# after-tax return on mortgage interest?



## joncnca (Jul 12, 2009)

Hi, 

Please forgive the novice question, but I ran across this pots in another thread I was reading and I had a question about it:
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Pay off the mortgage on the primary residence as this will earn you a guaranteed after tax return of the mortgage rate (and more importantly the future mortgage rate should interest rates begin to rise significantly) without risk. This is a much better deal than a leveraged investment in equities, especially now. 
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Can someone explain or point me towards some good books/articles/links that'll explain that's meant by "guaranteed after tax return of the mortgage rate"? does this mean there's a tax credit on the interest we pay on a mortgage? i had understood that mortgage interest was tax deductible in the US, and that the Smith maneuver was like a Canadian roundabout way of gaining this same tax advantage, but I wasn't aware that interest paid on a mortgage in Canada could have any tax benefits (like a tax return)

Can anyone clarify this for me? Thanks!


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## ssimps (Dec 8, 2009)

My understanding is that you can not deduct the interest you pay on a mortgage of your primary residence, unless you also run a business from it and then you can deduct what ever % of the house you use for your business.

You can deduct interest payments made on invest real-estate from your tax though, assuming the real-estate is in the name of the tax payer.


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## MoneyGal (Apr 24, 2009)

There's no tax credit for paying down the mortgage on your principal residence. 

What the original sentence is intending to communicate is that when you pay down your mortgage, because you are "saving" (not paying) the interest you would ordinarily pay on those borrowed funds, it is as though you are earning a rate of return equivalent to your mortgage rate. 

Additionally, because gains on the sale of your principal residence are tax-free, the original sentence is (I presume) saying the return is best expressed as an after-tax rate. 

Here's how this conversation is typically expressed: given that gains on a principal residence are tax-free, should I pay down my mortgage, or invest (for capital gains, in a taxable account)? 

Here's the calculation for that simple expression of the problem:

*divide your mortgage interest rate by 1 minus (your marginal tax rate x .5)*

Say your mortgage rate is 7%, and your MTR is 21.5% (randomly-chosen numbers):

The "breakeven rate" for calculating whether you should pay down your mortgage or invest (in an open account) is 8.92%. That is, you'd need to earn 8.92% (in capital gains in an open account) in order to beat the rate you'd implicitly earn by paying down your mortgage. 

There are a bunch of other considerations in this conversation (with respect to timing, investment decisions, and predicting future tax rates), but that's the back-of-the-envelope calculation.


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## MoneyGal (Apr 24, 2009)

Duh. I really am in a stupor (it is still relatively early on New Year's Day...at least I have that excuse). 

I think all the original sentence is saying is that the imputed return (the interest savings you "earn" from paying down your mortgage) are expressed as after-tax returns because the "gain" (not really a gain, but unspent money) is not taxable. If you earned the same investment return in a taxable account, you'd need to pay tax on the gains. 

I also gave you the break-even formula which is intended to allow you to evaluate a capital-gains-producing investment in an open account versus paying down a mortgage. But the original sentence didn't go that far.


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## joncnca (Jul 12, 2009)

thanks for clarifying that for me!

that's what i thought, no tax deduction from interest for principal residence. i thought i had missed some sort of tax benefit and was paying the full interest like a sucker, haha.

i understand the implied gain obtained by not having to pay mortgage interest (i.e. having paied the mortgage down). but is this still true if i don't plan to stay at my current residence for more than a few years? 

that is, assuming that my mortgage interest rate is higher than rate of return on open investment account, is it still more advantageous to pay down the mortgage if i don't intend to pay off the whole mortgage before i sell the place and move somewhere else and get a different mortgage?

also, this formula doesn't apply the same way to investments in an RRSP, right? your x0.5 MTR applies because the open account is taxed at half MTR, right?

that formula that you gave, again let's say mortgage rate is 7%, and MTR is 21.5% (randomly-chosen numbers):

the expression would be 7/(1-(0.215/2)) = 7.84% wouldn't it? i'm not sure where 8.92% comes from, could you please explain this to me?

thanks!


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## MoneyGal (Apr 24, 2009)

I should probably not post equations early on New Year's Day. I gave you the correct equation - but did it incorrectly in Excel. The result I posted is =7/(1-.215), not =7/(1-(.215/2)).

You ask whether the equation holds true if you do not plan to remain in your house long-term. This is why I don't particularly like these "rules" of financial planning: they overly simplify, in my view, real-world scenarios. 

The issue with housing is that it is partly consumption and partly investment. I don't particularly like evaluating principal residences as investments. 

In general, though, as long as your mortgage rate is higher than the rate you would get on an open investment account, you are farther ahead to pay down your mortgage than you would be to invest in an open account. This is even more true if you invest in interest-bearing investments in an open account (and in fact, the equation I actually posted is the break-even formula for open accounts earning interest taxed as ordinary income, as opposed to open accounts earning capital gains). 

Make sense?


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## OhGreatGuru (May 24, 2009)

_In general, though, as long as your mortgage rate is higher than the rate you would get on an open investment account, you are farther ahead to pay down your mortgage than you would be to invest in an open account. _

I think the point in the original post about "after-tax return" is:
a) that the after-tax return on your open investment account has to be more than the mortgage interest in order to be ahead, because you are paying your mortgage with after-tax dollars; and,
b) that paying down a mortgage is a "guaranteed no-risk" return, so you shouldn't compare it to what you can make on equity investments. You need to compare it to what you can get in a guaranteed risk-free investment, which would be something interest-bearing, that is taxed at a 100% inclusion rate.


