Monday, June 12, 2017

Let's Crank Some Numbers!


Let's crank some numbers on "opportunity cost" and see where it gets us.


In my last posting, I discussed Math versus English in making an argument.  And in a previous posting I linked to that, I discussed some real-world numbers.   But let's crank some more numbers and see where they get us.

Suppose, for example, I was to get a home equity line of credit or other type of mortgage for $250,000 and then invest this.   Now, money doubles in value, generally, every 7-10 years.  So, after 10 years, I have $500,000, pay back the mortgage and come out $250,000 ahead!  Sweet deal!

Or is it?  Or am I missing some relevant numbers?

Let's compare it to the alternative - I don't get a mortgage and instead have to take less money out of my IRA over the next ten years and pay less taxes as a result.

Depending on whose website you visit, the average return on a mutual fund or the stock market is about 10-12%.  Let's be conservative and say 10%, which is a damn good rate of return these days.  It is also a risky rate of return, but we'll get to that later.  After a decade, we have $648,435.62 in our investments, a gain of  $398,435.62!  You can see why this is so attractive.

But, we had some expenses during that decade.  Mortgage rates are around 4%, which yields a $1194 monthly payment for a 30-year amortization.  At the end of 10 years, we owe $190,396 on the loan, which means we paid off $59,604 on the balance, and paid a total of $143,280 in payments, of which $83,676 was interest.

OK, so you subtract the interest from the profit, you still have over $300,000 in profits!  $314,759.62 to be exact.  This has to be a good deal, right?

Well, there are taxes to consider.   In order to make this $143,280 in payments, you will have to withdraw an additional $14,328 per year from your IRA to pay this amount.  And you will have to pay taxes on that additional amount you take out.   But wait, maybe you get a tax deduction and thus effectively pay no taxes on that income?

Well, in this instance it could go either way.  The standard deduction for married couples in 2016 was $12,600.   So in terms of "increased deductions" it is sort of a wash.  You are not really getting that much more of a deduction if you go this route.  Now, of course, once you start itemizing, you can take other deductions - for charity, for example.   But quite frankly, I've never had much other than mortgage interest in terms of deductions, so I am not sure this is such a big deal for the lower and middle classes.   Maybe if I borrowed more, I'd get a bigger deduction, but then again, how much can you borrow on a house worth $400,000 on a good day?

So the tax thing is a wash, I think.  Since my income would be $14,328 higher, I would have to pay that much more tax - the itemized deduction would not exceed the standard deduction by much.  This illustrates how the "deduction" argument is sort of a cruel joke to the middle and lower classes.   I would have to pay 15% of that in taxes, if our joint income was under $75,000, 25% if above.  Let's assume this doesn't bump us into the next bracket, and we are paying an additional $2149.20 in taxes.  Per year.   So we are looking at $21,492.00 in additional taxes over ten years.

"But Bob!" you say, "You're still coming out over $300,000 ahead in profits!"  And you would be right about that, if our assumption of a 10% return was correct.  But that is comparing apples and oranges.  My house is paid-for.  That is a 100% guaranteed rate of return on my "investment".  It isn't going away, it isn't going to be taken away from me.  It is not going to go down to zero in value.   And stocks and mutual funds can drop in value - by half, or even whole.   Recent experience shows this to be a predictable outcome.  What is the rate of return on debt you have paid off?  Simple, the interest rate on that debt.  In this case, the 4% mortgage rate.

Over 10 years, I have saved $143,280 in interest payments I didn't have to pay.  And this is a sure thing.

So instead of comparing apples to oranges, let's compare oranges to oranges.   What other investment is 100% bulletproof guaranteed never to go down in value other than paid off debt?   Well, there isn't one, really.  But the closest thing you can find is government backed debts, such as treasury bills, treasury notes, savings bonds, and maybe FDIC-insured CDs.

