Anderson, PUBLIC FINANCE
Chapter 16
End-of-chapter problems with solutions
1. For each of the following pieces of property, explain whether the property is real or personal.
a. A personal computer.
b. A mainframe computer.
c. Computer network wiring in the walls and ceiling of a building.
d. The office building for a computer marketing firm.
Answer:
a. Personal property
b. Personal property
c. Real property
d. Real property
2. For each of the following properties, explain which method of valuation is most likely to be
used and why (based on data availability):
a. A McDonalds franchise store in suburban Washington, D.C.
b. A cornfield somewhere in the middle of Iowa.
d. A General Motors assembly plant in Flint, Michigan.
d. The lavish home of Bill Gates in suburban Seattle.
Answer:
a. Market comparison approach, since there is an active real estate market for such
commercial properties and there is not likely to be net income available to use the
income capitalization approach.
b. Market comparison approach.
c. Cost approach, since there is no active real estate market for such properties and there
is not likely to be net income available to use the income capitalization approach.
d. Cost approach, since the property is unique ruling out the market comparison
approach and it is not rental property for which we have net income ruling out the
income capitalization approach.
3. Suppose that a property is assessed at AV=$120,000 for tax purposes while its market value is
MV=$150,000. The nominal property tax rate is tn=0.02.
a. Compute the effective tax rate te.
b. Explain the difference between the nominal and effective tax rates.
c. Suppose that a reassessment occurs that raises the assessed value to AV=$130,000.
Explain the effect of the reassessment on the effective tax rate.
Answer:
a. te=tnr, hence te=(120/150)(0.02)=(0.8)(0.02)=0.016, or 1.6%.
b. The effective rate is less than the nominal rate because the assessment ratio r is less
than one.
c. The effective rate of tax rises due to the increase in the assessment and hence an
increase in the assessment ratio. te=tnr, hence te=(130/150)(0.02)=0.0173, or
1.73%.
4. Suppose that property can be considered a perpetuity, generating a perpetual income stream
Ri each year forever. Assume that the constant discount rate is r. In the case of a perpetuity, the
value of the property is simply V=Ri/r.
a. Assume that Ri = $4,000 and r = 0.05. Compute the value of the property.
b. Assume that Ri = $4,000 and r = 0.06. Compute the value of the property. Explain the
effect of a higher discount rate on the value of the property.
c. Assume that Ri = $5,000 and r = 0.06. Compute the value of the property. Explain the
effect of a higher net income stream on the value of the property.
d. Assume that Ri = $5,000 and r = 0.06. Assume further that there is a property tax
Ti=$1,000 per year and public service provision value of Si=$800 per year. Compute the
value of the property. Explain the effects of the property tax and public services on the
value of the property.
Answer:
a. V = 4,000/0.05 = 80,000.
b. V = 4,000/0.06 = 66,667. A higher discount rate reduces the value of the property.
c. V = 5,000/0.06 = 83,333. Higher net income increases the value of the property.
d. V = 5,000/0.06 - 1,000/0.06 + 800/0.06 = 4,800/0/06 = 80,000. Property taxes are
capitalized negatively and services are capitalized positively.
5. Most states permit assessments for agricultural land to be based on the value of the land in its
agricultural use, ignoring potential developed uses for the land.
a. Using a graph like that in Figure 16.1, explain the difference between agricultural use
value and market value for agricultural land.
b. Explain the foregone revenue to local government units due to use-value assessment.
Answer:
a. Market value reflects the value of land in its highest and best use, while agricultural usevalue reflects the value of land solely in its agricultural use (ignoring other potential
uses). Figure 16.1 illustrates a divergence between the market value of land (the blue
line) and the agricultural use-value of land (the horizontal agricultural land value line).
