# Mortgage: first house & picking APR vs. points

Home Mortgages and Home Buying Mortgage: first house & picking APR vs. points

•  Wulfman
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I a similar question, but wonder if its better to invest or pay for points.  I am getting a physician loan and each point I pay down brings my rate down about 0.2%.  Ultimately paying a point still means the interest rate is applied to the full loan, its not as if now your loan is worth the total minus the cost of the point payment.  So, even with a break even of 8-10 years, and keeping the home for the long term, would it be better to take that money and invest it?

I did some quick math and if I take my payment per point, and calculate what it saves me in mortgage interest over the duration of the loan, its pretty much the same as having invested it with an annual return of 4.0%, which also happens to be what the mortgage interest rate it.

So is buying a point basically like investing that money at the purchased interest rate of the loan for the duration?  Or is there a point where the rate of return on your point investment, and the amount saved in mortgage payments diverge.  I may be missing something.

ENT Doc
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Joined: 01/14/2017

I a similar question, but wonder if its better to invest or pay for points.  I am getting a physician loan and each point I pay down brings my rate down about 0.2%.  Ultimately paying a point still means the interest rate is applied to the full loan, its not as if now your loan is worth the total minus the cost of the point payment.  So, even with a break even of 8-10 years, and keeping the home for the long term, would it be better to take that money and invest it?

I did some quick math and if I take my payment per point, and calculate what it saves me in mortgage interest over the duration of the loan, its pretty much the same as having invested it with an annual return of 4.0%, which also happens to be what the mortgage interest rate it.

So is buying a point basically like investing that money at the purchased interest rate of the loan for the duration?  Or is there a point where the rate of return on your point investment, and the amount saved in mortgage payments diverge.  I may be missing something.

Click to expand…

Take a look at this spreadsheet (1st tab) and change to your parameters in the green boxes.  Break-even is not a good way of looking at points.  This shows you the return on the points decision given interest deduction or no interest deduction.  It shows your hurdle rate per year, so if you’re going to be in the home X years your return on the points decision will be Y.  If you think you can beat it elsewhere in your marginal account and asset allocation given the expected duration of living there then don’t do the points.

Other risks of buying points is if you move or if rates tank and you are able to refinance to a lower rate in the no points scenario.

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Wulfman
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Thanks, that is an excellent chart.  That reply is Next-Level!

CordMcNally
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Joined: 01/03/2017

Thanks, that is an excellent chart.  That reply is Next-Level!

Click to expand…

All of @ENT_Doc’s spreadsheets are next level!

“But investing isn’t about beating others at their game. It’s about controlling yourself at your own game.”
― Benjamin Graham, The Intelligent Investor

Liked by Tim, Lordosis
Wulfman
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After a brief review I have some questions.  Ill use an example.

If I have a 100,000 loan and each point is 1000, which drops my rate 0.18% each time (which is true my case where I go from 4.125 to 3.575 after 3 points).  Then after 30 years on the mortgage I go from a total interest paid of \$74,474, to \$70,730 after 1 point.  Consider that a savings of \$3,744 over 30 years for my \$1000 payment.  This amounts to about the same as a 4.5% rate of return compounded annually had I just invested that \$1000 (not factoring taxes).

However, your sheet shows that at 30 years that \$1000 point will have rewarded me 12.85% (or 11.24% without tax savings).  I think the difference comes from the early losses that your chart does not average out over time.  While its a rad chart, it looks like it overstates the return when you look at the real rate of the cost of the point over the full 30 years.  Again, I may be missing something, but it looks like these points can be highly overrated.  There is nothing bad about 4.5%, but then there is the added risk that I don’t actually break zero unless I hold the home 9 years which makes it not worth it to me.

ENT Doc
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This amounts to about the same as a 4.5% rate of return compounded annually had I just invested that \$1000 (not factoring taxes).

