Author Topic: All Cash v Mortgage; even if I invest annual savings of NOT having a mortgage?  (Read 12441 times)

Widjet

  • 5 O'Clock Shadow
  • *
  • Posts: 14
All the literature I see that gives the pros and cons of purchasing a house all cash versus using a mortgage looks at it as a static equation. They all start and end with the assumption, which I will simplify here to make my point, that you have an amount (we'll say $500,000) that you can either use to buy a house or you can use a mortgage in which case you can then invest the $500k lump sum and earn a return on that which exceeds the interest rate on the loan (adjusting for tax savings of deductible mortgage interest) and therefore a mortgage is better.   OK, but what they don't look at is the fact that with the loan you will have an annual P+I+Insurance debt service of $37k a year (15 year loan) to $21k a year (30 year loan).  If you don't have the loan then you can invest that $37k each year, every year for the next 15 years.  Use an investment return calculator and at 15 years the returns more or less wash on the one-time lump sum and the annual investment scenarios. Increase the time span and the annual investment actually exceeds the one-time investment because all the interest you are not paying is additional capital that gets invested.  I get that you "may" also benefit from an interest rate play with a fixed payment loan and that with leverage from a mortgage you are putting less of your money at risk should housing go south, but just looking at this from the investment perspective, why does the literature not account for the investment returns you can otherwise make off the debt service you won't have to pay? Do they just assume people will spend the savings on fancy cars and vacations? Or perhaps I am missing something.   

rubybeth

  • Handlebar Stache
  • *****
  • Posts: 1401
  • Location: Midwest
I don't totally get what you are asking; can you clarify?

If you invest $500k and just leave it in the market with an average of 5% returns, accounting for inflation, for either 15 or 30 years, here's what you get (with no additional annual investment), using a simple compound interest calculator (compounding 12 times a year, just because):

http://www.moneychimp.com/calculator/compound_interest_calculator.htm

15 years: 1,056,851.97
30 years: 2,233,872.16

You still have to pay taxes and insurance even if you have a fully paid off house...??



BarkyardBQ

  • Pencil Stache
  • ****
  • Posts: 666
All the literature I see that gives the pros and cons of purchasing a house all cash versus using a mortgage looks at it as a static equation. They all start and end with the assumption, which I will simplify here to make my point, that you have an amount (we'll say $500,000) that you can either use to buy a house or you can use a mortgage in which case you can then invest the $500k lump sum and earn a return on that which exceeds the interest rate on the loan (adjusting for tax savings of deductible mortgage interest) and therefore a mortgage is better.   OK, but what they don't look at is the fact that with the loan you will have an annual P+I+Insurance debt service of $37k a year (15 year loan) to $21k a year (30 year loan).  If you don't have the loan then you can invest that $37k each year, every year for the next 15 years.  Use an investment return calculator and at 15 years the returns more or less wash on the one-time lump sum and the annual investment scenarios. Increase the time span and the annual investment actually exceeds the one-time investment because all the interest you are not paying is additional capital that gets invested.  I get that you "may" also benefit from an interest rate play with a fixed payment loan and that with leverage from a mortgage you are putting less of your money at risk should housing go south, but just looking at this from the investment perspective, why does the literature not account for the investment returns you can otherwise make off the debt service you won't have to pay? Do they just assume people will spend the savings on fancy cars and vacations? Or perhaps I am missing something.   

Your loan rate and stock return rate should not be the same. If your loan rate is 3.5% and the average return on the stock market is 7%.

Assuming you have to put 20% down (doesn't matter though).

Investing 400000, into VTSAX for 15 years will net you $1,103,000, while paying off 400,000 of a mortgage will cost you $270,000 in interest at 3.5%.

In 15 years, you would have $1,103,000 plus a paid off house worth approx 600k or $1,700,000.

If you bought the house with cash and invested 37k/year (producing $977,000) with paid off house worth approx 600k, should net about $1,577,000.

$130,000 difference for 15 years. For 30 years, you would see a 7 figure spread.

Stocks are about time in the market, the longer they play, the more they compound. Real estate is about protecting a dollar over a life time, except the last mortgage payment costs considerably less than the first after inflation. Debt service doesn't matter when the compounding interest from investment return (stocks) is better than another (low rate mortgage).

« Last Edit: March 29, 2016, 03:29:12 PM by BackyarBQ »

Widjet

  • 5 O'Clock Shadow
  • *
  • Posts: 14
Exactly, so that is the case for using the mortgage.  Using your same calculator (thanks for the link) let's run my other scenario.

The annual P+I (we'll just keep it to this) is $42,156 a year for the 15 yr fixed loan (at 3.25%) and $28,645 a year for the 30 year (at 4%).  So go to the moneychimp calculator and use those respective amounts as the current principal and the annual addition and you get:

15 years:  $1,050,945
30 years:  $2,122,100

Those basically seem like a wash to me.  I realize there are other factors at play such as tax savings (although you can get Peased out of those).  Some of those other factors cut the other way too such as loan costs.   

