Mortgage Like a Bond

Paid Off Mortgage is Equivalent to a…Perpetuity?…Bond?…Dividend Paying Stock?

In Financial Analysis, Mortgage Snowball by Gen Y Finance Guy25 Comments

Having a fully paid mortgage sure does get a bad wrap around personal finance circles. I constantly see arguments about money being super cheap and that paying off the mortgage will lead to a loss of the interest tax deduction. I won’t argue that rates are historically cheap and that eliminating your mortgage will lead to eliminating the tax deduction.

First, remember that with the tax deduction you get 30 cents on the dollar. So, although this is a step up from renting (in my opinion, and situation dependent), if you don’t have to pay interest, why do it?

Why doesn’t anyone talk about a fully paid mortgage as a bond substitute? Or compare it to that of a dividend paying stock (at least synthetically). Look I am not suggesting you pay off your mortgage in lieu of investing in the stock market. I know the conventional wisdom is to pay the minimum payment for the 30 year term and invest the difference. But there are two problems with this:

  1. Most people won’t invest the difference…that is just stating the facts.
  2. What about asset allocation?

If you are going to allocate some of those funds to bonds anyways, why not consider early payment of the mortgage as a contender for that bond allocation? The rule of thumb for your bond allocation is 100 minus your age. So, at 29 this says I should be allocating 71% to riskier assets (those with potential for higher returns) and 29% to safer assets like bonds.

PeerStreet

I have been thinking about this a lot lately especially in light of the fact that my wife and I plan to have our mortgage paid off in another 6 years as a part of our plan to kill it in 7 years and 3 months. Of course I want to make sure this doesn’t make up more than 25% of our total net worth, but I think I can make a logical argument that it has a place in my asset allocation model (and potentially yours).

Let’s not ignore the fact that a mortgage that is paid in full does represent a freed up cash flow.

A Paid Off Mortgage Is Like A Perpetuity (but not really)

It probably makes sense to first define what a Perpetuity is. So, here is the definition from Wikipedia:


A perpetuity is an annuity that has no end, or a stream of cash payments that continues forever. There are few actual perpetuities in existence (the United Kingdom (UK) government has issued them in the past; these are known and still trade as consols). Real estate and preferred stock are among some types of investments that affect the results of a perpetuity, and prices can be established using techniques for valuing a perpetuity.[1] Perpetuities are but one of the time value of money methods for valuing financial assets. Perpetuities are a form of ordinary annuities.


As the definition above states, a perpetuity is one of the time value of money methods for valuing a financial asset. I know that many if not most that read this blog do not have the finance background that I have, but hang in there with me. I don’t plan to get overly in depth here, but I do want to make sure those unfamiliar with these concepts do get a high level primer.

The time value of money is based on the simple idea that a dollar today is worth more than a dollar tomorrow due to the potential earnings from interest or other investment returns. You may be more familiar with the term present value, which essentially discounts future cash flows based on some assumed rate of return an converts it to its worth in today’s dollars.

Let’s get back to explaining how a paid off mortgage is like a perpetuity.

If you pay off your mortgage, you no longer have a mortgage payment, which essentially creates a new annual cash flow equal to what used to be your mortgage payments. And this cash flow by definition never ends.

Real Life Example

We always like to use real life examples here on the GYFG blog. Let’s use my primary residence as the example. As I have mentioned many times on the blog, my wife and I bought our current residence for $370,000, and the original loan for the 5/5 ARM was $352,000 @ 3.625%. Our current principal + interest payment is $1,605.30/month or $19,263.60/year.

Therefore when we officially pay off our mortgage we will be freeing up $19,263.60/year in free cash flow.

How do we value a Perpetuity?

That is a great question. The present value formula for a perpetuity is:

PV = A / r

Where PV = Present Value of the Perpetuity, A = the Amount of the periodic payment, and r = yield, discount rate or interest rate.

That said the value of this stream of cash flows from paying off the mortgage would be as follows:

PV = 19,263.60 / 3.625%

Or

PV = $531,409

Translation: Paying off your mortgage would be equivalent to investing $531,40 that pays you an annual return of 3.625% or $19,263.60 forever.

But this is only part right. Because this would assume no terminal value for the house itself in the event it was sold.

A Paid Off Mortgage Is Like A Bond (but not really)

I don’t think I have to go through a mathematical exercise to cover why a paid off mortgage is like a bond but different. It’s like a bond in that your annual savings of $19,263.60 would act as a 5.21% coupon payment.