Click to expand…

This is the problem with your calculation.  The \$1,000 isn’t “growing” to \$3,744 over the course of 30 years.  In financial terms, it would not be appropriate to make -1000 your present value (money invested) and 3744 as your future value with 30 periods.  The reason is because you are not accounting for the time value of money and aren’t matching the cash flow benefits to the rate of return.  In simpler terms, you are benefiting from the additional saved cash flow every month given your \$1,000 “investment”.  The cash flows stop after 30 years.  The \$3,744 is just the cumulative total of cash flows, which is relatively meaningless.  Money given earlier has more value and can be invested.  Cash later has less value since it doesn’t have the opportunity to be invested.

First, you have to find out the payment difference between the interest rates on a \$100,000 loan.  The do nothing option has an interest rate of 4.125% APR, or 4.125%/12 = 0.34375% per month.  There are 360 months in a 30 year loan, so your payment function (=PMT in excel) will yield a payment of \$484.65.  Do the same thing for the reduced rate (4.125% – 0.18% = 3.945%) and you get \$474.25, for a positive cash flow difference of \$10.40.  You can also get this by dividing \$3,744 total interest saved by 360 months.

In order to find the rate of return you do the rate formula in Excel:

=rate(360,10.40,-1000,0,0) = 1.012%

where 360 are the periods (months), 10.40 is your positive cash flow per period, -1000 is your initial investment (negative because cash is going away from you), 0 is future value (you have no lump sum coming to you or going away at the end of this – it’s just one negative cash flow at the beginning and 360 positive cash flows), and 0 as the last term indicates that the cash flow comes to you at the end of the period, as it does with mortgages.

The rate of 1.012% is a PERIODIC RATE, or monthly rate of return.  In order to get the annualized rate of return, as we are used to thinking about things for stock/bond returns, you need to calculate the APY (annual percentage yield) from the periodic rate.  It just so happens that there’s a formula for that!

APY = (1 + Periodic Rate)^Periods per Year – 1 = (1.001012)^12 – 1 = 12.847% or 12.85%

All the above stuff is embedded in the Excel spreadsheet and the math is automatically done, but it helps to see the breakdown to really understand it.  Hope it helps.

Liked by LIFO, Tim
Wulfman
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Thanks for the explanation, and the chart.  I will keep an eye out for the other spreadsheets you have shared.  Very helpful.

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LIFO
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This amounts to about the same as a 4.5% rate of return compounded annually had I just invested that \$1000 (not factoring taxes).

Click to expand…

This is the problem with your calculation.  The \$1,000 isn’t “growing” to \$3,744 over the course of 30 years.  In financial terms, it would not be appropriate to make -1000 your present value (money invested) and 3744 as your future value with 30 periods.  The reason is because you are not accounting for the time value of money and aren’t matching the cash flow benefits to the rate of return.  In simpler terms, you are benefiting from the additional saved cash flow every month given your \$1,000 “investment”.  The cash flows stop after 30 years.  The \$3,744 is just the cumulative total of cash flows, which is relatively meaningless.  Money given earlier has more value and can be invested.  Cash later has less value since it doesn’t have the opportunity to be invested.

First, you have to find out the payment difference between the interest rates on a \$100,000 loan.  The do nothing option has an interest rate of 4.125% APR, or 4.125%/12 = 0.34375% per month.  There are 360 months in a 30 year loan, so your payment function (=PMT in excel) will yield a payment of \$484.65.  Do the same thing for the reduced rate (4.125% – 0.18% = 3.945%) and you get \$474.25, for a positive cash flow difference of \$10.40.  You can also get this by dividing \$3,744 total interest saved by 360 months.

In order to find the rate of return you do the rate formula in Excel:

=rate(360,10.40,-1000,0,0) = 1.012%

where 360 are the periods (months), 10.40 is your positive cash flow per period, -1000 is your initial investment (negative because cash is going away from you), 0 is future value (you have no lump sum coming to you or going away at the end of this – it’s just one negative cash flow at the beginning and 360 positive cash flows), and 0 as the last term indicates that the cash flow comes to you at the end of the period, as it does with mortgages.

