Is it worth it to pay off debt?

I recently got into a few lengthy discussions about whether you should pay off your house or use that money to invest in a retirement fund. The scenario we were talking about was if you had a lump sum drop in your lap, would it be better to get out of debt or simply invest the money at a higher rate than the debt you were carrying.

All of you Ramsey fans out there would know he would ask "If you were debt free, would your take a loan out on your house to invest for retirement?" -- which is what I asked during my discussions.
Surprisingly, the answers I got back were in favor if investing the money. Even with the risk of the stock market, those involved in my discussions were willing to invest the money (to varying degrees of enthusiasm).

Their arguments basically hinged on the fact that mortgage rates are fairly low, and investment returns are rather high. So, based on this, I decided to crunch some numbers to see exactly how this would break down.

The hypothetical situation is as follows:

You have a $150,000 mortgage at a rate of 5%. You have an investment that will give you 10%. You have $150,000 cash on hand... what do you do?

The first scenario is to keep the house and invest the money over the 15 years. First off, paying a 15 year fixed mortgage at 5% on $150,000 would result in a monthly payment of $1186.19. Over the lifetime of the loan, you would pay back $214,054.20 in principle and interest. Now let's take the $150,000 and invest it at 10%. Without adding any money to it and letting it build over the 15 years, you would end up with $446,274 after taxes (at a 28% tax rate). So, to summarize, we have the following:

• $150,000 Mortgage, 15 year fixed at 5%
• $1186/month payment
• Cost of $214,054.20 over 15 years

• $150,000 Invested for 15 years at 10% with a 28% tax rate
• Gain of $446,274

So, after you subtract out the cost of your house from the gain of your investment, you have netted $232,219.8, not a bad little investment.

Now, let's examine the second scenario. This time, you take the $150,000 and pay off your home. However, instead of pocketing the house payment, you put it into that same investment at 10% for 15 years. After the 15 years and 28% tax rate, you end up with $378,339. The first thing you should notice is that this number is substantially less than the $446,274 you gained in the investment in the first scenario. However, after you subtract out the cost of your mortgage, you have actually GAINED $146,119.20 after paying off your house. To summarize:

• $1186.19/month invested over 15 years at 10% with a 28% tax rate
• Gain of $378,339
• Net Gain in Scenario 1: $232,219.8
• Difference in Scenraio1 vs Scenario2: $146,119.20 in favor of Scenario 2
  

So, by paying off your house with $150,000 and investing your would-be house payment, you end up almost $150,000 ahead of where you would have been if you had gone with the first option. Notice that this is essentially the principal that you were initially thinking of investing. Just at looking at the value of the two choices (aside from investing revenue), option 2 gives you a 100% return over option 1.

Sure, you could find an investment that was over 10% and make the numbers work. However, the risk involved with such any investment that returns a steady rate above 15% would far outweigh the potential gains you would have.

I think the numbers speak for themselves :)