Annual CF / Investment (purchase price)

$19,263.60 / $370,000 = 5.21%

But this is only part right as well. Because with a bond, at maturity, you would get the face value of your investment back. In this case the face value would be your original purchase of $370,000. Bonds can go up and down in value based on current interest rates, but at maturity there is no such thing as appreciation or depreciation, just face value.

Then what can we compare a paid off mortgage too?

A Paid Off Mortgage Is Like A Dividend Paying Stock

Okay, a paid off mortgage can be compared to that of a dividend paying stock. I would argue that it is a synthetic dividend paying stock.

Your dividend is equal to the formula we used above to compute the coupon payment for a bond.

Annual CF / Investment (purchase price)

$19,263.60 / $370,000 = 5.21%

The kicker is that you also get appreciation. Let’s be conservative and say that we can expect a 3% appreciation rate for real estate here in Southern California. Let’s also assume a 30 year holding period to line it up with that of a mortgage.

Over 30 years the $370,000 house at 3% appreciation increases in value to $898,087.

Let’s not forget 30 years of $19,263.60 in annual cash flow or $577,908. We will ignore investing this cash for this particular post to keep this simple.

This puts the total return at $1,105,995 or 300%.

[Calculation] (Appreciated Value – Purchase price) + (CF * 30)

= (898,087 – 370,000) + (577,908)

= $1,105,995

You have essentially 4X’ed your money in 30 years (898,087+577,908).

This is equivalent to a Compounded Return of 7.9%.

Now remember this assumes no investment of that annual CF savings of $19,263.60. For us, I can guarantee you that will not be the case, we will find ways to put that money to work in other investments.

So what say you? Does this shine a different light on paying off the mortgage early? Do you agree with the math?

-Gen Y Finance Guy




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Comments

  1. Hmmm, a great alternative to paying off your mortgage without using your money is living Ina rental income property, of course, you are sacrificing space but you are also living cheap:). In this situation, you don’t have to worry whether to pay off your mortgage because you aren’t. This reduces your cost of living and focuses your money on other opportunities.

    I think a lot of people have exercised this option including you:). A great and smart way to pay off your mortgage without having to worry about the pros and cons so much.

    Thanks for building the arguments and comparisons to bonds an dividend stocks, stimulates my thinking.

    1. Author

      Great point Tracy! We have absolutely used rental income from the room we rent out to pay down the mortgage faster, it’s makes it pretty easy.

      Just another perspective!

  2. I guess this is where our thoughts diverge! Good points, but the appreciation is the same whether you have a mortgage or not so don’t think it should be included in the calculations here.

    What about the risk of this “bond”? I just posted this comment on Financial Samurai and would be curious to get your take as well:

    Most people in California don’t pay for earthquake insurance because it is so expensive. But if they are using their mortgage as a forced savings account, it is a very risky one. It can all be wiped out.

    If you have earthquake insurance and have the house paid off, do you think it’s going to be easy to collect if there is a big earthquake? I would much rather have a bank in my corner that owns 70% of the house and has a team of lawyers.

    Curious to hear if you think there is anything to this? It’s not limited to just earthquakes, but any big disaster or difficult insurance claim.

    I know you are shooting to keep your net worth in your house to less than 25%, but the average homeowner has almost all their wealth in their home – the standard advice of paying down the mortgage as fast as possible is a horrible idea for them. I think your <25% net worth decision is the important nugget of advice here and maybe you should write a post that focuses on it.

    1. Author

      Brian – You really keyed in on a critical piece of this strategy. In any financial decision it is really important to think risk management first. What could go wrong? Just like you would never put all your money into a single stock, nor should you put all of your net worth in your house.

      I agree for the majority that this is not a strategy that I would advise for them if their net worth already includes 25% or more due to their primary residence. I also would not recommend it to someone that isn’t first already maxing out tax advantage retirement accounts and making other investment allocations. I also would not recommend it for anyone that doesn’t have at least 6 months of living expenses in the bank. And lastly I would not advise it to anyone that does not have at least another couple of years in other investable assets that if in a pinch they could liquidate to cover living expenses beyond their 6 months of savings.

      You are also correct, the value of the home will appreciate regardless of paying it off early. However, I would argue that a large portion of that appreciation if left mortgaged will get eaten up by the interest expense. For this example, at 3% appreciation the increase in value is approximately $578K, based on my own strategy (including multiple refinances) we will save around $200K in interest expense. Therefore my net appreciation would be closer to $378K. But that is a bit besides your point, and I understand that.

      Even if you exclude the appreciation, the paid off mortgage still works out to be a 5.21% return. I should also point out once again that I look at my mortgage as my bond allocation. I have no interest in buying 30 year treasury bonds paying less than 3% when I can put that into my mortgage instead. Those that don’t believe in portfolio allocation and would be comfortable with 100% stocks or 100% rental real estate, this probably isn’t for you. But I am personally trying to build a diversified net worth of stocks, real estate, gold, P2P lending, bonds (my paid of mortgage as a substitute).

