A local county government experiences an increase in spending needs. To help pay

Question

A local county government experiences an increase in spending needs. To help pay for these, it decides to permanently increase annual mill rates from $10 to $25. Instead of making the increase all in one year, it decides to increase the rate from $10 to $15 in the first year, and then from $15 to $25 in the second year. The mill rate is to remain at $25 each year thereafter. The Uys own a house in this county valued at $500,000 before the change in property tax policy. Assume interest rates are 10%. a) What is the value of the Uys’ house after the change in property tax policy under 100% capitalization? Explain your calculation carefully. (15 points) b) Now suppose that the county does not phase in the property tax changes. Instead it increases the mill rate from $10 to $25 in the first year. The mill rate remains at $25 each year thereafter. What is the value of the Uys’ house after the change in property tax policy under 60% capitalization? (10 points)

Explanation / Answer

a) Mill Rates (R1) = $10

Mill rates (R2) = $15

Mill Rates (R3) = $25

Interest rate (I) = 10%

Value of the Uys' House = (R1/(1+I))+(R2/((1+I)^2))+((R3/I)/((1+I)^3))

=(10/(1+0.10))+(15/((1+0.10)^2))+((25/0.10)/((1+0.10)^3)) = $209.31

Value of house = $500,000+$209.31 = $500,209.31

b) Mill Rates (R1) = $10

Mill rates (R2) = $25

Interest rate (I) = 10%

Tax rate (T) = 40%

Value of the Uys' House = ((R1(1-T))/(1+I))+((R2(1-T)/I)/((1+I)^2))

=((10(1-0.40))/(1+0.10))+((25(1-0.40)/0.10)/((1+0.10)^2)) = $129.42

Value of house = $500,000+$129.42 = $500,129.42

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