The mathematics of real estate

02.25.09
By Randy Johnson

I have always been astonished at how poorly some people make the mathematical calculations involved in real estate. Of course, few people use a lot of math in their everyday lives, so when they do have a calculation to make, their skills may be rusty.

I do this math everyday and have for years. In each of the 4,500 transactions I have done, there almost always has been at least one calculation. Most transactions require quite a few calculations. The answers will likely drive the decisions; otherwise, why bother making the calculation in the first place? The problem is that if you do the math wrong, you will get an incorrect answer.

Actually, this is not always true. You can make really awful mathematical calculations and still have things turn out okay. Here's the story that proves it.

In the second century BC, the Greek astronomer Eratosthenes calculated the diameter of the earth to within 1% of the real number (24,000 miles). The distance from Europe to Hong Kong going from West to East is 120 degrees. At 30 degrees North Latitude each degree is about 60 miles, and the distance is about 7,000 miles. That distance is known because Marco Polo went that way.   

Now in 1492 Christopher Columbus wants to go the other way to China. You and I now know that if you are going to go to China the other way, you need to go 240 degrees, or 360 minus 120. That's twice as far! Your journey is going to be over 14,000 miles. In that day and age, ships were not even capable of carrying food and water for such a lengthy journey, so why did Columbus even start?

But he did, and when he made landfall in America, he had only traversed about 75 degrees of longitude, a little over 4,000 miles. Theoretically, he should have said, "Wait a minute. What's this? We should have to go another 10,000 miles before we get to Asia."

So it is possible to be waaaaaay off on your math and still have things turn out okay, but in this case it is because Columbus was lucky. He had North America to bump into, a new land the world had yet to discover (not counting Leif Ericson and a few other explorers who arguably had landed previously).

If you are making decisions about real estate, you aren't going to be lucky like that, so you had better be sure of your calculations. Let's go back to the current problem, figuring out a refinance. What we want to do is figure out the benefit of a refinance and compare it with the cost. If the benefit were greater than the cost, then you would want to do it right?

Let's take a simple example, a refinance of a $400,000 loan currently at 5.75%. The new interest rate is 5%. The cost of doing the refinance is $7,000 (1 point plus $3,000 in title, escrow, and other fees). Left to do it themselves, ninety percent of people will calculate the difference in monthly payments, or $187. To many people, that doesn't seem all that much. They look at $7,000 as A LOT OF MONEY and the savings as being miniscule.

But let's not be fooled – let's do some quick math, The quick way to figure out the cost–benefit ratio is to consider the cost to be an investment and then calculate how quickly your investment will be returned. In this example, with a savings of $187 each month, it would take 37 months to break even, and then you would continue to save $187 each month. That may not sound attractive; based upon that calculation many people would conclude that it "isn't worthwhile."

But the problem is that when you lower the interest rate, you also change the percentage of each monthly payment that goes to reducing principal. Comparing payments is the WRONG way to do it. A $1 reduction in principal is just as valuable to you as a $1 saved in interest. Look at this table:

$400,000	5.75%	2334.29	417.62	1916.67
$400,000	5%	2147.29	480.62	1666.67
Difference		187.00	63.00	250x12=$3,000 per year

In this example, lowering the rate increases the amount of principal reduction by $63 per month. Added to the $187 interest reduction, the total benefit is $250 per month. When you do the cost-benefit analysis this way, the payback period is only 28 months – even better than before!

A simpler way is to forget the monthly payments. Just calculate the difference in interest payment, in this case a reduction of .75% x $400,000 = $3,000 per year. Same answer.

So if you are thinking of a refinance, use the difference in interest multiplied by the loan balance and divide that into the costs. That will give you an accurate measurement. 

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When making decisions about real estate be sure of your calculations.