My point was that if you read an article on the subject of buying a property all cash versus using a mortgage and investing the proceeds they never mention investing the P+I savings from not having a mortgage.  What strikes me is that when you do the benefit of the mortgage/invest approach is much less evident.   

Widjet

  • 5 O'Clock Shadow
  • *
  • Posts: 14
All the literature I see that gives the pros and cons of purchasing a house all cash versus using a mortgage looks at it as a static equation. They all start and end with the assumption, which I will simplify here to make my point, that you have an amount (we'll say $500,000) that you can either use to buy a house or you can use a mortgage in which case you can then invest the $500k lump sum and earn a return on that which exceeds the interest rate on the loan (adjusting for tax savings of deductible mortgage interest) and therefore a mortgage is better.   OK, but what they don't look at is the fact that with the loan you will have an annual P+I+Insurance debt service of $37k a year (15 year loan) to $21k a year (30 year loan).  If you don't have the loan then you can invest that $37k each year, every year for the next 15 years.  Use an investment return calculator and at 15 years the returns more or less wash on the one-time lump sum and the annual investment scenarios. Increase the time span and the annual investment actually exceeds the one-time investment because all the interest you are not paying is additional capital that gets invested.  I get that you "may" also benefit from an interest rate play with a fixed payment loan and that with leverage from a mortgage you are putting less of your money at risk should housing go south, but just looking at this from the investment perspective, why does the literature not account for the investment returns you can otherwise make off the debt service you won't have to pay? Do they just assume people will spend the savings on fancy cars and vacations? Or perhaps I am missing something.   

Your loan rate and stock return rate should not be the same. If your loan rate is 3.5% and the average return on the stock market is 7%.

Assuming you have to put 20% down (doesn't matter though).

Investing 400000, into VTSAX for 15 years will net you $1,103,000, while paying off 400,000 of a mortgage will cost you $270,000 in interest at 3.5%.

In 15 years, you would have $1,103,000 plus a paid off house worth approx 600k or $1,700,000.

If you bought the house with cash and invested 37k/year (producing $977,000) with paid off house worth approx 600k, should net about $1,577,000.

$130,000 difference for 15 years. For 30 years, you would see a 7 figure spread.

Stocks are about time in the market, the longer they play, the more they compound. Real estate is about protecting a dollar over a life time, except the last mortgage payment costs considerably less than the first after inflation.

I do appreciate the inflation hedge a fixed rate, long term mortgage offers. No one knows what the future will bring but that could be a very valuable asset down the road (but it is not a sure bet).   I also was overly generous with the tax savings used to calculate the annual P+I payments in my original post.  If you ignore the tax benefits altogether and just use the P+I numbers with the interest rates I assumed (which are roughly market at the moment) then the numbers come out much closer.   In fact as you increase the time-line enough it flips ... which is not a profound conclusion on my part, it's just a fact that adding an annual addition each year at the levels involved here at some point overcomes the magic of compounding that initial $500k lump sum.

BarkyardBQ

  • Pencil Stache
  • ****
  • Posts: 666
I do appreciate the inflation hedge a fixed rate, long term mortgage offers. No one knows what the future will bring but that could be a very valuable asset down the road (but it is not a sure bet).   I also was overly generous with the tax savings used to calculate the annual P+I payments in my original post.  If you ignore the tax benefits altogether and just use the P+I numbers with the interest rates I assumed (which are roughly market at the moment) then the numbers come out much closer.   In fact as you increase the time-line enough it flips ... which is not a profound conclusion on my part, it's just a fact that adding an annual addition each year at the levels involved here at some point overcomes the magic of compounding that initial $500k lump sum.

Are you arguing that if you continue investing $37k/year and increase this investment past a defined term, that you will eventually have more than a lump sump that never got new additions? Obviously if you continue to infuse cash into an investment, you are not only getting the compound rate, but you adding to the existing investment, that's definitely going to outpace a lump sum no matter what. Sorry if I've misunderstood your statement, but it looks like you either need to define a set dollar amount, a term, or both.

What are the tax benefits you're referring to?
« Last Edit: March 29, 2016, 03:45:46 PM by BackyarBQ »

Widjet

  • 5 O'Clock Shadow
  • *
  • Posts: 14
I do appreciate the inflation hedge a fixed rate, long term mortgage offers. No one knows what the future will bring but that could be a very valuable asset down the road (but it is not a sure bet).   I also was overly generous with the tax savings used to calculate the annual P+I payments in my original post.  If you ignore the tax benefits altogether and just use the P+I numbers with the interest rates I assumed (which are roughly market at the moment) then the numbers come out much closer.   In fact as you increase the time-line enough it flips ... which is not a profound conclusion on my part, it's just a fact that adding an annual addition each year at the levels involved here at some point overcomes the magic of compounding that initial $500k lump sum.

