Buying a house with cash or with a mortgage?

Should I buy a house in cash or take out a mortgage

I recently read a question on the social media site Reddit, where a user asked whether he should be buying a house with cash or taking out a mortgage. This is a very interesting question and we take a deep look at whether a prospective homeowner should buy a house with cash or take out a mortgage, if they can afford both options.

 

 




 

Should I be buying a house with cash or taking out a mortgage?

The question came from an American reader (and hence the figures are shown in dollars). However, it is equally applicable for any country and any currency. His exact question read:

“I’m 29 years old, single, with $245k sitting in an online savings account, earning a measly 0.95% interest. I make roughly $70k/yr and my credit score is 819. I’m looking to purchase my first home, which will cost around $220k.

I’m tempted to buy the house outright with cash and start building my savings account back up, which I feel like I could do rather quickly with no rent/mortgage to worry about (aside from HOA, insurance, property tax, maintenance, etc., which would still be dramatically less than what I’m currently paying in rent).

Any advice for/against buying a house with cash in my situation would be greatly appreciated. Thank you for your time.”

 

The answers on reddit

I find this question, and the general topic of buying a house with cash or mortgage, very interesting, mainly due to the wide array of answers provided in the comments. The responses are generally split. However, for me, this is a maths problem and hence there is a definitive answer. Some of the answers provided on Reddit included:

  • “Pay for it in cash. Don’t try to beat some interest rate because that’s just a gamble. Just do the smart thing and pay for things in cash. Your financial situation is pretty amazing, especially for your age. You’ll be solid either way though.”
  • “You can’t always just take the conservative way out. Put down 20% and toss the rest in a conservative mutual fund.”
  • “Buy the house. You can still follow the other advice here on investments when you build your savings back up. At your age you can still save handsomely for retirement or just about anything else.”
  • “I bought mine with cash because of the tremendous peace of mind it brought. Just knowing that you can’t ever lose the house (for the most part), is an amazing feeling.”

 

Buying a house in cash or a mortgage – Its a maths question

As I say, these answers are not looking at the problem from a cold hard mathematical perspective. If we do, I would argue that buying a house with a mortgage is currently the most preferable option.

Note that the person asking the question is from the US and hence my reply is focused on the US and will use historical figures from US markets, discussion of Roth and 401ks etc. However, the alternatives in the UK are about the same (market returns are similar, a “Roth” is the equivalent of an ISA and a 401k is a tax-free retirement account).

Personally, I would take the mortgage on a 70-80% LTV, given that the reader has consistent future income. Then I would dollar average my investments into the market in a tax efficient manner (matched 401k, Roth, etc) over a period of a few years (you will need a few years with annual limits on tax wrapped accounts).

The reader will benefit from 4 key things by doing this:

1) Inflation: if you take out a $175k mortgage, it is the equivalent of 2.5 times your annual salary (annual salary of $70k). If you take out a 30 year mortgage, and assume that your salary increases only with inflation (usually it will increase more as you move through your career), in 30 years’ time your salary will be $182k. However, when you repay your mortgage, you still only have to repay $175k. It will therefore cost less than 1 times your annual salary.

2) Market returns: The return on the S&P 500 over the past 50 years is 11.3% per year. This greatly exceeds current mortgage rates of around 4.25% per year. Therefore, you could earn a significantly greater return from investing in the market than the interest you will pay on the mortgage.

3) Leveraging: According to the National Association of Realtors, the price of US existing homes increased by 5.4% annually from 1968 to 2009. If you therefore assume capital gains on your property of 5.4% per year (it’ll probably be more than that), your $220k house would be worth $1,066k after 30 years. If you pay with cash, your ROI on your cash is 5.4% per year. However, if you take out a $175k mortgage, your ROI on your $45k investment (down payment) will be the equivalent of 9.4% per year.

4) Taxes: At the highest level, the reader’s $70K income per year makes him a high marginal tax rate payer. With tax benefits on mortgage interest in the US, your 4.25% would effectively come down to around 3%.

