Betterment taxes, capital gains and benefit cost ratios
Andrew Coleman
a,b
, Arthur Grimes
a,c,
⁎
a
Motu Economic and Public Policy Research, New Zealand
b
University of Otago, New Zealand
c
University of Waikato, New Zealand
abstractarticle info
Article history:
Received 8 October 2009
Received in revised form 13 August 2010
Accepted 20 August 2010
Available online 22 September 2010
JEL classification:
H21
H22
R51
Keywords:
Betterment tax
Land tax
Capital gains tax
‘Betterment’ taxes can be used to fund infrastructure investments. We relate betterment taxes to the benefit:
cost ratio, deriving conditions under which a project can be funded by such taxes, and relate betterment
taxes also to a capital gains tax.
© 2010 Elsevier B.V. All rights reserved.
1. Introduction
The funding mechanism for local infrastructure and amenity
investments can be influential in determining (a) whether a project is
undertaken, and (b) the incidence of the project costs. This note
examines the circumstances in which ‘betterment’ taxes can fully
fund such investments. We relate the use of two types of betterment
tax to the project's benefit: cost ratio (BCR) and derive conditions
under which a project can be fully funded by such taxes. We also
demonstrate how a betterment tax is related to a capital gains tax.
We define a betterment tax as one that taxes land value on an
ongoing basis in order to capture the uplift in land values that may occur
following a public infrastructure investment. With a betterment tax, a
government body funds the investment through debt that is subse-
quently serviced and repaid through the betterment tax revenues. Some
economies raise a material proportion of tax revenues by way of land
and/or property taxes (Dye and England, 2009; Franzsen, 2009). Some
have specifically employed betterment taxes; for instance, New Zealand
local authorities had the legal ability to impose a 50 percent betterment
tax between 1926 and 1953 (Harris, 2005).
Mill (1865, Book 5, Chapter 2, §5) advocated a land tax levied on
the increment to land values above those at a fixed point in time. He
argued that that the increment in land values was due to general
societal influences and this increment should form the basis for
government revenues required for the upkeep of society. Modern
spatial economics analyses of the impacts of new infrastructure
investments on land values embody a related analytical approach
(Roback, 1982). The observation that land values impound the value
of location-specific factors (Ricardo, 1817) implies that a new
infrastructure or amenity investment that is valued locally will be
reflected in a step change in local land prices. In this situation, a tax
applied to local land values, and especially to changes in those values
consequent on an infrastructure investment, may be considered as a
method for funding that investment.
2. Taxation of betterment
Local landowners experience a real capital gain when a specific
infrastructure investment raises local land values. A related situation
occurs where land is rezoned, for instance from agricultural to
residential use (Grimes and Liang, 2009). The rise in land values
through betterment can be captured by the infrastructure investor if
that investor owns the land serviced by the new investment. Otherwise
(in the absence of taxation or development levies) it accrues to private
landowners who may not have funded the investment. In this latter
situation, at least some portion of betterment can be captured by
government if the rise in land values is taxed.
For analytical purposes, we concentrate here solely on the taxation
of real capital gains due to betterment (i.e. nominal gains due to
generalised inflation are exempt). We consider two alternatives. First,
Economics Letters 109 (2010) 54–56
⁎ Corresponding author. PO Box 24390 Wellington 6142, New Zealand. Tel.: +64
49394250; fax: + 64 49394251.
0165-1765/$ – see front matter © 2010 Elsevier B.V. All rights reserved.
doi:10.1016/j.econlet.2010.08.012
Contents lists available at ScienceDirect
Economics Letters
journal homepage: www.elsevier.com/locate/ecolet
we consider the effectiveness of a general real land tax in taxing
betterment values. Second, we consider the effectiveness of an
incremental real land tax for the same purpose, reflecting Mill's
proposed tax. We relate this latter form to a direct capital gains tax.
As a general case, consider the purchase price of a plot of land at
the end of year i= 0 that is expected to pay the owner an annual after-
income-tax rental stream of Y
i
=Y in years i =1,…,∞. Rents may
reflect the imputed value of the property to the owner–occupier, or
may be the explicit contractual amount paid by a tenant to a landlord.
Let ‘r’ be the real interest rate, ‘t’ the land tax rate, and ‘k’ other net
costs or benefits associated with the land (expressed as a ratio of the
land value); r, and k are treated as known, fixed rates. When the tax
rate is t, the value of the property at the end of year i is denoted V
i
t
.
Extending the analysis of Oates and Schwab (2009), the purchase
price of the property at the end of year 0 is given by the discounted
value of future rents less tax and other payments:
V
t
0
= ∑
∞
i =1
Y
1+r
ðÞ
i
−∑
∞
i =1
kV
t
0
1+r
ðÞ
i
−∑
∞
i =1
tV
t
0
1+r
ðÞ
i
ð1Þ
From the solution of a discounted infinite sum:
V
t
0
=
Y
r
−
kV
t
0
r
−
tV
t
0
r
ð2Þ
Equating terms and solving for V
0
t
gives the purchase price:
V
t
0
=
Y
r + k + t
ð3Þ
For the first betterment tax alternative, assume that initially no land
tax is in place. The initial value of the plot is therefore: V
0
0
=Y/(r+k). A
public infrastructure project is then built that raises the annual real
rental stream to Y⁎ and an annual land tax at rate t is levied; the new plot
value becomes: V
⁎
0
=Y⁎ / (r+k+t). If the tax rate were set to capture all
value uplift from the project (so that V
⁎
0
=V
0
0
), it would be given by:
t =
r + kðÞY⁎−YðÞ
Y
ð4Þ
For example, if r = 0.05, k= 0.00, and (Y⁎ −Y) / Y=0.1, the
required tax rate is t = 0.005.
