under this special assumption, property currently under the threshold is uneffected by the tax, but property above the threshold will still have to pay. Figure 1 calculates the size of the de facto 'death tax' that will have to be paid by the owners of such property, using the NSW Government's framework:

Figure 1: The 'death tax' on property above the threshold

Figure 1 has three curves: the top curve corresponds to an owner who has T = 40 years to live; 35 years to live for the middle curve; and 30 years to live for the bottom curve. Clearly, the longer one lives in NSW, the higher is the 'death tax'. Consider say the middle curve (the dashed line). If the owner passes away in 35 years time, what proportion of the sale price will be taken by the NSW Government ? From the diagram, we see that for many properties, the 'death tax' will exceed 100%; that is, by the time the property is sold, the tax liability will exceed the sale price.

Historically, property prices do not grow at the rate of inflation; they grow faster. In fact, between 1960 and 1997, the median price of Sydney property grew at a rate of 3.5% p.a. above inflation. Because the land tax threshold is indexed to inflation (and not to property prices), it is inevitable that property that is currently below the ceiling will move above the ceiling and start to incur land tax. Figure 2 calculates the de facto 'death tax' that will have to be paid by the owners of such property.

Figure 2: A 'death tax' on middle Australia

Figure 2 plots the 'death tax' for different land values currently under the threshold (again assuming our home owner is 50 years old). It shows that 'death tax' will have to be paid on all residential property whose current value exceeds $300 000. For instance, consider a piece of land whose current value is $550 000. Upon death, the land is sold, and the State Government will take (or will have taken) 10% of the proceeds. At the upper end, on a $1million block, the government's claim rises to 1/3 of the sale price. Land under $300 000 is unaffected (but see Figure 4).

What would the 'death tax' diagram look like if the threshold was lowered from $1 million to $500 000, or even to $200 000 (as used in Victoria). Figure 3 illustrates the three regimes:

Figure 3: Lowering the threshold

The difference between the regimes is perhaps smaller than one might expect. Of course, the magnitude of the tax increases, but the main difference is the entry point at which one becomes eligible for a 'death tax'. Table 1 summarises:

Table 1

Under the status quo of a $1million threshold, all property currently valued at $300 000 or more will have to pay 'death tax', as defined in section I. If the threshold is lowered to $500 000, then land currently valued between $150 000 and $300 000 is added to the net. Finally, if the threshold is lowered to $200 000, then all property above $60 000 will pay a 'death tax'.

Just as the income tax system is subject to bracket creep over time, so too is the land tax framework, despite the fact that the threshold is indexed to inflation. Figure 4 illustrates this phenomenon under the assumption that historical growth in land prices continues:

Figure 4: Bracket creep: what will the next generation pay ?

Figure 4 has two curves:
• The bottom curve is identical to Figure 2, and plots the 'death tax' that the present generation of 50 year olds will pay on their property.
• The top curve calculates the 'death tax' the next generation will pay.

III. Formal Analysis

Let today be defined by period 0, and let death be defined by period T > 0. Further, let:

If v₀ denotes the current assessed land value, while c₀ denotes the current ceiling ($1million), the tax liability payable during time t is:

[1] where

Since the Office of State Revenue does not compound interest, the net future value of the tax stream,
F_T, evaluated at the time T of death, can be shown to be:

[2]

For finite T, and
, this sum can be expressed as the following elegant closed-form solution [ see footnote 3 ], so that F_T
= f(v₀, g_v, c₀, g_c, i, h, T) :

[3]

If , the property's land value is currently below the ceiling and so it will not accrue taxes in the first few periods. However, if g_v > g_c , it is only a matter of time until it eventually attracts a tax liability. Let n denote the time period in which the first tax payment will be required. Then the net future value of the tax stream is
f(v_n, g_v, c_n, g_c, i, h, T-n).

Finally, at time T, the future value of the land is:

[4]

It is now a simple matter to compare the tax liability at the time of death [3] with the value of the land [4] at the time of death. This yields the 'death tax' measure.

IV. Coda

• for those who do defer their tax payments, the 'death tax' calculation simply tells us how much they will have to pay at death;
• for those who cannot defer, the 'death tax' calculation provides an estimate of how much land tax they will have paid by the time they die.

• The tax on properties already above the threshold can be remarkably large, often exceeding 100% of the land's value upon sale at death.

• Residential land tax is actually surprisingly broad-based. Indeed, a de facto 'death tax' will have to be paid by all middle-aged people living in NSW, on land currently valued at $300 000 or higher . The younger you are, the greater will be the tax rate you will have to pay.

• Lower thresholds not only increase the magnitude of the tax, but further widen the tax base. For instance, if the threshold is lowered from $1m to $500 000, then properties in the $150 000 to $300 000 range are added to the tax basket.

• Finally, like income tax, land tax is subject to bracket creep. The next generation will pay dramatically higher tax rates than the present generation.

Sydney
19 March 98

About the author:

Colin Rose is director of the Theoretical Research Institute. He holds a PhD in economics. He has published in leading international journals in areas such as economic theory, international finance, and computer algebra systems. His work has been presented at venues such as the Bank of England, the Reserve Bank of Australia, the Federal Reserve, the IMF, Oxford, and the NBER. His first book, Mathematical Statistics with Mathematica, is to be published in 1999 by Springer-Verlag (with Murray Smith).

people have read our land tax papers since 12 Dec '97.