 

To conclude on the figures, if you buy a $220k house in cash, your final pot will be the value of your house after 30 years which, at 5.4% capital growth, will be $1,066k. If you buy with a 30 year 4.25% fixed mortgage (assuming interest only and the interest is paid out of your investments each year), your final pot (house value less mortgage repayments (tax adjusted) plus market investments) in 30 years’ time would be $3,852k.

“Buy in cash” final pot: $1,066k.

“Buy with mortgage” final pot: $3,852k.

 

 

Breakeven analysis

This section was not in the original article, but was inspired by the comment and reply by Tom G below. Check it out in the comments section below.

Generally, your choice between cash and mortgages comes down to your risk tolerance. People tend to say:

“I would rather have a ‘fixed rate’ of 8% (effectively earned by paying down the mortgage) than a ‘variable return rate’ of 10%”.

However, before you reach such arbitrary conclusions, I think it is very important to look at the break-even analysis and the actual figures in some examples. Firstly, breakeven analysis between the two options:

 

Scenario 1: we pay for the house in cash

$220,000 in cash, invested for 30 years at 5.4% return (average real estate increase), gives us a final value of $1,066k. This is calculated as $220000*(1.054^30). This is our base case example and will never change assuming a 5.4% return on the property. The real estate return percentage we take actually doesn’t matter one little bit as we shall use the same figure in scenario 2 (also see comments below explaining why).

 

Scenario 2: we pay for the house using a mortgage

We shall assume a market average return of 11%. The figures below show that since 1929, the average 30 year return is actually 11.34% per annum, so this assumption is not unreasonable.

Every year, we earn 11% on our investment, but we need to take out a certain amount to pay down the mortgage interest (to make our two scenarios equivalent).

From this figure, we will need to repay $175k principal at the end. Our house value will still be $1,066k at the end of the 30 year period.

Therefore, simply, our investment value less mortgage repayments need to equal $175k at the end of the 30 years to make us at breakeven point.

To do this, our breakeven interest rate on the mortgage will be equal to the return of the market (11%). However, this ignores the tax advantages of real estate ownership and hence the real break-even point (for US marginal tax rate payers) is 15.7% mortgage interest rate.

Using the same 11% returns form the market, here are some figures for different mortgage interest rates :

House in cash or mortgage

 

Therefore, before you jump to the conclusion that you would rather pay down your 6% mortgage because you would “rather not take the risk”, just make sure you know that over 30 years, that decision is costing you, on average $2.4 million over the course of 30 years on a property only costing $220k.

 




 

What about market risk and breakeven points?

In our comparison, we assumed annual increases in real estate of 5.4% in both examples. Therefore, we can ignore possible volatility in this return as it will impact both options in the same way.

The risk comes with our market investment. The original user was concerned that his returns would not exceed his mortgage interest rate and that he would lose money. This is essentially the risk of this problem.

Firstly, to calculate this risk from an investment standpoint, we need to know what our “break-even” point is on the investment assuming a fixed mortgage rate. This will be the rate returns from the market which would provide, in our above example, only $0.34m in returns (as the house pot is $1.07m when bought with cash, but $0.73m when bought with the mortgage).

Out breakeven point on a 4.25% fixed mortgage needs to create a pot of $340k with our investment of $175k. To achieve this, we would need an annual investment rate of 2.25%.

Well, over a 30 year time frame invested in the S&P 500, there really doesn’t seem to be any chance of being anywhere near this low.

After analyzing every 30 year period from 1930 onwards, the very lowest annual return over a 30 year period (with dividends invested) is between 1955 and 1985 is 9.3%. The highest is 13.69%. There is very little volatility over this length of time and hence our risk is extremely low:

 