The rate of 1.012% is a PERIODIC RATE, or monthly rate of return.  In order to get the annualized rate of return, as we are used to thinking about things for stock/bond returns, you need to calculate the APY (annual percentage yield) from the periodic rate.  It just so happens that there’s a formula for that!

APY = (1 + Periodic Rate)^Periods per Year – 1 = (1.001012)^12 – 1 = 12.847% or 12.85%

All the above stuff is embedded in the Excel spreadsheet and the math is automatically done, but it helps to see the breakdown to really understand it.  Hope it helps.

Click to expand…

Points essentially function as an annuity.  You give a fixed amount (\$1000 up front) in return for periodic payments (\$10.40 monthly discount or ~\$124/yr) for a defined period of time (30 years).  As you collect your cash on a recurrent basis, the principal erodes.  In order to sustain the cash flow for the defined period, the principal will need to compound at 12.85%.  At the end, you will have collected \$3,744 in payments and the principal will be zero after the 360th payment.

ENT Doc
Participant
Status: Physician
Posts: 3500
Joined: 01/14/2017
This amounts to about the same as a 4.5% rate of return compounded annually had I just invested that \$1000 (not factoring taxes).

Click to expand…

This is the problem with your calculation.  The \$1,000 isn’t “growing” to \$3,744 over the course of 30 years.  In financial terms, it would not be appropriate to make -1000 your present value (money invested) and 3744 as your future value with 30 periods.  The reason is because you are not accounting for the time value of money and aren’t matching the cash flow benefits to the rate of return.  In simpler terms, you are benefiting from the additional saved cash flow every month given your \$1,000 “investment”.  The cash flows stop after 30 years.  The \$3,744 is just the cumulative total of cash flows, which is relatively meaningless.  Money given earlier has more value and can be invested.  Cash later has less value since it doesn’t have the opportunity to be invested.

First, you have to find out the payment difference between the interest rates on a \$100,000 loan.  The do nothing option has an interest rate of 4.125% APR, or 4.125%/12 = 0.34375% per month.  There are 360 months in a 30 year loan, so your payment function (=PMT in excel) will yield a payment of \$484.65.  Do the same thing for the reduced rate (4.125% – 0.18% = 3.945%) and you get \$474.25, for a positive cash flow difference of \$10.40.  You can also get this by dividing \$3,744 total interest saved by 360 months.

In order to find the rate of return you do the rate formula in Excel:

=rate(360,10.40,-1000,0,0) = 1.012%

where 360 are the periods (months), 10.40 is your positive cash flow per period, -1000 is your initial investment (negative because cash is going away from you), 0 is future value (you have no lump sum coming to you or going away at the end of this – it’s just one negative cash flow at the beginning and 360 positive cash flows), and 0 as the last term indicates that the cash flow comes to you at the end of the period, as it does with mortgages.

The rate of 1.012% is a PERIODIC RATE, or monthly rate of return.  In order to get the annualized rate of return, as we are used to thinking about things for stock/bond returns, you need to calculate the APY (annual percentage yield) from the periodic rate.  It just so happens that there’s a formula for that!

APY = (1 + Periodic Rate)^Periods per Year – 1 = (1.001012)^12 – 1 = 12.847% or 12.85%

All the above stuff is embedded in the Excel spreadsheet and the math is automatically done, but it helps to see the breakdown to really understand it.  Hope it helps.

Click to expand…

Points essentially function as an annuity.  You give a fixed amount (\$1000 up front) in return for periodic payments (\$10.40 monthly discount or ~\$124/yr) for a defined period of time (30 years).  As you collect your cash on a recurrent basis, the principal erodes.  In order to sustain the cash flow for the defined period, the principal will need to compound at 12.85%.  At the end, you will have collected \$3,744 in payments and the principal will be zero after the 360th payment.

Click to expand…

I’d modify this.  It’s more like a single premium immediate annuity with no death benefit.  The principal isn’t a loan to be eroded in a traditional sense.  The premium, or \$1000, is lost immediately never to be seen again, like a SPIA.  Points are a gamble based on duration of cash flow benefits.