      Re: Earthquakes and Risk

      Again, investing and capital allocation is all about risk management. It’s true that we have earthquakes to deal with in California. Your right most people don’t pay for earthquake insurance and we don’t either. We do have the added benefit that my father in law is a designer and contractor that would likely be able to re-build our house for far less than replacement costs should such an event happen in our lifetime (could happen today or 100 years from now). No one really knows.

      It is the same reason I continue to invest even though I realize that WWWIII could cause nuclear proliferation. It could happen…But to me you could ask the same question about investing in cashflow real estate out of state. What happens if natural disaster hits and your rental is destroyed and it’s not covered by insurance? Or what happens if another (worse) financial crisis hits and your rentals go un-rented and your liquidity dried up before you can sell the properties and they go to foreclosure?

      More importantly your questions bring up an even more important point. There are rarely ever absolutes in answering questions in personal finance.

      I think that is why it is important to approach this from a portfolio approach. Make sure you don’t have too much risk concentration.

      You are right, this probably deserves an entire post describing who and who should not consider paying their mortgage off early.

      1. Wow, lot’s to respond to!

        “I would argue that a large portion of that appreciation if left mortgaged will get eaten up by the interest expense” – not sure I understand this, but to me it boils down to this: if you look at paying off the mortgage early + appreciation and compare it to paying the minimum, you have to include the appreciation on paying the minimum. And they cancel each other out. You might be saying refinancing changes it, but only if when you refinance you pull cash out.

        A 5.21% bond strategy is good, especially considering all the caveats for who should do this. But from there it all comes down to how you price the risk.

        Your portfolio approach is spot on so there isn’t too much concentrated risk. Which is exactly what most people have who are trying to pay off their mortgage early. It’s just a narrative that is far too common and only applies to a small percentage of people, not everyone.

        Same goes for my rental properties. There are risks and I am not a doomsday, worse case scenario type of worrier. But I’m also really spreading out the risk (each <10% net worth and going to stay that way, not be paid off early).

        If there is a large insurance claim needed? I buy into the idea that it is better to have a bank that is in the fight with you. For example, if I have 33% equity and the bank owns 67%. The bank has a team of lawyers and the know how to get the claim done if it is contested. Compare this to if I own 100% and I personally have to take the insurance company to court – ponying up lawyer fees that can drag out for a long time.

        I of course have no experience with that and hope I never will. But I do buy into the argument that it is less risky when you have a partner (the large bank) who is on your side.

        1. Author

          Hey Brian – sorry for the late reply.

          I agree that when comparing a home with a paid off mortgage to one that is paid in alignment of the 30 year term that the appreciation would be the same regardless. What I was trying to say is that between paying the mortgage off early and through several strategic refinances, based on our own 7 year plan to put the mortgage to bed that we will have saved $200K in interest expenses. Contrary the person who got a mortgage and paid the minimum payment for 30 years would have paid an additional $200K. So, on a net basis the person with a paid off mortgage has a greater return, of course everything else remaining constant.

          You make a good point about keeping the bank involved to shoulder a majority of the risk, at least in the early days of the amortization schedule.

          Your points make a lot of sense. This post is not intended to convince anyone either way. Rather it’s to look at financial instruments/problems/strategies from a different angle and perspective.

          And further I do often think about the liquidity risk of tying up so much capital in the property before we are able to afford to pay it off. I have even suggested in past financial reports that we may at some point let the money accumulate until we can pay it in full. That is what will happen actually after our current refinance closes next week.

          But trust me the pure finance nerd in me agrees with everything you type. And in contrast to you or even Sean who commented below, I probably come across as very conservative, but I am very aggressive in certain aspects of my life.

          I believe there is a time and a place for everything. And based on the things I am currently working towards this is what works for my unique situation. Details slowly get leaked on the blog.

          I appreciate the thoughtful discussion and questions.

          Cheers,

          Dom

          1. Well said. This is a good example where putting a little thought into your finances up front can save hundreds of thousands of dollars over thirty years. So important to think this stuff through, which most people don’t.

        2. Brian,
          Not sure your info is correct re: “If there is a large insurance claim needed? I buy into the idea that it is better to have a bank that is in the fight with you. For example, if I have 33% equity and the bank owns 67%. The bank has a team of lawyers and the know how to get the claim done if it is contested”.

