### Author Topic: PMI Payoff ROI?  (Read 12538 times)

#### myllanac

• Posts: 9
• Age: 34
• Location: Grand Rapids, MI
##### PMI Payoff ROI?
« on: December 17, 2013, 10:52:23 AM »
How do I compute the return on investment (ROI) of paying down my mortgage principal to eliminate PMI early, in order to compare that to other investment prospects? I am not locked into a specific timeframe to pay PMI, I just need to get the balance to 80% of the original value (purchase price). This can be done via extra payments and/or appreciation (I have to pay for an appraisal, though).

Details:
- Original amount (September 2012): \$119,900
- Interest Rate/Term: 3.5% 30-year fixed
- PMI: \$59.95 monthly
- Total PMI according to amortization schedule: \$4,560 (80% LTV reached on 4/1/19)

Between now and reaching 80% LTV, I'll pay an average of \$4,200 in interest annually (3.5% of original amount). Adding \$720 in annual PMI payments to that is \$4,920, or an effective interest rate of 4.10% of the original amount.

So if I invested \$720 in principle reduction in January 2014: I would save \$720 (a year of PMI I no longer have to pay), plus the interest savings (\$1,225), for a total return of \$1,945, or 70% ROI. Is that right?

#### nawhite

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##### Re: PMI Payoff ROI?
« Reply #1 on: December 17, 2013, 11:56:41 AM »
It depends on how much money you have to pay to hit 80% LTV.

Lets say you originally had a down payment of 10%. So you need to pay off an additional \$11,990 before you lose the PMI. In this case, think about it like a loan for \$11,990 with an interest rate of 3.5% plus a fixed rate of \$59.95/month. So yearly, the cost to carry this loan of \$11,990 is:

59.95*12= \$719.40

719.40 / 11,990 = 6%

6% + 3.5% = 9.5% (so every dollar you put towards this loan gives you a risk free return of at least 9.5%)

Lets say instead that you only had \$5,000 left to go before you hit 80% LTV. In this case, you still have to pay the \$719.40 every year to have that \$5000 in loan. So the rate becomes:

719.40 / 5000 = 14.388% + 3.5% = 17.888% (so every dollar you put towards this loan gives you a risk free return of at least 17.888%)

The closer you get to paying it off, the higher the effective rate of each additional dollar used to pay it off.

• Stubble
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• Age: 45
• Location: Portland, OR
##### Re: PMI Payoff ROI?
« Reply #2 on: December 17, 2013, 12:04:10 PM »
Treat PMI as a hair-on-fire emergency. You will not be able to reliably beat the cost of it using investment.

#### Heart of Tin

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##### Re: PMI Payoff ROI?
« Reply #3 on: December 17, 2013, 04:58:29 PM »
Treat PMI as a hair-on-fire emergency. You will not be able to reliably beat the cost of it using investment.

I would agree if myllanac weren't already paying PMI. As it is, we have been asked to evaluate the eventual return on an extra \$720 paid to principle in January.

First of all myllanac, I'm really confused by your post. You estimate that an extra \$720 paid to principle in January will eliminate PMI a year early. For that to be true, your amortization schedule would need to show that only about \$840 is paid to principle between May of 2018 and April of 2019. That does not make sense in the context of a 30 year fixed rate, equal payment mortgage. The rest of your numbers are equally suspicious.

Below is a link to a Google Docs spreadsheet that I made up to find the annual internal rate of return on this extra payment. There are two sheets, one assumes that combined payment to principle and interest is equal every year. The other snowballs the PMI payments as extra payments to principle once PMI is eliminated. If myllanac initially pays \$600.25 to principle and interest every month and myllanac's house is worth \$121,800, then the annualized IRR of the two payment methods is 4.195% and 4.1914% over about 20 years for the equal payment method and the snow ball method, respectively. For the equal payment method this is a total return of \$1,757.26 on the original \$720 paid as \$119.90 in 2019 and \$1,637.46 in 2037 for a total ROI of 144%. For the snowball method this is a total return of \$1,724.35 on the original \$720 paid entirely in 2035 for a total ROI of 139.5%.

Here's my Google Docs spreadsheet. Don't change any cells that aren't grey, and don't reduce the payments to less than \$600.25:

#### myllanac

• Posts: 9
• Age: 34
• Location: Grand Rapids, MI
##### Re: PMI Payoff ROI?
« Reply #4 on: December 18, 2013, 05:11:55 AM »
Thanks for the replies!