Are you arguing that if you continue investing $37k/year and increase this investment past a defined term, that you will eventually have more than a lump sump that never got new additions? Obviously if you continue to infuse cash into an investment, you are not only getting the compound rate, but you adding to the existing investment, that's definitely going to outpace a lump sum no matter what.

Sorry if I've misunderstood your statement.

Apologies, I shouldn't even have mentioned that. It was an aside. I am trying to keep the analysis straightforward as calculating the tax savings gets complicated given the decreasing amount of interest paid each year, Pease limitations, an individuals tax brackets (Federal & State).  So for the sake of argument I am ignoring that.  Likewise there are other factors that could weight the other way, for example you could be in a flood zone and a mortgage would require several thousand dollars a year in flood insurance you could forgo without a mortgage.

So keeping it simple it is investing the lump sum versus investing the annual savings each year.   As the mortgage products are 15 and 30 year it makes sense to keep those as the time horizon since once they end, you no longer have to pay P+I.  The two scenarios from the above posts give you:

Mortgage & One Time Investment:
15 years: 1,056,851.97
30 years: 2,233,872.16

No Mortgage & Invest the "savings" each year:
15 years:  $1,050,945
30 years:  $2,122,100

That's basically a wash right?


 

BarkyardBQ

  • Pencil Stache
  • ****
  • Posts: 666
I guess. $100k wash? Still the compounding on that initial lump sum will outpace any DCA dumped in over 30 years.

Widjet

  • 5 O'Clock Shadow
  • *
  • Posts: 14
I guess. $100k wash? Still the compounding on that initial lump sum will outpace any DCA dumped in over 30 years.

$100k in 30 years will be the cost of a candy bar right?  I'm not trivializing the amount but on an annual return basis over 30 years a $100k difference doesn't strike me as the "slam dunk" he pundits usually proffer for the mortgage versus cash case when it comes to buying a home.   

BarkyardBQ

  • Pencil Stache
  • ****
  • Posts: 666
I guess. $100k wash? Still the compounding on that initial lump sum will outpace any DCA dumped in over 30 years.

$100k in 30 years will be the cost of a candy bar right?  I'm not trivializing the amount but on an annual return basis over 30 years a $100k difference doesn't strike me as the "slam dunk" he pundits usually proffer for the mortgage versus cash case when it comes to buying a home.

My favorite thing to say is you can't eat your drywall, but you could sell some stocks to survive if needed... but that has been debated all over this forum and elsewhere.

Midwest

  • Handlebar Stache
  • *****
  • Posts: 1358
I guess. $100k wash? Still the compounding on that initial lump sum will outpace any DCA dumped in over 30 years.

$100k in 30 years will be the cost of a candy bar right?  I'm not trivializing the amount but on an annual return basis over 30 years a $100k difference doesn't strike me as the "slam dunk" he pundits usually proffer for the mortgage versus cash case when it comes to buying a home.

My favorite thing to say is you can't eat your drywall, but you could sell some stocks to survive if needed... but that has been debated all over this forum and elsewhere.

HELOC solves the eating drywall problem.  If you are comparing investing in stocks versus  a 30 year mortgage, stocks should win.

If you have enough in other stock investments, I believe a more appropriate comparison may be the bond rate versus the mortgage rate.  I have no bonds because my mortgage is effectively a liquid bond (via the Heloc).

beltim

  • Magnum Stache
  • ******
  • Posts: 2964
When I run the numbers using your $42k annual mortgage payment I get:

Pay cash: end up with $1,059,339 plus house
Have mortgage: end up with $1,379,515 plus house
using a 7% return.

Using a more accurate market return over the long term, 9.5%, I get:
Pay cash: end up with $1,287,454 plus house
Have mortgage: end up with $1,950,661 plus house

That's a 50% difference, which is quite substantial.  The numbers would be even more favorable for a 30-year mortgage.  Again, using your calculated $28645 annual payment:

Pay cash: end up with $4,287,798 plus house
Have mortgage: end up with $7,610,156 plus house

That's a 77% difference.

Widjet

  • 5 O'Clock Shadow
  • *
  • Posts: 14
I guess. $100k wash? Still the compounding on that initial lump sum will outpace any DCA dumped in over 30 years.

$100k in 30 years will be the cost of a candy bar right?  I'm not trivializing the amount but on an annual return basis over 30 years a $100k difference doesn't strike me as the "slam dunk" he pundits usually proffer for the mortgage versus cash case when it comes to buying a home.

My favorite thing to say is you can't eat your drywall, but you could sell some stocks to survive if needed... but that has been debated all over this forum and elsewhere.