Start date End date Return
1930 1960 10.11%
1931 1961 13.10%
1932 1962 13.16%
1933 1963 12.28%
1934 1964 12.96%
1935 1965 11.96%
1936 1966 10.50%
1937 1967 12.64%
1938 1968 12.41%
1939 1969 11.87%
1940 1970 12.35%
1941 1971 13.26%
1942 1972 13.41%
1943 1973 11.82%
1944 1974 10.02%
1945 1975 10.20%
1946 1976 11.12%
1947 1977 10.72%
1948 1978 10.75%
1949 1979 10.80%
1950 1980 10.87%
1951 1981 9.93%
1952 1982 9.94%
1953 1983 10.67%
1954 1984 9.40%
1955 1985 9.30%
1956 1986 9.87%
1957 1987 10.24%
1958 1988 9.70%
1959 1989 10.19%
1960 1990 10.11%
1961 1991 9.88%
1962 1992 10.79%
1963 1993 10.40%
1964 1994 9.85%
1965 1995 10.61%
1966 1996 11.72%
1967 1997 12.04%
1968 1998 12.36%
1969 1999 13.56%
1970 2000 13.24%
1971 2001 12.24%
1972 2002 10.67%
1973 2003 12.10%
1974 2004 13.69%
1975 2005 12.73%
1976 2006 12.47%
1977 2007 12.95%
1978 2008 10.81%
1979 2009 11.16%
1980 2010 10.70%
1981 2011 10.84%
1982 2012 10.76%
1983 2013 10.96%

 

Based on historical data, there is VERY little (almost no) risk that over 30 years, your investment won’t exceed the required 2.25% returns required to break even in this example. In fact, the returns are very consistent over this time frame and therefore your overall risk on this is low.

 

What if I can’t make my payments?

This is the only other risk which may impact buying a house with cash or taking out a mortgage. Everything is fine until you can’t make your monthly payment and then things can quickly go down hill.

The fixed rate mortgage will mean (after tax impact) that you need to make an annual interest payment of $5,250 or $438 per month. If you lose your job, you may be worried that you won’t be able to make this payment. However, the risk of this is completely unjustified.

Firstly, after the $45k deposit and putting $175k in the markets, the reader still has $25k left in his savings to act as an emergency fund.

Assuming a savings rate (the amount you save divided by the amount you earn) of 25% per month, this would mean that the reader’s monthly expenses are $70k * 75% * (1/12) = $4,375.

The $25k would therefore represent an emergency fund equal to 5.7 months of expenses (including taxes), which is generally considered to be sufficient.

It also means that he could make 4 years and 9 months’ worth of mortgage interest payments (2 years and 10 months if using a non-interest only mortgage).

This should therefore cover the majority of risk that this person cannot make their mortgage payments.

However, more pertinently, let’s imagine something bad does happen. If we burn through the remaining emergency fund, we still have access to $175k which is invested in the market. We don’t WANT to touch this as it will obviously have a dramatic impact on our final results. However, with market investments in large market tracking index funds / ETFs being so liquid, you can get access to this money within a couple of days.

The alternative is that you buy the whole house in cash. If you do then have a disaster and lose your emergency fund, then the only way to release any extra cash is by selling the house, which is much harder (and more expensive) to do.

 

 




 

Conclusion – Buying a house with cash or with a mortgage?

Based on this analysis, my short answer is that you should definitely take out the mortgage for three reasons:

  1. Math. The returns are so much greater when taking advantage of the mortgage (final pot of $6,414k vs $1,066k).
  2. Over a 30 year time frame, the market risk is actually very low.
  3. When considering the liquidity of your investment, in the case of a disaster, the mortgage may be the less risky option.

 

27 thoughts on “Buying a house with cash or with a mortgage?

    • In a way, it does, but it doesn’t really change the conclusion. For example, some areas may have better than 5.6% annual growth, some may have worse. For these areas, this will change the amounts in the “final pot” comparison. But, it will effect both pots comparatively.

      The real comparison we are doing when decided between buying our home in cash or via a mortgage is the interest rate (tax adjusted) vs the market return. With an interest rate of 2.25%, the market has ALWAYS returned more than this on an annual basis over a 30 year time frame.

      Therefore, the geographical location isn’t an important factor in our decision making – only the interest rate and our potential market returns are.