          I do not know of any cases where the bank will step in to help you in the claims adjustment process. Can you elaborate? As far as I understand the process, the claim will be between you and the insurance company, with the bank holding the funds until the repairs are made. (If anything, having a mortgage makes complicates the process). Banks will however still require you to make your mortgage payments regardless. You could always exercise your option to simply walk away if the damages leave you too far underwater and you don’t mind leaving your equity behind (and trashing your credit in the process).

  3. It is one way to look at it. Not sure it quite jibes with my thinking though.
    I do agree with your 25% plan (any more than that locked into a non-liquid asset makes me twitchy). I just refinanced (rolling the cost into the loan, so I am rolling the savings back into the loan over time (with the extra money I put away by skipping a payment and getting my escrow back also slowly being rolled back in, I plan to pay down to until the terms (length and when it would end, match and then evaluate)). Odds are I will probably keep paying down after that since the theory is that the house won’t appreciate at the same rate as my other investments (and I am adding 4.5 times more money into those accounts than I am paying down on the mortgage). Right now the house value (using the optimistic Zillow value) sits at 25.3% (in the last rollercoaster 10 months it has been as low as 23.4 and as high as 26 (its a number I already had in my net worth spreadsheets)).

    1. Author

      Hey Daniel – You know what they say…different strokes for different folks 🙂

      Nice job on putting almost 5X your principal reduction towards other investments. That is a healthy margin my friend.

  4. Very great analysis and a couple ways of thinking about it that I haven’t thought of myself. The point you hit on which I think is the most important one, is that people won’t invest the difference in the market. And the ones that do? A large number of them will make emotional decisions and sell their stocks during a sell off, further exacerbating the problem. For this reason, I think your logic and reasoning is quite sound.

    Personally, I don’t buy into the whole bond allocation theory. I Spend my entire life immersed in the stock market and feel I have a decent grasp of it. Funny enough I preach the bond allocation to my clients because people often have a very hard time dealing with volatility, even when working with professionals. The biggest reason people would want a bond allocation is to smooth out any volatility, while I personally welcome the volatility. I’d love nothing more than the market to correct 25%+, even though 90% of my assets are allocated to this. That, of course, is for my personal wealth, the damage a 25% correction would do to the potential growth of my book of business would be difficult 🙂

    It’s funny, both 100% of my personal wealth and 100% of my employment income depend on the market, and people often call me crazy for literally having all my eggs in one basket. But if you think about it, my eggs aren’t in “the market”, my eggs are in the biggest and most successful businesses in the world. What could I do, carve out 50k and go invest in the local Laundromat? No thanks.

    1. Author

      I personally welcome the volatility. I’d love nothing more than the market to correct 25%+

      You and me both my friend. I would be much more aggressive in deploying the mountains of cash we are building over here in the GYFG household. Think of a guy like John Templeton who averaged 16% returns for 38 years. He was more than happy to hold high levels of cash & bonds when it was hard to find stocks that were cheap.

      100% is what suits your situation and risk profile. If it works for you, then do it.

      Cheers,

      Dom

  5. Paying off any form of debt is a relief, as you rightly said it free’s up cash. Question is will people invest the available cash? Will the ‘forced saving’ now turn into ‘forced spending’?
    Just getting rid of my car loan was a relief freeing up 17k which went back straight to investments.
    Hey +1 to that volatlity, I want more of it. 😀

  6. Hi Dom, interesting post and I have a couple thoughts for you to consider.

    First, regarding the view of your home similar to a bond in terms of diversifying. Bonds have traditionally been used as to diversify from stocks as they were typically (although not always) countercyclical (going up when your stocks were down, etc). Not sure if residential real estate would act in a similar manner, I don’t believe it would. Not to say it isn’t still a good diversification play, just not one akin to bonds.

    Secondly, re: the residence as a perpetuity. You are right, it saves you $19K, but it doesn’t make you $19K. So paying off your mortgage does not give you a PV of $531K. That $531K value is basically the value of the work you do to make $19K in perpetuity (that’s where you ‘make’ the money).

    Lastly, the 5.21% you calculated is assuming the home is making you the $19K each year. In actuality, the home only goes up in value with appreciation, or the 3% estimate you give. That equates to $11.1K per year. To calculate a return on the equity investment, that’s obviously 3% if you have no mortgage. But say you have a 80% mortgage (20% down on the home), that would equate to a 15% return. Factoring the interest cost would bring that return down a bit, but may be more of an argument to keep your home levered and reinvest the $296K (80% mortgage amount) in bond/equity mix portfolio earning 6-8%.

    I like the post, it is a different way of looking at your mortgage. If you have confidence in the market though, it may be worth keeping some debt on the home.

    Thanks!