This is exactly my point. My question isn't an either or, because forgoing the mortgage means that each month you have an additional $3,000 in your budget.  That is the $3k that you otherwise would have paid to service the P+I on your mortgage.  You are going to invest that $3k each month.  So you will own both the drywall and have stocks you can sell to buy food.  No need to develop a taste for drywall at all.     

Widjet

  • 5 O'Clock Shadow
  • *
  • Posts: 14
When I run the numbers using your $42k annual mortgage payment I get:

Pay cash: end up with $1,059,339 plus house
Have mortgage: end up with $1,379,515 plus house
using a 7% return.

Using a more accurate market return over the long term, 9.5%, I get:
Pay cash: end up with $1,287,454 plus house
Have mortgage: end up with $1,950,661 plus house

That's a 50% difference, which is quite substantial.  The numbers would be even more favorable for a 30-year mortgage.  Again, using your calculated $28645 annual payment:

Pay cash: end up with $4,287,798 plus house
Have mortgage: end up with $7,610,156 plus house

That's a 77% difference.

Good point, the return matters. I think your numbers on the pay cash side are off though no?  I get $1,249,802 for the 15 year 7% return scenario and $1,574,226 at 9.5% return.  Which is still less than your mortgage numbers (which I calculate the same).  Likewise on the 30 year I get a bit higher at $5,131,125 on the cash side but still that is considerably less than the mortgage side so I do see your point. 

However, is that what it comes down to? You need to get 7.5% or better returns over the long term to make it work? Because that is a very different story than I read in the literature where you "come out ahead" if you can just earn a return that beats the interest rate on your mortgage (i.e., something in the 4 to 5 % return range).   

beltim

  • Magnum Stache
  • ******
  • Posts: 2964
When I run the numbers using your $42k annual mortgage payment I get:

Pay cash: end up with $1,059,339 plus house
Have mortgage: end up with $1,379,515 plus house
using a 7% return.

Using a more accurate market return over the long term, 9.5%, I get:
Pay cash: end up with $1,287,454 plus house
Have mortgage: end up with $1,950,661 plus house

That's a 50% difference, which is quite substantial.  The numbers would be even more favorable for a 30-year mortgage.  Again, using your calculated $28645 annual payment:

Pay cash: end up with $4,287,798 plus house
Have mortgage: end up with $7,610,156 plus house

That's a 77% difference.

Good point, the return matters. I think your numbers on the pay cash side are off though no?  I get $1,249,802 for the 15 year 7% return scenario and $1,574,226 at 9.5% return.  Which is still less than your mortgage numbers (which I calculate the same).  Likewise on the 30 year I get a bit higher at $5,131,125 on the cash side but still that is considerably less than the mortgage side so I do see your point. 

However, is that what it comes down to? You need to get 7.5% or better returns over the long term to make it work? Because that is a very different story than I read in the literature where you "come out ahead" if you can just earn a return that beats the interest rate on your mortgage (i.e., something in the 4 to 5 % return range).

Here's my year by year calculation:
Year  Balance
1   42156
2   87262.92
3   135527.3244
4   187170.2371
5   242428.1537
6   301554.1245
7   364818.9132
8   432512.2371
9   504944.0937
10   582446.1803
11   665373.4129
12   754105.5518
13   849048.9404
14   950638.3662
15   1059339.052

BarkyardBQ

  • Pencil Stache
  • ****
  • Posts: 666
However, is that what it comes down to? You need to get 7.5% or better returns over the long term to make it work? Because that is a very different story than I read in the literature where you "come out ahead" if you can just earn a return that beats the interest rate on your mortgage (i.e., something in the 4 to 5 % return range).

The spread between the mortgage rate and market returns are important. While your mortgage rate is fixed, market returns are not, and have the potential for much greater returns.

beltim

  • Magnum Stache
  • ******
  • Posts: 2964
However, is that what it comes down to? You need to get 7.5% or better returns over the long term to make it work? Because that is a very different story than I read in the literature where you "come out ahead" if you can just earn a return that beats the interest rate on your mortgage (i.e., something in the 4 to 5 % return range).

Obviously the better the stock return the bigger the difference.  But even at the 5% range, without accounting for any tax savings, over a 15 year mortgage, the difference in wealth is ~14%.

I don't think I'd risk it if I thought I'd only make 5% too much risk for too little reward.  At 7%, though, the difference is 30% in wealth for a 15 year mortgage and 40% for a 30 year mortgage.  That's more significant.  And since the long-term market return is closer to 9.5%, the average result of this strategy is much better at 51 and 77% (and that 77% is >$3 million).
« Last Edit: March 29, 2016, 05:05:36 PM by beltim »

Widjet

  • 5 O'Clock Shadow
  • *
  • Posts: 14
However, is that what it comes down to? You need to get 7.5% or better returns over the long term to make it work? Because that is a very different story than I read in the literature where you "come out ahead" if you can just earn a return that beats the interest rate on your mortgage (i.e., something in the 4 to 5 % return range).