      Thanks for your comment Jen and I’m happy that the article made you reconsider your views on home purchases…
      moneystepper recently posted…Should I buy a house in cash or take out a mortgage?My Profile

  1. With interest rates so low, I would take out a loan at this point. Add in the tax breaks you get here in the US and the interest you pay is less than inflation (assuming you have good credit). I’d rather leave my money in the stock market earning 7-8% over the next 30 years than not having a mortgage.
    Jon @ Money Smart Guides recently posted…Ready For Zero ReviewMy Profile

  2. Interesting that all of the examples of stock market returns start AFTER 1929…. Hmm wonder if something happened that year? Lol. I think the answer is pretty simple take out the mortgage and as long as you find a return on investment higher than your mortgage percentage – tax break, then you are money ahead!
    Davey Pockets recently posted…Is the Stock Market Set to Crash in 2015?My Profile

    • Fair point Davey, fair point. This wasn’t intential, but rather when the data began from in my extraction.

      If we take the WORST period in financial history (381 in mid 1929 to $679 in mid 1959), the market increased by 1.9%. If you suffered this worst case scenario, your “cash purchase” final pot would be $1,065,715 vs your “mortgage & investments” final pot of $1,041,011. We would be around $25k worse off taking out the mortgage.

      In the the BEST period from the charts above, for comparison, the “cash purchase” final pot would still be $1,065,715, but the “mortgage & investments” final pot would be…wait for it…$8,950,078. Here you would be almost $8 MILLION better off taking out a mortgage.

      Given that the average is much nearer the best case scenario than the worst case, I am happy to take the risk of comparatively losing $25k compared to the possibility of gaining $8 million…
      moneystepper recently posted…Should I buy a house in cash or take out a mortgage?My Profile

  3. Was location mentioned at all? The only thing I’d add is that some cities return higher rates on real estate than others. For example, in Los Angeles, the real estate market is crazy. You can own a home for 10 years (if you purchased when the market was down) and double your money. Case in point – when I check out Zillow.com, homes in my area today selling for $430K 10 years ago sold for $207K. I think this is a great way to look at whether to buy with cash or not, but I’d also factor in the local real estate market.
    Little House recently posted…Welfare RamblingsMy Profile

    • Location doesn’t play a factor in the analysis. I’ve taken a real estate annual growth figure of 5.6%, but left it constant whether we buy in cash or take out a mortgage. The house market values really do not matter in the comparison.

      What is really important, as highlighted above, is the available market returns on the investments vs the mortgage interest payable on your debt.

      I would recommend you read this again if that wasn’t clear, because when it hits you, it hits you!! 🙂
      moneystepper recently posted…Should I buy a house in cash or take out a mortgage?My Profile

  4. Very comprehensive analysis and great advice. I must admit I sort of cringed when I read that the reader was contemplating paying with cash for the house. Now I’m all about eliminating debt and mortgages, but there’s a time and a place. This reader is so young, has lots of time, so mortgage and investing at the same time are definitely the way to go. For me, different story, because I’m a lot older. In any scenario, paying of mortgage as fast as possible is very prudent. I like a 25 year term mortgage with a prepayment strategy to have it gone in 15 years.
    debt debs recently posted…The New Multitasking – FragmentaskingMy Profile

    • Yeah, the decision about buying a house with cash or a mortgage changes with age, as the forward investment period reduces and peoples’ risk appetites definitely change over time.

      However, anyone with a 15-20 year time period for investing without touching the investments should definitely consider a mortgage in the current interest rate environment.
      moneystepper recently posted…Save Money On Your Mobile Phone Bill With GiffGaffMy Profile

    • I suppose there comes a point where people can afford to pay with cash and just don’t want to look to a mortgage because they can’t be bothered with the effort!! However, I’m not sure there are many people at that stage, and those who are financially, usually got there by caring about the optimal financial decisions and hence would probably still go with the mortgage option!
      moneystepper recently posted…Session 02: GoalsMy Profile

  5. Personally I view this as more of a “what are the current mortgage rates” question. I think for me I would say that when it starts to be more than 6% then I would start paying down my mortgage a little quicker. I don’t think that I would put all of my money towards it but I would pay it off quicker because it’s a guaranteed 6% return. I know that from a mathematical standpoint having a mortgage is better due to tax write offs and other investing strategies. But there is a peace of mind that you get with a guaranteed return.
    Zee @ Work To Not Work recently posted…Saver’s Block: How to begin when you don’t know where to startMy Profile

    • Indeed. Its a completely different argument when interest rates go back up above 6%. The margin available between interest rates and investment returns in the market is currently great enough to make the “risk” worthwhile.

