Saturday, June 23, 2007

The $200,000 Blunder: Housing Myths Part 2

Part of a series of articles on housing myths.

Some people will make a $200,000 blunder but think that they are making money.

Chasing Unicorns

Never Prepay Mortgage? Housing Myths Part 1 covered how would-be moguls fail to assess different risk levels when keeping mortgage debt to chase possible investment profits. Some people (real people, not hypothetical people) think that a money market (unlikely to go below 0%) might be the solution to avoid stock volatility. However, less risk means lower possible returns, plus money markets fluctuate too (some crashed below 1% a few years ago). Unfortunately, some people think that they can make money even when their investment rate is lower than their borrowing rate.

Avoid Major Math Mistakes

The first problem is that people apply income tax modifiers essentially backwards, doubling the error. People vastly overestimate their tax reductions by (for instance) applying a 28% discount to every penny of mortgage interest (more on this in a coming article) and then compound the error and also overestimate their investment growth by not applying 28% taxes to their money-market interest. The first step is to estimate a realistic, after-tax return on investment (ROI).

An easy way to account for taxes on compounding interest is to discount the interest rate by your tax bracket (a 28% tax on 5.05% interest is 5.05 x 0.72 = 3.636% effective interest rate). This method is imperfect (it assumes that tax payments/withholdings and compounding occur almost simultaneously) but is much less wrong than ignoring taxes entirely. One blogger who thought that he would have $134k actually would have closer to $119k, a $15k error.

The even bigger mistake is when people make a false comparison at the 15-year mark, which ignores half the costs of the unpaid 30-year mortgage, or they mix up a 15yr scenario with a 30yr scenario. A proper comparison must be at the 30-year mark for both altertnatives.

Our Example (from a real person)

  • $200k 30yr 5.875% mortgage (at calculator).
  • $1,183.08/mo minimum mortgage payment.
  • $500/mo extra available in budget.
  • 5.05% money market investment opportunity (annual interest compounded monthly at
  • 28% federal marginal tax bracket (no state tax included here).

Keeping mortgage to invest loses over $100k

Minimum mortgage payments total $426k ($200k loan + $226k interest), offset by $325k after 30 years of money market for a net loss of $101k.

Paying mortgage early gains over $100k

Paying an extra $500/mo on the mortgage principal would pay off the mortgage after 15 years, for a total cost of $300k ($200k loan + $100k interest).

What people forget to count is that if you pay off your mortgage after 15 years, you then can invest your old mortgage-payment amount ($1,183.08/mo) plus your over-payment amount ($500/mo) for the next 15 years (remember that you paid both these amounts for the whole 30 years in the investment scenario too). In our example, $1,683.08 @ 3.636% for 15 years is $402k, or a net gain of +$102k more than the mortgage cost.

The $200k blunder

So, borrow to invest for a net loss of $101k, or eliminate debt and then invest for a net gain of $102k. That is a difference in fortunes of $203k, the difference between buying a second house or paying twice for one house.

A future article in this series will cover why the vaunted mortgage deduction would not fundamentally change these conclusions.

Home Mortgages Are Bad Investment Tools? Housing Myths Part 3


traineeinvestor said...

I would assume that anyone who decides to invest in something that earns less than the cost of borrowing (after adjusting for tax) is in need of some financial advice. The math in your example is pretty compelling on the issue.

However, a more valid comparison would be investing in something which earns more than the cost of funding the mortgage. Here the math should work the other way and favour investing in, say, an index fund or similar. So long as you are prepared to live with the volatility risk (which usually requires a reasonable time horizon), investing in an index fund should be a better bet than paying off a mortgage early. (And it certainly will in a low tax jurisdiction like Hong Kong where I live.)

J at IHB and HFF said...


Hello. Unfortunately, some people think that their after-tax net return is positive when it is not.

On your second point about when investing rates appear higher than loan rates, please see "Never Prepay Mortgage? Housing Myths Part 1" for an example.

Thank you for the visit and comment.

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Sausalito said...

Your math makes for an interesting argument. I agree with most of it.

J at IHB and HFF said...

Sausalito, thank you.

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