@nawhite: Thanks for that analysis. You are almost right on the amount we have left until 80% LTV, about \$11,000. The \$60 PMI payment on a monthly basis (average monthly principle payment is \$211 between now and 80%) represents a load of over 28%. Does that mean every \$211 in extra principle payments returns 28% (2.33% annualized: .28 / 12 = .0233) in future PMI not having to be paid on future principle below 80% LTV?

@Heart of Tin: Thanks for making the spreadsheet. I plan to do the "snowball method" you mentioned. My mortgage is not through my regular credit union, so synced with my biweekly paychecks I have half my monthly principal, interest, and escrow amount transferred from my checking to the mortgage bank's checking. When PMI comes off, that checking account will accrue \$60 a month that I will apply to the principal once or twice a year. Transferring biweekly also means I can make an extra principal payment (worth my entire PITI amount) once a year. Eventually, as our income grows, I'd like to pay my 30-year like a 15-year, mostly for the peace of mind of being home-free. It also represents \$6,456 less in annual expenses and puts financial independence that much closer.

So the big-picture point I'm getting is that there is literally nothing (when taking risk into account) that can return more than paying extra on mortgage principal to get out of PMI. We'll now frame our principal balance to 80% as a loan. This will motivate us to throw every extra dollar at principal.

#### Grindin' Away

• Posts: 20
• Location: Midwest
##### Re: PMI Payoff ROI?
« Reply #5 on: December 18, 2013, 08:28:26 AM »

This is a great thread for visualizing what each dollar does.  Great question, and great replies.

Just to play Devil's Advocate, wouldn't each dollar applied to Principal only provide a 3.5% return on investment until the PMI is gone completely?  Would a better strategy be investing the money until the amount is large enough to wipe out the PMI?  I know investment returns are not guaranteed, but it seems like the dollars spent towards mortgage principal can be used more efficiently until you're able to get to 20% equity.

Please let me know if there is a flaw in my logic.

Thanks

#### nawhite

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##### Re: PMI Payoff ROI?
« Reply #6 on: December 18, 2013, 09:37:29 AM »
Just to play Devil's Advocate, wouldn't each dollar applied to Principal only provide a 3.5% return on investment until the PMI is gone completely?  Would a better strategy be investing the money until the amount is large enough to wipe out the PMI?  I know investment returns are not guaranteed, but it seems like the dollars spent towards mortgage principal can be used more efficiently until you're able to get to 20% equity.

Brilliant! You took the idea to its conclusion and have changed my thinking about how I will handle this. I agree with your analysis and am surprised I never thought of it. *nawhite sulks off to his bank's website to implement your plan and save... about \$300 over the next year*

I love it when I'm convinced by someone here that there is a better way to optimize things. It makes the engineer brain in me all happy.

#### myllanac

• Posts: 9
• Age: 34
• Location: Grand Rapids, MI
##### Re: PMI Payoff ROI?
« Reply #7 on: December 18, 2013, 01:27:48 PM »
So, which is it? Is \$1 invested in principal reduction worth the 3.5% interest rate, or 3.5% plus the effective 0.6% for PMI, or something higher (treating the balance to 80% LTV as a loan and the PMI in the numerator)?

My credit union checking account pays 3% on up to \$15,000. We earn about \$12-15 a month that way. The monthly interest on \$11,000 is about \$28, which pays for almost half the PMI cost.

Would it be better to save up ~\$11,000 in our 3% checking account and then pay it all at once, or to pay down the principal with recurring one-time payments?

#### Heart of Tin

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##### Re: PMI Payoff ROI?
« Reply #8 on: December 18, 2013, 04:22:24 PM »
So, which is it? Is \$1 invested in principal reduction worth the 3.5% interest rate, or 3.5% plus the effective 0.6% for PMI, or something higher (treating the balance to 80% LTV as a loan and the PMI in the numerator)?

My credit union checking account pays 3% on up to \$15,000. We earn about \$12-15 a month that way. The monthly interest on \$11,000 is about \$28, which pays for almost half the PMI cost.

Would it be better to save up ~\$11,000 in our 3% checking account and then pay it all at once, or to pay down the principal with recurring one-time payments?

