Friday, May 11, 2007

Fun with math

Lets say you have a $200,000 home that’s paid in full.

Should you take out a loan on the home and invest the money in the stock market?


Common sense says “Yea!  Sure!  With interest rates so low, why not?!?”

Math doesn’t agree.


Let’s go with a 15 year time line and the cheapest possible loan—an interest only loan where you only pay interest and at the end of the 15 years you liquidate your investment and pay off the loan.  At the end you should be ahead anyway and you can take the profits and live fat and large.


Ok, so the interest only loan is going to be 5%, your home is going to appreciate in value 2% a year, or 10% every 5 years, and the investment will give an average 8% a year—roughly what the market does over time.


You cash out the loan into $185,000, or almost 93% of your home, because you want to have a little for home improvement or something.  You then take the $185,000 and invest it all, less 10% commission, into something that is a sure fire 8% return (something that doesn’t exist, but I’ll humor you for awhile).


The carrying cost for the financing is $770.83.  The monthly appreciation of your home is $333.33 and your assets appreciate at a rate of $1110 a month.  It’s a net worth increase of $672.5 a month.  You’re getting richer each month by sitting on your ass.


At the end of 15 years your balance sheet will look like this:

Loan:  -$185,000

Home value: $269,173.67

Investment:  $550,602.43


There will also have been a cash outlay of $138,750.0 to cover the interest of the loan, which is part of this calculation as well.  Plus, there’s a “hidden” item that I’ll discuss later.

The net result over 15 years is a net worth of $496,026.09  Not bad considering the alternative would have simply been a house worth $269,173.67.


But there’s another alternative.


If you can afford $770.83 in carrying costs for the loan, why not forgo the loan and simply plow that money into an investment account for 15 years?

The resulting stream of payments and earnings on the payments would have been $266,737.80.  About 48% of the future value of the $166,500 investment made from the financing option.  However, there are 3 big differences.

1 is that you don’t have to pay off that big loan that’s been looming over your head for the last 15 years.  Another is that you didn’t have negative cash flow going to some finance company.

The net result is that your home and asset totals $498,931.59.  All of which is yours.  Compared to the $496,026.09 net value from the financed option.


But wait, I mentioned 3 big differences and only described 2.


The third is the “hidden” item mentioned earlier.  That $770.38 you sent to the finance company to carry your loan was a straight expense in the financed option.  Those lost payments would have generated $127,987.80 had they been invested (the difference from the future value of the series of payments in the unfinanced model).  So the $496,026.09 that the financed option yielded doesn’t show the $127,987.80 in opportunity costs that don’t get added into that model that are captured in the cash model.


So it turns out that mortgaging your home to invest in the market really doesn’t get you ahead—which is what you’re doing if you choose to invest in the market rather than pay off your home.


The difference is even greater if the returns on the investments are flat—0% for 15 years, which never, ever, ever would happen—and the resultant net worth at the end of the game is $111,923.67 versus $370,943.79.

To actually end up ahead of the game using financing, you’d have to invest to earn 11% over the course of 15 years—an unprecedented return on investments in the history of the market.  Not that it can’t be done, just that you shouldn’t normally plan for abnormal returns.


Much better to pay off your house (as quickly as possible) and continue to invest that house payment into something that brings returns free and clear of any liability.



Blogger ~*Vica*~ said...

Math to me is the same as greek...

5:09 PM  
Blogger Holden said...

Yawn..... Did you pay off the note on your house?

2:08 PM  

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