Notice that the market value declines with distance from the CBD, so there is a large
difference between the two measures downtown, but virtually no difference at great
distance from the edge of the city.
b. If a preferential assessment is provided to agricultural land owners, valuing their land in
its agricultural use-value rather than in its market value, local government units receive
less property tax revenue. The vertical distance between market value of land (the blue
line) and the agricultural use-value of land (the horizontal agricultural land value line) in
Figure 16.1 is a measure of the reduction in the tax base. The amount of revenue lost at
any given distance from the CBD is the tax rate multiplied by that vertical distance for
each property in the jurisdiction.
6. In 1992 the State of Nebraska changed property tax law in a way that lowered the rate of
taxation on capital in the non-residential sector of the economy while the rate of applied
on residential capital was unchanged. (This policy change was known as Amendment
One.)
a. Analyze the effects of such a policy change in the context of a two-sector general
equilibrium graphical model and explain the capital flows that result and the
incidence of the tax reduction.
b. Explain who benefits from the reduction in capital taxation of non-residential capital.
Answer: Set up two demand and supply diagrams for capital--one for the nonresidential sector and another for the residential sector. Show the initial rate of
return to capital equal in the two sectors. Amendment One reduces the rate of tax
on non-residential capital. Show this with an upward shift in the demand curve in
the non-residential capital diagram. The effect is a higher rate of return to capital
and an increase in the equilibrium quantity. There is an implication for the
residential sector as well. Shift the supply curve leftward, reflecting capital flight
out of this sector (equal to the capital that migrates into the non-residential
sector). The effect is a higher equilibrium rate of return to residential capital and
a smaller equilibrium quantity. Capital flees the residential sector and goes into
the non-residential sector. The rate of return to capital rises everywhere,
conferring benefits on all capital owners, not just those in the non-residential
sector.
7. Suppose that a city-wide property reassessment has just been conducted. The last
comprehensive reassessment occurred thirty years ago. The effect of the recent
reassessment was to raise the city-wide assessment ratio from 0.3 to 0.9.
a. Explain the impact of such an increase in the assessment ratio on the effective rate
of taxation.
b. Won’t the tax rates simply be adjusted by the local government units to generate
the same revenue?
c. What equity issues arise in this situation? Explain.
d. What difference does it make that school aid is distributed to districts partly on
the basis of property wealth per pupil? Explain.
Answer:
a. The increase in the assessment ratio may increase the effective rate of taxation,
but only if the local government units do not reduce their nominal rates of
taxation proportionately. It is possible for local government units to collect the
same revenue at lower tax rates, given the higher assessment ratio.
b. The local tax rates may well be adjusted downward proportionately, but there
is not assurance that this will occur.
c. The city-wide reassessment should increase the equity of the property tax,
making sure that long-time homeowners are treated equally with newer
homeowners. Since the last comprehensive reassessment was thirty years ago, it
is certainly the case that homeowners who have lived in the city for a long time
have been under-assessed relative to newer homeowners who have purchased
homes in recent years and whose assessments are undoubtedly closer to market
value.
d. The city-wide reassessment will make all school districts in the city appear to
have greater property value wealth per pupil and therefore may result in reduced
state aid (usually distributed in part based on property value per pupil).
8. The Clemente family lives in Wasatch County, while the Law family lives on
adjacent land in San Pedro County. The parcels of land the families occupy are both
in the Murtaugh School District and happen to have identical market values of
$500,000. The property tax rate for the school district is 2% of assessed value.
a. Identify the equity issue regarding these land parcels if the Wasatch County
assessor assess land at 100% of market value, while the San Pedro County
assessor assess land at 80% of market value.
b. Calculate the property tax paid by each family if the equity issue is not addressed
and if it is addressed.
Answer:
a. The equity issue is equalization. If the assessed values of the land in the two
counties is not equalized, residents of Wasatch County such as the
Clementes will pay more taxes per dollar of market value than will
residents of San Pedro County such as the Laws. The two families receive
identical services, but pay different taxes. Equalization is necessary to
attain equity in taxing jurisdictions that cross assessment jurisdictions.
b. The Clementes will pay $10,000 in property taxes both before and after
equalization, whereas the Laws would pay $8,000 without equalization
and $10,000 with equalization.