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.
b) Why does this capitalization occur? What factors lead to 100% capitalization versus lower rates of capitalization?
c) 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?