The spread between the mortgage rate and market returns are important. While your mortgage rate is fixed, market returns are not, and have the potential for much greater returns.

Right but you need to remember that I am taking the "savings" from not having to service the debt and investing it.   What I am gathering (and thanks to the posters for the help) is that you need to achieve returns above 7%.  I don't want to start a whole debate about achievable returns and past performance maybe not reflecting future returns ... suffice it to say those are returns on the high side and would require an aggressive exposure. 

Widjet

  • 5 O'Clock Shadow
  • *
  • Posts: 14
When I run the numbers using your $42k annual mortgage payment I get:

Pay cash: end up with $1,059,339 plus house
Have mortgage: end up with $1,379,515 plus house
using a 7% return.

Using a more accurate market return over the long term, 9.5%, I get:
Pay cash: end up with $1,287,454 plus house
Have mortgage: end up with $1,950,661 plus house

That's a 50% difference, which is quite substantial.  The numbers would be even more favorable for a 30-year mortgage.  Again, using your calculated $28645 annual payment:

Pay cash: end up with $4,287,798 plus house
Have mortgage: end up with $7,610,156 plus house

That's a 77% difference.

Good point, the return matters. I think your numbers on the pay cash side are off though no?  I get $1,249,802 for the 15 year 7% return scenario and $1,574,226 at 9.5% return.  Which is still less than your mortgage numbers (which I calculate the same).  Likewise on the 30 year I get a bit higher at $5,131,125 on the cash side but still that is considerably less than the mortgage side so I do see your point. 

However, is that what it comes down to? You need to get 7.5% or better returns over the long term to make it work? Because that is a very different story than I read in the literature where you "come out ahead" if you can just earn a return that beats the interest rate on your mortgage (i.e., something in the 4 to 5 % return range).

Here's my year by year calculation:
Year  Balance
1   42156
2   87262.92
3   135527.3244
4   187170.2371
5   242428.1537
6   301554.1245
7   364818.9132
8   432512.2371
9   504944.0937
10   582446.1803
11   665373.4129
12   754105.5518
13   849048.9404
14   950638.3662
15   1059339.052

I was just using that calculator an earlier poster had linked to.  Input 42156 as the initial investment and use 42156 for the annual addition. Leave it set to compound once a year and then vary the interest rate and period as we've been doing.  So with 7% and 15 years it give a result = $   
1,249,802.52.   It doesn't show the year by year though so I can't compare to your results. Let me look for another calculator. 

beltim

  • Magnum Stache
  • ******
  • Posts: 2964
When I run the numbers using your $42k annual mortgage payment I get:

Pay cash: end up with $1,059,339 plus house
Have mortgage: end up with $1,379,515 plus house
using a 7% return.

Using a more accurate market return over the long term, 9.5%, I get:
Pay cash: end up with $1,287,454 plus house
Have mortgage: end up with $1,950,661 plus house

That's a 50% difference, which is quite substantial.  The numbers would be even more favorable for a 30-year mortgage.  Again, using your calculated $28645 annual payment:

Pay cash: end up with $4,287,798 plus house
Have mortgage: end up with $7,610,156 plus house

That's a 77% difference.

Good point, the return matters. I think your numbers on the pay cash side are off though no?  I get $1,249,802 for the 15 year 7% return scenario and $1,574,226 at 9.5% return.  Which is still less than your mortgage numbers (which I calculate the same).  Likewise on the 30 year I get a bit higher at $5,131,125 on the cash side but still that is considerably less than the mortgage side so I do see your point. 

However, is that what it comes down to? You need to get 7.5% or better returns over the long term to make it work? Because that is a very different story than I read in the literature where you "come out ahead" if you can just earn a return that beats the interest rate on your mortgage (i.e., something in the 4 to 5 % return range).

Here's my year by year calculation:
Year  Balance
1   42156
2   87262.92
3   135527.3244
4   187170.2371
5   242428.1537
6   301554.1245
7   364818.9132
8   432512.2371
9   504944.0937
10   582446.1803
11   665373.4129
12   754105.5518
13   849048.9404
14   950638.3662
15   1059339.052

I was just using that calculator an earlier poster had linked to.  Input 42156 as the initial investment and use 42156 for the annual addition. Leave it set to compound once a year and then vary the interest rate and period as we've been doing.  So with 7% and 15 years it give a result = $   
1,249,802.52.   It doesn't show the year by year though so I can't compare to your results. Let me look for another calculator.

Oh, I see.  The initial investment should be 0.  Your calculation has 16 years of contributions instead of 15.  It also assumes a return on that year's contributions, whereas mine didn't, but that's a much smaller difference.