10-year T-Bills are running about 2.5%.   FDIC insured CDs are even less.  Let's assume 2.5% rate of return.  Right off the bat, you see this is less than the 4% we are paying in mortgage interest.  Over ten years, you end up with $320,021.14 from your $250,000 investment, or about  $70,021.14 in interest earnings, which is less than the $83,676 you paid in interest.  In fact, you have to have an earned interest rate higher than your loan interest rate for this to start to work.  Factor in the amount of extra taxes, and you might need 5% or more to make this work.   Getting 5% or more reliably and consistently in the market is hard to do.

And if you think about this, it makes sense.  Banks loan money at one rate, and then borrow (pay interest) at a lower rate.  If they did the reverse, they'd go bankrupt!  So mortgage rates are always going to be higher than savings rates on safe, government-backed investments.  It will never be otherwise.

Getting a higher rate of return, is tricky.  In fact, it is usually the people trying to sell you investments that argue that the average rate of return is going to be 10% or more.   Warren Buffet makes the pitch for 6-7%, and that is in risky stocks.  And yes, that is a credentialist argument.  So is saying that Dave Ramsey argues for 11% or more.  It seems like a simple thing to calculate, right?  Take total returns, divide by number of years.   But as one site notes, the "average" and "median" mean two different things, and the market hits "average" or better in only one out of 10 years.  And of course, by "market" do you mean DJIA, S&P 500, or what?

So in our scenario, we have to hope our ten year window includes those average-or-better years and not, say, February of 2008, when the market lost half its value.   You are taking a risk and to risk-takers go the rewards.   When you are 30 and young and helplessly in debt anyway, getting a mortgage is maybe the only way you'll own a house.   Very few of us are in the situation were we have a choice to get a mortgage and then "invest" the money we would have used to buy the house, in stocks and bonds.

I am in such a situation, however, I am not 30.  I am not in a situation where I can afford to lose money or lose my house.   To the risk-takers go the rewards.   But there are also risks.  What sort of risks?   Well, let's say we have another 2009 scenario.   My $250,000 investment drops to $125,000 in value.  My $250,000 mortgage still has to be paid back.   But of course, I have less money to pay it back with!  And if the house has dropped in value as well, then I cannot simply refinance, either.   I have to pay back this loan, over 30 years, and likely be perpetually in debt in retirement, and my income stream may be reduced because I lost so much in the market.

Farfetched?  It happened to millions of people in the United States from 2005 until even today.  There are plenty of people even today who are "upside-down" on houses.   If you are young and can declare bankruptcy and start over, then this is just horrible.  If you are older, well, it might mean you lose your house - a house you once owned free and clear - and now are too old to "start over".  Retirement will suck in a very big way.

The way I look at it is this - most financial advisors who are not trying to sell you something will say that your percentage of "safe" investments should equal your age.   At age 57, I should have most of my investments in "safe harbors" that can't decrease in value and leave me high and dry.   And a "paid for house" is one of those safe investments, saving me $14,0000 a year in payments I don't have to make.   Sure, I could leverage the house and gamble on stocks, but retirement age is no place to be gambling.   Besides, I already have far too much invested in stocks as it is.

"But Bob!" you say, "You always have to have a place to live!  You can't liquidate a house, it's not an investment!"   And you are partially right about this.   I am not talking about the house as an investment but the debt you don't have to pay back.   At the end of 10 years, I come out ahead not paying interest on a loan.  And compared to the paltry 2.5% you get on a T-bill, the 4% I don't pay is a better deal.   Oh, and by the way, you can downsize to a smaller house, and spend the difference.   And I plan to do just that, by the time I am 70 or so.

So what is the mathematical conclusion I come to?   Yes, if you are willing to take a huge risk and get lucky and make 10% or more in the market, you could come out hundreds of thousands ahead.  You'd have to beat the market by a substantial amount - get lucky and not hit one of those dry spells that comes along every so often.   If you compare apples to apples however, the rate of return on a "safe" investment is always going to be less than your loan rate and this is by design.  If you are willing to make some wild-ass assumptions and compare apples to oranges, well, you can "prove" just about anything, right?


Having a paid-for house in retirement is a 100% safe investment with an effective rate of return higher than what you'd get with a government-backed security.  Can't beat that!

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