Question

Suppose you own a house where you live and a condo for rent. The monthly rent is $1,600 and you will get it at the
end of each month. Yet you have to pay maintenance fees and insurance premium. They are
$600 per month in total. The property tax is proportional to the (present) value of the property.
The tax rate is 0.1% per month and you pay the tax every month on the last day of each month
with maintenance fees and insurance premium. Assume there is no depreciation
and the condo will generate the same cash-flows forever. The first net cash flow is one month
from now. The discount rate is 0.2% per month, compounded monthly. What is the fair price of
the condo using the present value formula?

Answer 1

Details given as follows :

Monthly Rent $1600

Insurance & Maintenance $ 600

Property Tax is .01% of Present Value

Discount Rate is .02%

Since, Cashflow is for forever, this is a problem of calculating PV of Perpetuity

PV of Perpetuity = D/r , where D= Periodic Payments, r = discount rate

For calculation, we should use net cash inflows and discount rate adjusting the property tax rate

PV of Perpetuity = ($1600-$600)/(.02%-.01%) = $1000/.01% = $10000000 or $ 10 Million

Hence, Fair Price of Property is $ 10 Million.