Tuesday, July 12, 2005

Knowing the math behind real estate

Have you attended any real estate seminars of late? To a widemouthed gullible audience, the real estate agent would be selling the American dream (which is basically to live the rest of your life in debt ;)). And he would be talking about some numbers and math and RoI and before you grasp his confounded logic, would conclude that "Hence, if you dont purchase a house now, you are losing $2000/week". Let's cut the crap out and take a look at how to exactly know if you are making any money out of selling the house.

The first thing you need to do is to calculate the opportunity cost of buying a home. i.e., the cost incurred because you bought a home ceteris paribus (everything else remaining the same).
For instance if by moving to your house, you drive more, then the marginal gas expense is the opportunity cost of buying the house. But if you have a new kid and there are expenses due to that 'life changing' event, even though you bear that extra cost, it is not an opportunity cost of buying the house.

Even though Mortgage interest and home equity interst are tax deductible, you cannot simply cut 30% from the mortgage you pay because your Alternate Minimum Tax (AMT) may kick in especially for double income families. So, for calculating the true saving on tax, (assuming T1 is the tax paid in the 'bought home' scenario and assuming T2 is tax paid in the 'did not buy home' scenario) one has to subtract T1 from T2. This is a huge difference from what is told to the consumers in the realtor expos. To take an example, let us say you pay $10000 in mortgage interest in the year, the realtor will tell you that the real expense is only $7000 because the mortgage is tax deductible. But using the above line of reasoning I gave, you should consider the actual expense as (($10000 + T1) - T2). In short, the realtor tells you that you can itemize the expenses when you buy a home. But what he does not tell you is that if you did not buy a home you still can get the standardized deduction.

If your home is big , then the utility charges are considerably more expensive, you have to add the differential to the cost of buying home as well. For full details of the elements in calculating opportunity cost, take a look at this presentation and feel free to modify it as per your needs.

The principal you pay towards your mortgage and home equity is not included in my presentation as opportunity cost as they build your equity in the house. But there is a hidden opportunity cost there as well. viz., the interest lost on the prinicipal. So one need to carefully include that loss of interest over years (because of the compounding).

In the slides, I have given the example that excluding the principal, you get an annual opportunity cost of $15000 and you paid $1000 towards principal. The opportunity cost on the principal is $70 (assuming 8% interest and $10 maintenance fee in well established funds such as Vanguard S&P 500 index fund). So, in that year the opportunity cost is $15070. Let's say you do the same for 2 years, then the opportunity cost is (($15070 * 1.08) + $15070). Let's say you do the same for 3 years, then the opportunity cost is ($15070*1.08*1.08) + ($15070*1.08) + $15070). You get the picture.

Let's now come to the fun part. If you sell the home for some sale price P, you wont get that in your hand. There are many middle men (wolves) in the way. For instance, you pay 5-6% of the sale price to your selling agent. The banks will want the unpaid loan amount (which is only fair). After all these overheads, if the money you get in hand is more than the opportunity cost you calculate in the above paragraph, then it means you had a lucrative deal. Otherwise you are sucker :) Note that if you decide to postpone your selling by a year to make the sale lucrative, the opportunity cost also goes up and you have to take that also in to account.

Peace out
ps. Caveat: This part of the story is told purely from the financial point of view. It is not possible to quantitatively describe the sense of pride of ownership, sense of satisfaction in smelling the rose in your backyard and other such intangibles.


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