If you are currently renting a house for $10,000 per year and have an option to buy it for $200,000, would you buy it?
Let's say that your tax rate is 35%, for income tax purposes. The maintenance and property taxes are esitated to be:
Maintenance $1,000
Property Tax $2,000
Total $3,000
These cost are currently included in the rent.
Let's assume that your objective is to provide yourself with housing at the lowest possible cost. Should you buy or continue to rent?
Because property taxes can be deducted from income for federal income tax purposes, the after tax outflow for property taxes per year is 0.65 X $2,000 = $1,300. If no date for selling a house ahs been specified, we can assume an infinite period.
First, we need to compute present value of the outflows, where period is 2 years, interest is 3%, future value is $0.00 and payment is $45,000. The present value of the outflows is $86,106.00.
Next, we compute the present value of the inflows or both periods; 2 and 43 years.
where period is 43 years, interest is 3%, future value is $0.00 and payment is $5,000, the present value of the inflows is $119,910, and where period is 2 years, interest is 3%, future value is $119,000 and payment is $0.00, the present value of the inflows is $113,026.
If you buy a house, then you will need to pay $200,000 immediatelly, and the expected after-tax cash outflow will consists of the maintenance and property tax expenses:
Cash outflow in Year n = $1,000 + $1,300 = $2,300
Let us assume there is no inflation and the real after tax rate equals (1 - tax rate) times the before-tax rate, which in our case is:
(1 - 0.03) X 3% = 0.7 X 3% = 2.1%
Because we are assuming that the property and maintenance costs are fixed in real terms, 2.1% should be a real interest rate. Therefore, we find the following:
Present Value of Owning = $200,000 + ($2,300 / 0.021) = $309,523.81 and
Present Value of Renting= $ 10,000 / 0.021 = $476,190.48
If Present Value of Renting is greater than Present Value of Owning, then it is better to own rather than rent, which is case in our example above.
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