Widjet

  • 5 O'Clock Shadow
  • *
  • Posts: 14
However, is that what it comes down to? You need to get 7.5% or better returns over the long term to make it work? Because that is a very different story than I read in the literature where you "come out ahead" if you can just earn a return that beats the interest rate on your mortgage (i.e., something in the 4 to 5 % return range).

Obviously the better the stock return the bigger the difference.  But even at the 5% range, without accounting for any tax savings, over a 15 year mortgage, the difference in wealth is ~14%.

I don't think I'd risk it if I thought I'd only make 5% too much risk for too little reward.  At 7%, though, the difference is 30% in wealth for a 15 year mortgage and 40% for a 30 year mortgage.  That's more significant.  And since the long-term market return is closer to 9.5%, the average result of this strategy is much better at 51 and 77% (and that 77% is >$3 million).

That's where I am coming out in my thinking too.   Although the numbers may be a little tighter than that depending on whether the calculation on the cash side is correct.   

Telecaster

  • Handlebar Stache
  • *****
  • Posts: 2425
  • Location: Seattle, WA
Right but you need to remember that I am taking the "savings" from not having to service the debt and investing it.   What I am gathering (and thanks to the posters for the help) is that you need to achieve returns above 7%.  I don't want to start a whole debate about achievable returns and past performance maybe not reflecting future returns ... suffice it to say those are returns on the high side and would require an aggressive exposure.

Not really.  I don't have the numbers in front of me, but IIRC since about the 1920s, each rolling 30-year period has returned 7.5% or greater (14% I believe is the high).  7.5% is a perfectly reasonable estimate on the low side.   


Widjet

  • 5 O'Clock Shadow
  • *
  • Posts: 14
I tired to respond to the post above but there was too much quote.  Thanks for the correct on the calculator.  If I set the initial amount to zero and keep the annual addition, interest rate (7%) and period (15 years) the same I get 1,133,492.79. In reality you probably wouldn't wait until the end of each year to invest the full amount.  So the calculator produces a very accurate result for the "one-time" mortgage scenario but it probably on the low side for the "annual addition" cash scenario.  The difference wouldn't be so great though that the poster's original point wouldn't still be true.  Returns > than 7.5% favor the mortgage scenario.  Still that is an aggressive return expectation.  It is not at all what I read in the literature where the suppose a much lower rate of 4 - 5% return favors a mortgage.

beltim

  • Magnum Stache
  • ******
  • Posts: 2964
However, is that what it comes down to? You need to get 7.5% or better returns over the long term to make it work? Because that is a very different story than I read in the literature where you "come out ahead" if you can just earn a return that beats the interest rate on your mortgage (i.e., something in the 4 to 5 % return range).

Obviously the better the stock return the bigger the difference.  But even at the 5% range, without accounting for any tax savings, over a 15 year mortgage, the difference in wealth is ~14%.

I don't think I'd risk it if I thought I'd only make 5% too much risk for too little reward.  At 7%, though, the difference is 30% in wealth for a 15 year mortgage and 40% for a 30 year mortgage.  That's more significant.  And since the long-term market return is closer to 9.5%, the average result of this strategy is much better at 51 and 77% (and that 77% is >$3 million).

That's where I am coming out in my thinking too.   Although the numbers may be a little tighter than that depending on whether the calculation on the cash side is correct.

On the other hand, 28 of the last 60 15-year periods have seen an annualized return on the S&P 500 higher than 12.8%.  If you had an above-average 15 year period, say at 15% (achieved 18 out of 60 periods), the difference would be an amazing $1.7 million over those 15 years.  So don't forget that there's an upside that's better than the long-term average, just as you shouldn't forget that there's a downside (17 of the last 60 15-year periods have had annual returns under 8% annually).

Widjet

  • 5 O'Clock Shadow
  • *
  • Posts: 14
Right but you need to remember that I am taking the "savings" from not having to service the debt and investing it.   What I am gathering (and thanks to the posters for the help) is that you need to achieve returns above 7%.  I don't want to start a whole debate about achievable returns and past performance maybe not reflecting future returns ... suffice it to say those are returns on the high side and would require an aggressive exposure.

Not really.  I don't have the numbers in front of me, but IIRC since about the 1920s, each rolling 30-year period has returned 7.5% or greater (14% I believe is the high).  7.5% is a perfectly reasonable estimate on the low side.   

Fair enough.  It seems you would not want to invest it in bonds though. 

beltim

  • Magnum Stache
  • ******
  • Posts: 2964
Right but you need to remember that I am taking the "savings" from not having to service the debt and investing it.   What I am gathering (and thanks to the posters for the help) is that you need to achieve returns above 7%.  I don't want to start a whole debate about achievable returns and past performance maybe not reflecting future returns ... suffice it to say those are returns on the high side and would require an aggressive exposure.