Since the account only accrues interest at 3% whereas the debt accrues interest at 3.5%, you should put the money towards principle immediately as opposed to parking it in the checking account.

The \$1 in principle is worth more the 3.5% since it will allow you to put some of the PMI payments towards principle thus eliminating the debt sooner and reducing the interest paid over the lifetime of the loan. Normally paying extra to principle is only worth the interest rate on the debt, but in your case you are eliminating a few PMI payments making your return higher.

#### nawhite

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##### Re: PMI Payoff ROI?
« Reply #9 on: December 18, 2013, 07:36:32 PM »
So, which is it? Is \$1 invested in principal reduction worth the 3.5% interest rate, or 3.5% plus the effective 0.6% for PMI, or something higher (treating the balance to 80% LTV as a loan and the PMI in the numerator)?

My credit union checking account pays 3% on up to \$15,000. We earn about \$12-15 a month that way. The monthly interest on \$11,000 is about \$28, which pays for almost half the PMI cost.

Would it be better to save up ~\$11,000 in our 3% checking account and then pay it all at once, or to pay down the principal with recurring one-time payments?

You're right, I should clarify. My way of looking at it oversimplified things a little bit too much I think.

Basically, if I have \$1000 extra I can put towards something, I have 3 options.
1. Put it towards the mortgage.
2. Put it towards some other account forever (401k, IRA, taxable, etc)
3. Put it towards some very accessible account (taxable, checking, maybe CD's if you did it right) until I have enough to bring my LTV to 80% and then put that much towards the mortgage.

Originally we were deciding between options 1 and 2 and I said that option 1 was almost always better especially when you get close to 80% LTV.

However now that Grindin' Away has introduced option 3, in my case, it beats option 1 because I can beat 3.5% in the short term (through a higher ESPP contribution in my case) and then use the difference to get to 80% LTV faster. In your case, if the only easily accessible account you trust is your checking account at 3%, then you'd be better off paying down the mortgage in the short term and getting the 3.5% there instead. If you think you can get a risk-adjusted return in the stock market (or some other asset class you can withdraw from at will) higher than 3.5% over the time period you'd be saving it for, then you can make the gamble. But, the safe bet is pay down the mortgage.

#### clarkm04

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• Posts: 182
##### Re: PMI Payoff ROI?
« Reply #10 on: December 19, 2013, 07:46:16 AM »
My wife and I are in the same boat as OP.

3.875% 30 yr. fixed

~ \$55 per month in PMI

We closed in June and should get the principal paid down to eliminate PMI in 1 to 1 1/2 years from now. We looked at investing in the stock market but with such a short time horizon to withdraw to pay down the mortgage, it just doesn't make sense for us to risk a crush or even a stock downturn and prolong the PMI.

Our strategy is to aggressively pay down the principal monthly while maintaining a minimal emergency fund and making appropriate contributions to our 403B plans.

#### myllanac

• Posts: 9
• Age: 34
• Location: Grand Rapids, MI
##### Re: PMI Payoff ROI?
« Reply #11 on: December 20, 2013, 08:55:50 AM »
I revisited this and think I have it framed properly:
- If we do nothing extra, we will reach 78% LTV and the lender will cancel PMI in February 2019. At that point we will have paid \$4,560 in PMI.
- Between estimated appreciation and direct payments, I believe we can reach 80% LTV by this time next year. If the house can appraise for at least \$139,000 (4.45% annualized growth in 24 months of owning the home), and we have the balance paid down to at least \$110,500, we will have reached 80% LTV. According to our area realty association, metro prices are up 10% from a year ago (when we bought). Even if next year is flat, that still gets us 4.45% annualized over a 24-month period.
- For an investment of \$3,200 in one year's time (\$3,000 in principal payments and \$200 appraisal fee), we would avoid \$3,900 in PMI over a period of five years (January 2015 to February 2019); this is a 111% total return, 22.2% annualized. Not bad.

#### Heart of Tin

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##### Re: PMI Payoff ROI?
« Reply #12 on: December 20, 2013, 04:56:43 PM »
- For an investment of \$3,200 in one year's time (\$3,000 in principal payments and \$200 appraisal fee), we would avoid \$3,900 in PMI over a period of five years (January 2015 to February 2019); this is a 111% total return, 22.2% annualized. Not bad.