    The Green Swan

    1. Author

      Hey TGS – Thanks for your thoughts.

      I would argue that the mortgage does play a good substitute for a bond…with a kicker, it has the ability to appreciate, unlike a bond that has a face value that at maturity does not change. I understand the theory of having a mix of stocks and bonds to smooth out volatility, however, the same is true for any diversified portfolio of different asset classes. Your right the value of the house will likely not act exactly like a bond, but the coupon interest payment will.

      Remember I say it is “LIKE” not exactly the same 🙂

      To your second point I would argue that from a net cash flow analysis perspective it doesn’t matter whether it is income earned or net savings…either way they both represent a cash flow. Please explain the different between earning an extra $19,000 or saving $19,000…either way I am $19,000 better off from a cash flow perspective. I don’t agree with your logic.

      And to your last point about the 5.21% return. I understand the inflation argument, however, you have to remember that one of the benefits of buying a house is to lock in or fix your cost of living…meaning you are protected from inflation. In other words this $19K is essentially like TIP Bond (Treasury – Inflation Protected). As a renter you are subject to rent increases that will likely move up at the rate of inflation over a long enough period of time. So, therefore the $19K savings actually grows in lock step with the appreciation of the house assuming they both only grow at the rate of 3%.

      But to your point, if the rate of appreciation on the house were to grow faster than inflation for a sustained period of time, and rents in my surrounding area for a comparable property were to only increase at the rate of inflation, then yes theoretically that return would change.

      I am not opposed to holding debt, but I personally have a maximum leverage ratio of about 2-3X of our annual income, which is dependent on where we are in the current cycle. Right now we are currently less than 2X as we make room for an additional investment property.

      Some are more comfortable using more leverage, but I have personally seen what too much leverage can lead to in my own circle of influence, not just form the 2008 financial crisis. I completely understand how leverage magnify’s your returns, but it is a double edged sword as well.

      We all have to figure out our own comfort level and risk tolerance.

      Thanks for the thoughtful comments.

      Cheers,

      Dom

      1. Hi Dom, thanks for the comments back. I appreciate the healthy dialogue and differences of opinion. And it is good to think critically on the benefits and drawbacks of fully repaying your mortgage.

        I understand your point on the using the home as a diversification play instead of using bonds. And over the long-term I think that makes sense. I hold that same opinion and personally am invested entirely in stocks in the investment accounts, although the equity in my home isn’t that significant. I think we are saying the same thing here.

        Yes, I agree in terms of your cash flow, making $19K or saving $19K has the same impact. I would attribute the $19K to your hard work in earning a salary or other income, not to the home though. In the return analysis, it looks as though the $19K is being earned from the home. Putting $370K in a dividend stock would give you that income, putting $370K in a home doesn’t. Not sure if that is clear or not, but just my viewpoint.

        I personally struggle with the risk tolerance of keeping my home levered. While I’m at maybe a 80-85% LTV right now (I’ve owned my home about 4 years) planning ahead, I’m not sure if I want to keep it that high. The risk is another home value crisis like you mentioned in 2008, but the obvious benefit is you can typically use that money to get a better return in the stock market. Personal choice obviously.

        Thanks again Dom!

        The Green Swan

        1. Author

          Likewise TGS! Different opinions and commentary are great, they make people think.

  7. Food for thought and nice discussions in the comments.

    The main issue that I have is that cash flow does not comes out of the house but from your work. With a bond or annuity, you can literally do nothing and have the cashflow. If tomorrow you do nothing, the 19K is not there.

    Off course, it is LIKE having it, not really having it. I do see the point from pure cash flow point of view.

    Keep these discussion topics coming

  8. I think of paying off my mortgage early as equivalent to a bond. I don’t think of it as a dividend yielding stock since the appreciation in my house is completely independent of my diverting additional capital toward principal.

    1. Author

      Hey Taylor Lee – I totally agree that appreciation will happen regardless of additional capital towards the principal. However, I would also argue that the appreciation of your stocks is also independent of you diverting additional capital to that investment. Just some food for thought!

  9. Like you I am surprised at the bad rap early mortgage payoff gets in the PF world. It frees up cash flow–usually a huge chunk of it. And it reduces the cost of early retirement dramatically, requiring far less of a return from invested assets for a successful early retirement.

    1. Author

      Could not agree with you more Mortimer. I think a big part of it is the bias behind what gets served as conventional wisdom. Obviously it is in the best interest of the banks and financial advisers to advise you to keep you mortgage for as long as possible. That way the banks earn their interest and the financial advisers get a piece of that “extra principal payment” that they convinced you to invest instead of pay down the mortgage.

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