Not really.  I don't have the numbers in front of me, but IIRC since about the 1920s, each rolling 30-year period has returned 7.5% or greater (14% I believe is the high).  7.5% is a perfectly reasonable estimate on the low side.   

Fair enough.  It seems you would not want to invest it in bonds though.

No.  Not at typical mortgage rates and current bond interest rates.  If you had locked in a 30 year mortgage at 4% and bond rates rose to 8%, then it'd be much more attractive.

Widjet

  • 5 O'Clock Shadow
  • *
  • Posts: 14
Thank you Beltim.  I appreciate the help in thinking this through. 

Drifterrider

  • Handlebar Stache
  • *****
  • Posts: 1118
I would think the better question is:  If I buy a house for cash, do I have enough "other" cash to live on?

Yes, you can always sell stocks but no, you don't always make a profit.  I think living in debt is a bad idea.  Most of us have to at some point because few of us can afford a house outright. 

So, if I had the money to pay off my mortgage and still have enough money to live on if I were to lose my job, I'd pay off the mortgage.  You can't eat your drywall but you can't live in a stock portfolio either.  Also, I believe the average time to foreclose on a house (actually take possession) is about one year. 

YMMV

brooklynguy

  • Handlebar Stache
  • *****
  • Posts: 2204
  • Age: 40
Returns > than 7.5% favor the mortgage scenario.  Still that is an aggressive return expectation.  It is not at all what I read in the literature where the suppose a much lower rate of 4 - 5% return favors a mortgage.

It sounds like you may still be under the misimpression that you expressed in your earlier post (quoted below) that the "literature" in incorrect in asserting that you will always come out ahead through leveraged-investing-via-mortgage as long as your net return on investments exceeds the net cost of your mortgage loan:

However, is that what it comes down to? You need to get 7.5% or better returns over the long term to make it work? Because that is a very different story than I read in the literature where you "come out ahead" if you can just earn a return that beats the interest rate on your mortgage (i.e., something in the 4 to 5 % return range).

But it definitely is true that all you need to come out ahead is for your investment returns to outpace your mortgage loan interest (in each case, net of all taxes, transaction costs, etc.).  To see why this is necessarily true, forget the specific arithmetic for a moment, and think about it conceptually in the abstract:  in your original example, in the "take out a mortgage loan" scenario, you are going to obtain a loan and invest all the proceeds of that loan in a pile of investments.  If that pile of investments earns a return that perfectly matches the mortgage loan's interest rate, then you can use that pile of investments to service the mortgage loan (i.e., you can pay the monthly mortgage payments out of the investment account), and the pile of investments will be depleted to exactly zero when the final mortgage payment is made at maturity (and throughout the life of the mortgage loan, you could have been making the same additional investments using your other sources of cash flow that you could have been making had you not obtained the mortgage loan).  Any rate of return on the pile of investments that is higher than the mortgage's interest rate would leave a positive balance in that investment account at the final maturity of the loan.  So, the hurdle for the "mortgage" scenario to come out ahead of the "no mortgage" scenario is in fact as low as the "literature" has asserted.  As discussed in this thread, most real-life investment options (like the stock market) have variable rates of return, but for purposes of the illustrative, simplified fixed-rate modeling you were doing in your examples, any assumed investment rate of return in excess of the mortgage interest rate (again, for simplicity, ignoring tax and similar considerations) will cause the "mortgage" scenario to come out ahead.

dogboyslim

  • Pencil Stache
  • ****
  • Posts: 512
I made a quick scenario.

I assumed buying a 500k property, 500k currently invested, Cash additions available of $2,690.76 per month for either investment or mortgage payment.
Further I assumed a Mortgage of $400k.  15 year rate of 2.65% and 30 year at 3.5%
I assumed equity increases of 3% per year and market return of 5%.

Given these scenarios, I get the following net worth results at 15 and 30 years:
Code: [Select]
Scenario: 15 years 30 years
Cash          $1,505,922.97 $3,477,160.22
15 Yr Loan $1,629,197.44 $3,737,725.94
30 Yr Loan $1,366,795.49 $3,763,142.94


Daleth

  • Handlebar Stache
  • *****
  • Posts: 1204
All the literature I see that gives the pros and cons of purchasing a house all cash versus using a mortgage looks at it as a static equation. They all start and end with the assumption, which I will simplify here to make my point, that you have an amount (we'll say $500,000) that you can either use to buy a house or you can use a mortgage in which case you can then invest the $500k lump sum and earn a return on that which exceeds the interest rate on the loan (adjusting for tax savings of deductible mortgage interest) and therefore a mortgage is better.   OK, but what they don't look at is the fact that with the loan you will have an annual P+I+Insurance debt service of $37k a year (15 year loan) to $21k a year (30 year loan).  If you don't have the loan then you can invest that $37k each year, every year for the next 15 years.