The present discounted value of the tax flow equals tV
⁎
0
/r. One
policy aim may be to set this value equal to the per property project
cost, P. The resulting tax rate becomes:
t =
rr+ kðÞ
Y⁎−rP
ð5Þ
To interpret Eq. (5), note that rP is the per property interest servicing
cost of the project. Consider a project with P=$10,000, r=0.05,
k=0.00 and let Y⁎ = $11,000 (=1.1×Y, where Y=$10,000); hence
rP=$500 and the BCR, defined as (Y*− Y)/rP, equals 2. The resulting
t≈0.0024. If, instead, P =$20,000 (hence BCR = 1), the required
t= 0.005, consistent with the full value uplift case. Generalising, the
project can be financed through a flat land tax and still leave some value
uplift for local landowners provided BCRN 1; if BCRb 1, full financing
through a flat land tax will lead to a decline in property values.
Now consider the second alternative in which only real incremen-
tal land value is taxed (at rate t). The value of a plot of land that
experiences an unexpected rise in land rents from Y to Y⁎ due to a new
infrastructure investment becomes:
V
0
⁎
=
Y
r + k
+
Y⁎−Y
r + k + t
ð6Þ
The first term on the right hand side of Eq. (6) is the land value
prior to the rise in rents which remains unaffected by the incremental
land tax. The second term reflects the rise in land value consequent on
the project; the tax is levied on this increment. Thus the present
discounted value of tax revenue is given by [t(Y⁎ −Y)] /[r(r+k + t)].
The tax rate required to finance a project with per property cost, P,
becomes:
t =
r + k
Y⁎−YðÞ= rP½−1
ð7Þ
Eq. (7) establishes that an incremental (real) land tax can fully
finance a project if and only if the BCRN 1. Even then the tax rate may
be ‘high.’ For instance, if we assume the same values for r, k, Y and Y⁎
as before but with P = $19,000 (BCR≈ 1.053), the result is t= 0.95. A
tax rate of less than unity requires BCRN 1 + r+k. If the BCR is
favourable, a more moderate incremental land tax rate can result; for
instance, with P = $5000 (BCR =4), t≈ 0.017. Realistically, therefore,
full financing of a project through an incremental (real) land tax may
be restricted to projects with high BCRs.
A real incremental land tax can be conceived as a replacement for a
tax on real capital gains on land. The latter option taxes the one-off
annual capital gain at rate c; by contrast, an incremental land tax
spreads the tax over time. We can equate the present discounted
revenue from an incremental land tax with the revenue from a capital
gains tax, as follows:
t =
r + kðÞc
1−cðÞ
ð8Þ
For instance (with r= 0.05 and k =0.00), instead of a capital gains
tax of 30%, an incremental land tax could be substituted with a rate of
2.14% p.a. Each approach would result in 30% of the real capital gain
being taxed (in present discounted value terms), with the same
present discounted revenues accruing to government. Cash-flows
from an incremental land value tax would differ from a capital gains
tax since the former would be spread over the indefinite future
whereas a ‘pure’ capital gains tax is due immediately (within one
year) of the capital gain being apparent. In many jurisdictions, cash-
flow concerns with regard to the taxpayer means that the capital gain
is only payable on realisation of the property, which creates lock-in
effects and other complications. These issues are much less problem-
atic in the case of an incremental land tax.
3. Conclusions
Provided that independent land valuations are performed on all
properties, a betterment tax can be levied to fund public infrastruc-
ture and amenity investments under certain circumstances. A flat rate
land tax is one possibility, but that option taxes pre-investment land
values unrelated to the specific investment. An alternative is an
incremental land tax that taxes only the uplift in values due to the
new infrastructure or amenity. The full project cost can be recovered
by the latter tax with a tax rate of less than 100% if the project's
BCRN 1 + r+k where r is the cost of capital and k is other costs
associated with ownership of the land (expressed as an annual rate).
Provided this latter condition is met, the project can be fully
financed from the incremental betterment tax while leaving some
value uplift available for local landowners. If a land tax is already in
existence, addition of a special betterment tax has virtually no
additional adm inis trat ive cost; in addition, the ability t o avoid
(or evade) the tax is virtually non-existent since the land is valued
by an independent agency and is available as collateral in cases of non-
payment of tax. Furthermore, use of a land tax has favourable
efficiency properties relative to other taxation or funding options.
A capital gains tax is another option an d we de monstrate the
55A. Coleman, A. Grimes / Economics Letters 109 (2010) 54–56
equivalence of the two taxes in terms of raising revenues. One
advantage of the land tax over a capital gains tax for the landowner is
that cash outflows are spread over time unlike a capital gains tax that
may cause cash-flow problems since the latter involves a lump-sum
tax payment.
Acknowledgement
The authors thank the New Zealand Treasury and Foundation for
Research, Science and Technology (programme MOTU0601 Infra-
structure) for the funding. The views expressed are solely those of the
authors.
References
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56 A. Coleman, A. Grimes / Economics Letters 109 (2010) 54–56