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## MoneyGal (Apr 24, 2009)

OGG, I agree with your first point. However, I think what the OP's quote is talking about is what I said, i.e., determining the break-even point for mortgage versus open account. 

And I pretty much agree with your second point, also; except I don't like these one-dimensional comparisons. Is the person making the comparison actually considering a leveraged equity investment?


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## joncnca (Jul 12, 2009)

yes, i think it'll be important to keep in mind that there're lots of little considerations that need to be made.

this really applies mostly to open account investments, right? so, it'd make more sense to repay a mortgage before open account investments, assuming the mortgage interest rate is higher than potential return on investment.

but if it's inside an rrsp, then you'd have to do the calculation with before tax tax dollars invested and the %return on that investment vs. mortgage rate, right? as opposed to after-tax return on investment, as with the case of an open investment.


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## MoneyGal (Apr 24, 2009)

Yes.


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## joncnca (Jul 12, 2009)

it just occurred to me that one key consideration in addition to the mortgage rate/% rate of return on investment would be the actual outstanding balance of the mortgage vs. the amount of money available for investment.

that is, if the mortgage is substantially greater than the amount of money available for investment, even if the % return on investment is greater than the mortgage rate, it may still be wiser to pay down the mortgage because a smaller % of a larger number may be greater than a larger % of a smaller number, right?

this almost seems to imply that if one has a large mortgage (i'm assuming that for most people, mortgage is much larger than any other debt and generally larger than a single year's income/savings/etc.), it may not be mathematically advantageous to buy investments unless a) you have sufficiently decreased your mortgage or b) put a sufficient amount of money into an investment that has a % return greater than the mortgage rate, according to your break even formula...

hope that made sense, haha.

so many considerations. it almost seems like the safest best is to pay off mortgage before any investing, but clearly this comes at the opportunity cost of missing out on an investment that could potentially (through higher rate of return than mortgage rate and/or accumulation from compounding interest) give you a better return than what you're paying in interest on the mortgage

i'd be really outta breath if i just said all of this in one go


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## MoneyGal (Apr 24, 2009)

Yes again, to all of that. Like I said, this is why I don't really like these very one dimensional "rules." 

Another consideration is that real estate is illiquid and undiversified. And, when you are young, your main source of wealth (really) is your unmonetized human capital, which is also illiquid and relatively undiversified. 

You need to come up with a plan you can live with, and the reality is you need to do it all -- invest and pay down your mortgage.


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## Potato (Apr 3, 2009)

joncnca said:


> it just occurred to me that one key consideration in addition to the mortgage rate/% rate of return on investment would be the actual outstanding balance of the mortgage vs. the amount of money available for investment.
> 
> that is, if the mortgage is substantially greater than the amount of money available for investment, even if the % return on investment is greater than the mortgage rate, it may still be wiser to pay down the mortgage because a smaller % of a larger number may be greater than a larger % of a smaller number, right?



No.

5% of $1k is $50 no matter whether that $1k goes towards paying down a $500k mortgage or into a $1k investment. The fact that your mortgage is large or small doesn't change the amount of available money you have in your hand that you're making the decision over.

There are other considerations where a large mortgage vs a small one (or a large investment portfolio vs a small one) may come into play though. For instance, if you have no money outside your mortgage, you may want to hold an emergency fund of some sort, even if it would be less profitable than putting that money towards paying down the mortgage. 

Also, you need to consider the estimated interest rate over some length of time for the mortgage (and likewise with the investment return) -- often if you're investing in stocks you could be facing a loss if you had to sell in the short term, and the rate of return can be quite variable. If you're assuming you'll make 6% after tax in the market on average, and your variable-rate-mortgage is only 3%, then on the surface it makes sense to invest. But if you anticipate that the rates will go up in a few year's time and your average rate would be >6% over some longer time period, it may be prudent to pay down the mortgage.

Here, a larger mortgage (or I suppose more properly, a longer-duration mortgage) can be a factor. If you have $X to invest and relatively small mortgage (though I think the more crucial factor would be if it was small in relation to your salary rather than in relation to X), it may be worth the risk to invest while rates are low on the theory that if rates rise you can sell your investment (even at a slight loss) or just pay the increased rate out of salary and not be too far off in the grand scheme of things from where you would have been if you took the safe route and paid down your mortgage. But if you have a large mortgage and a higher interest rate would squeeze affordability in the future, you may want to take the safe route and pay it down rather than invest.


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## MoneyGal (Apr 24, 2009)

I assumed "larger mortgage" = "earlier in the mortgage term" which means there's a bigger payoff from paying down mortgage vs. equity investing. 

But that introduces another dimension, which is total interest paid on the mortgage over its duration. 

Someone who genuinely has mortgage affordability concerns likely shouldn't be investing in equities at all.


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## Jungle (Feb 17, 2010)

Sorry to bring this one up from the dead.. but can anyone post the math above in simpler form? I tried moneygal's equation, but I didn't come up with the same answer.


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## MoneyGal (Apr 24, 2009)

Post your equation, and we will work through it. I didn't help matters any earlier in this thread...I can't remember what I was doing that New Year's Eve but it was not brushing up on my math presentation skilz.


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## Jungle (Feb 17, 2010)

Our mortgage rate is 5.14%. My MTR is 31.15%. My wife's MTR is 24.15%. We have a joint account, not sure if that makes a difference.


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## andrewf (Mar 1, 2010)

If you take the simple average of your MTRs 27.65%, 5.14% after tax return is equivalent to 7.1% pre-tax on an income bearing investment (like a bond or GIC). If I were you, I'd be paying down the mortgage right now!


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## Jungle (Feb 17, 2010)

Thanks Andrew. Now I do not feel so guilty for paying down the mortgage!


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