This is a minor point in terms of the cost, but you need insurance regardless of whether you have a mortgage. It's just stupid not to have it. If somebody slips on your sidewalk or gets bitten by your dog or whatever, and sues you, your insurer will hire and pay for lawyers to defend you, saving you easily tens of thousands of bucks. The Mustachian thing to do isn't forego insurance, but to set the deductible as high as possible.

So let's say that you have $35k a year to invest over 15 years, because you bought insurance. So what? If you'd gotten a mortgage you would have $500k to invest right up front. That will take you a lot farther a lot faster than $35k a year for 15 years.

zephyr911

  • Magnum Stache
  • ******
  • Posts: 3620
  • Age: 42
  • Location: Northern Alabama
  • I'm just happy to be here. \m/ ^_^ \m/
    • Pinhook Development LLC
I have yet to EVER see a thread on this topic that doesn't vastly overcomplicate the topic with shitloads of extraneous data (real or notional) and wildly unnecessary calculations.

If you are in a phase of life where maximum return on investment is the highest priority, pay just enough down to avoid exorbitant PMI or other costs. I did the math and elected to pay 10% down because even with a little PMI, the ROI on any further down payment was lower than my typical investment return.

If you are in, or if you enter, a phase of your life where reducing total lifestyle cost, risk, and taxes (via lower income requirements) are more important, take all the cash you earned by investing the difference, and pay off the loan.

undercover

  • Pencil Stache
  • ****
  • Posts: 990
This thread is basically hinting at a topic that has been beat to death over and over again. The short answer is that it doesn't matter - do what you want. While you may have more money investing, you may have more peace of mind when the house is paid off sooner. Others will have other perfectly justifiable justifications for their decisions. To each their own. As zephyr said, it also depends on where you are in life.

Not that this school of thought is a completely rational way of looking at it, but there are a SHIT load worse things you could be putting your money towards rather than paying off a house or investing. People seem to forget that here and just argue about the nitty gritty details day in and day out. The point is that you're going to turn out fine either way because you're here on this forum asking a thoughtful question about where to put your money responsibly rather than buy a new car or take an expensive vacation.

arkcom

  • 5 O'Clock Shadow
  • *
  • Posts: 1
Where does the $500k lump sum come from?  If you liquidate assets, you could have a big tax bill eat a chunk out of it, tilting the equation even further towards getting a mortgage.

Widjet

  • 5 O'Clock Shadow
  • *
  • Posts: 14
Thanks as well for the other thoughtful posts.  I have come around to the later views expressed here.  Principal payments on a loan aren't your money.  But in the cash scenario, that same amount of money you have locked-up in the house isn't your money either ... in the sense that you can't use it for another investment to earn a return.  So the mortgage analysis is whether you can earn more on that principle on an after-tax basis than the tax savings adjusted interest rate you are paying on the loan.

Daleth

  • Handlebar Stache
  • *****
  • Posts: 1204
Where does the $500k lump sum come from?  If you liquidate assets, you could have a big tax bill eat a chunk out of it, tilting the equation even further towards getting a mortgage.

Great point.

zephyr911

  • Magnum Stache
  • ******
  • Posts: 3620
  • Age: 42
  • Location: Northern Alabama
  • I'm just happy to be here. \m/ ^_^ \m/
    • Pinhook Development LLC
Thanks as well for the other thoughtful posts.  I have come around to the later views expressed here.  Principal payments on a loan aren't your money.  But in the cash scenario, that same amount of money you have locked-up in the house isn't your money either ... in the sense that you can't use it for another investment to earn a return.  So the mortgage analysis is whether you can earn more on that principle on an after-tax basis than the tax savings adjusted interest rate you are paying on the loan.
I may be quibbling over semantics, but of course it's your money. Paying down principal doesn't change your net worth and is therefore best described as an internal transfer between two of your accounts.

I support the simplified view that it all comes down to (tax-adjusted) ROI, subject to the caveats above. Many people do elect to pay off a mortgage right before retiring for those reasons, and I may do so myself... it depends on a lot of things.

LadyMaWhiskers

  • Stubble
  • **
  • Posts: 137
  • Location: SF Bay, peninsula
I have yet to EVER see a thread on this topic that doesn't vastly overcomplicate the topic with shitloads of extraneous data (real or notional) and wildly unnecessary calculations.

If you are in a phase of life where maximum return on investment is the highest priority, pay just enough down to avoid exorbitant PMI or other costs. I did the math and elected to pay 10% down because even with a little PMI, the ROI on any further down payment was lower than my typical investment return.

If you are in, or if you enter, a phase of your life where reducing total lifestyle cost, risk, and taxes (via lower income requirements) are more important, take all the cash you earned by investing the difference, and pay off the loan.

Word up! I'm aiming to elliminate mortgage debt, not because the future wealth math favors it, but because that's half my monthly budget, and it would be rad to reduce my income requirements ASAP.