January of 2015 – February of 2019 is only four years and one month, not five years. Thus, you are able to snowball only 49 payments, not 60, reducing PMI by \$2,937.55, not \$3,900. That might sound like a bad deal (paying \$3,200 to eliminate \$2,900), but the PMI payments are not your only return. You will also save at least \$3,000 in future payments realized at the end of your mortgage. To find, approximately, how much you will save at that time compute 3000*(1+.035/12)^n where n is the number of months between when you pay \$3,000 to principle and the end of your mortgage based on the size of your future payments (an exact formula for Excel would be: =ROUNDDOWN(NPER(.035/12, payment, -3000*(1+.035/12)^months), 0)*payment-FV(0.035/12, ROUNDDOWN(NPER(0.035/12, payment, -3000*(1+0.035/12)^months), 0), -payment, 3000*(1+.035/12)^months)*(1+0.035/12) where payment is your future payment amount and months is the number of months until you pay off the mortgage with the \$3,000 principle payment in 2015). Your annualized effective internal rate of return  can then be computed using guess and check (or a financial calculator or Excel). The internal rate of return on the \$3,200 will exceed the annualized effective rate on the loan, 3.557%.

However, you are snowballing your PMI payments into your mortgage, so your overall profit will be even bigger than above but realized entirely at the end of your mortgage. Consequently, your annualized effective internal rate of return will be lower than as is implied by the calculations in the last paragraph, perhaps significantly so. This is because the PMI payments are rolled into the mortgage earning 3.5% nominal annual return compounded monthly for the period of time between their occurrence and the end of the mortgage. Since 3.5% nominal annual return is less than the initial interest on the principle payment, the internal rate of return will be lower than above. However, your profit will be bigger because the payments to principle will further reduce the overall amount of interest paid on the mortgage. Less interest paid means fewer payments or a smaller last payment at the end of the mortgage.

As nawhite pointed out, the marginal return on money put towards principle later in the life of the PMI will be larger than money contributed sooner. However, the money contributed sooner has a longer period over which to compound, making the later payments worth less than the sooner payments in the broader context of the entire loan. In the example of 9.5% interest when \$11,900 is owed versus 17.9% interest when only \$5,000 is owed, paying off the \$11,900 will take more than twice as long as paying off the \$5,000 at the same payment level and interest rate. So, as \$1 is worth \$1.20 at the end of two years at 9.5% interest whereas \$1 is only worth \$1.18 at the end of one year at 17.9% interest, the earlier payment is actually worth more despite what you might conclude from looking only at the marginal rates as quoted above. Remember, money has a time value. It is not always correct to directly compare money or interest rates from different times.

BTW, it looks like you applied the formula r = R/t where R is the rate of return over the entire period, t is the time in years (you seem to have used 5 years), and r is the annualized return. That formula is for investments where you invest a certain amount, wait for a while, then profit all at once at the end of the time period. You cannot apply that here for two reasons. First, the PMI payments that you’re avoiding occur in small monthly installments over five years instead of all at once. Second, the time period is much longer than five years since you will not realize the profit until the end of your mortgage unless you plan on using the marginal equity for a loan between the time the marginal equity is realized and the time that it would have been realize if not for the \$3,000 payment to principle and \$200 reappraisal. In short, this formula is not valid in this situation.

#### FastStache

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• Posts: 257
##### Re: PMI Payoff ROI?
« Reply #13 on: January 13, 2014, 09:38:52 PM »
I've been thinking about calculating this myself lately. Does anyone take into account any tax savings on carrying PMI and mortgage interest? I'm not saying this is a reason not to pay it down, but should be factored into the decision.

#### Cromacster

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##### Re: PMI Payoff ROI?
« Reply #14 on: January 14, 2014, 06:25:59 AM »
Sort of off topic, but sorta not.

With PMI, does the 20% account for a newly appraised value?  Ie I put 10% down, but over a year or two the appraised value went up 8 or 9% so now I owe less than 80% of the value?

#### Grindin' Away

• Posts: 20
• Location: Midwest
##### Re: PMI Payoff ROI?
« Reply #15 on: January 14, 2014, 06:47:20 AM »

My understanding is that if you have an official appraisal, and work with your mortgage lender, they will calculate a new equity percentage to end your PMI payments.  You will more than likely have to choose a third party appraisal company off of a list that your mortgage lender provides.

Some mortgage companies do it a little different than others, and make you get to 22% equity before the PMI is removed instead of just the 20% that would have been needed up front.  I would ask your mortgage lender the following direct questions:

-What percentage of equity do I need to stop paying PMI
-Can I hire an appraisal company on my own, or do you have a list for me to choose from
-Ok, I am getting a new appraisal, please let me know exactly what I need to do to have a new equity percentage calculated

Then, you basically have to be pretty confident that the new appraisal value will get you to the equity percentage you need to stop paying PMI, or at least very close.  Otherwise it isn't worth the money and hassle.

#### nawhite

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##### Re: PMI Payoff ROI?
« Reply #16 on: January 14, 2014, 10:27:30 AM »
Sort of off topic, but sorta not.

With PMI, does the 20% account for a newly appraised value?  Ie I put 10% down, but over a year or two the appraised value went up 8 or 9% so now I owe less than 80% of the value?

That is what I thought too but I called my mortgage company and they said that I could only include the appreciation if the appreciation was due to improvements I had made to the property, not appreciation due to a rising market. Sounds like it is different from one company to the next. Worth asking about.

#### FastStache

• Bristles
• Posts: 257
##### Re: PMI Payoff ROI?
« Reply #17 on: January 14, 2014, 11:03:08 AM »
Sort of off topic, but sorta not.

With PMI, does the 20% account for a newly appraised value?  Ie I put 10% down, but over a year or two the appraised value went up 8 or 9% so now I owe less than 80% of the value?

That is what I thought too but I called my mortgage company and they said that I could only include the appreciation if the appreciation was due to improvements I had made to the property, not appreciation due to a rising market. Sounds like it is different from one company to the next. Worth asking about.

This is the same info I got too. It needs to be improvements I make. I wonder if I could make a cheap improvement like a fence and then get a new appraisal taking into account the new property value.

#### anneinpdx

• Posts: 20
##### Re: PMI Payoff ROI?
« Reply #18 on: January 14, 2014, 02:21:36 PM »
Sort of off topic, but sorta not.

With PMI, does the 20% account for a newly appraised value?  Ie I put 10% down, but over a year or two the appraised value went up 8 or 9% so now I owe less than 80% of the value?

In my PMI cancellation document, my servicer says that I either need to get the loan to <80% of original home value or the loan needs to be >2 years old and <75% new appraised value.  I had hoped to get a reappraisal this year given the market appreciation but no cigar.

Ugh, PMI.  We put down 20% when we bought the house but got a low appraisal when refinancing to lock in at 3.375 last year.  The interest savings nets us a couple hundred dollars even with the PMI but that extra hundred dollars/month really grates especially when my realtor friends were surprised by the selected comps.

Thanks for the discussion.  We had been funneling our savings into extra retirement contributions but maybe it makes sense to knock off the PMI first.  It will drop in 2 years if I do nothing or maybe next year with a reappraisal.

#### Heart of Tin

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##### Re: PMI Payoff ROI?
« Reply #19 on: January 14, 2014, 07:49:24 PM »
I've been thinking about calculating this myself lately. Does anyone take into account any tax savings on carrying PMI and mortgage interest? I'm not saying this is a reason not to pay it down, but should be factored into the decision.

The PMI deduction expired on December 31, 2013, and hasn't yet been reinstated. Congress may retroactively extend PMI deductibility by the end of the year, but then again they might not. Check your numbers both with and without the PMI deduction just in case. Also keep in mind that PMI deductibility is phased out for an AGI between \$100,000 and \$110,000 under 2013 guidelines.

I think you should definitely include tax benefits when calculating the return on early principle payments to eliminate PMI. Just remember that deducting mortgage interest requires you to itemize instead of taking the standard deduction (\$6,100 for an individual in 2013, \$12,200 for married couples filing jointly). Only the amount of interest paid above the standard deduction minus your other itemized deductions should be counted as a return, so including a tax benefit in the later years of a mortgage is probably inappropriate unless you have enough deductions to itemize without the mortgage interest deduction. If you have a relatively modest mortgage at a decent rate you might not benefit from a mortgage deduction at all, even in the first year when interest payments are at their largest, especially if you are married filing jointly.