      However, at 6%+, this becomes a much tighter decision whether to buy a house with cash or take out a mortgage. Thanks for your comment Zee.

  6. Great study! It makes it all the more clear that investing in the stock market is the way to go if your risk tolerance is high enough.

    One other benefit of having a mortgage is if the absolute worst does happen and the housing market crashes. You always have the choice to walk away and only be out your principle. If you bought the house 100% outright, you are stuck if you want to move somewhere else!
    Derek at MoneyAhoy recently posted…Make Money on Craigslist with FlippingMy Profile

    • True. People often state that buying a house with cash rather than with a mortgage is a better option from a risk perspective, but I would disagree for the reasons highlighted in the post and your comment.

      Thanks Derek!

    • This ignores the negative externality/ethical hazard of reneging on your debt. The ability to stiff your creditors is not a good thing from a moral point of view.

  7. I think this question should be answered annually based on the current mortgage interest rate.

    The problem boils down to whether there is a good chance you will make more money by putting your cash into investments rather than paying down your mortgage. Both the money put into investments and the money used to pay down the mortgage will compound in a similar fashion. The money in investments will compound in the usual sense, the money used to pay down the mortgage will compound by reducing the regular mortgage interest payments.

    As mortgage rates are subject to fluctuation and are currently at the lowest levels they have been for a while it may make sense to borrow money for a mortgage at a low rate (4.25% was mentioned above) and invest spare cash into a low-cost index fund. As mentioned above the S&P has returned around 10% on average over multi-decade history.

    The idea would then be to make a decision every year based on the mortgage interest rate of whether you should funnel new cash into investments or into paying down the mortgage. For example; if the interest rate on your mortgage spiked to 8% over the next few years you could re-direct cash away from purchasing investments into paying down your mortgage, thereby securing an 8% return on that money (all the while your existing investments will continue to grow in the background). If the mortgage interest rate spiked to high levels, say 10% or higher, you could then consider paying down your mortgage further by re-directing dividend payments or selling a chunk of shares.

    Hope this helps someone as it is the strategy I’m in the process of following. Any critique appreciated.

    • Excellent Tom G!! Thanks for the very thoughtful comment.

      Awesomely, it made me think of something that I had previously omitted regarding break-even analysis on the investments and what effect people’s attitude to risk has.

      Generally, I completely agree with your strategy, and you should check it every year. However, its important to note the actual figures involved when saying that you would rather take the cash option at a certain percentage.

      I have added this into the article above as I believe its incredibly important. Thanks a million (or several million) Tom G, and I hope that answers your question.

  8. A very interesting post and I’ve also seen and heard a lot of people as such questions. Would you agree that a lot of people are afraid of the stock market? I think finding out what the current mortgage rates are is a step towards dealing with the problem. This particular reader is quite young and is doing well with his savings. Moreover, interest rates are still low so I think it would be beneficial to invest the money into the stock market.
    Kayleb Holden recently posted…East Ewell Estate AgentsMy Profile

    • Very much so Kayleb. The sensationalist headlines in the press about stock market crashes and highlighting the horror stories makes the average saver very frightened of “investing” for the longer term.

      Its important to understand the level of risk in the long-term (e.g. the stat that the market has never returned negative annual returns over a 15 year period).

      When this is taken into account, borrowing at a very low fixed interest rate and investing the funds (if you have a suitable risk appetite) can be a very profitable option.

    • I think that they should consider it, yes…!

      Obviously this decision will be based on the expected investing time-frame, risk-appetite and so on. However, from a purely mathematical standpoint, it seems that buying a house with a mortgage rather than with cash is indeed the optimal decision.

  9. You made a lot of errors and thereby biased the result towards taking out a mortgage being the best option. First, your point about inflation is made incorrectly, because you discounted the interest rate by inflation but not also the investment return. Comparing a real interest rate to a nominal return rate is apples to oranges. Second, the market returns are variable, not constant. You can’t just assume that a single figure pulled from the past 50 years is correct. Third, leveraging only gives you an advantage to the extent that you can earn a higher return on your assets than your debt costs – so in effect points #2 and #3 are two ways of looking at the same thing, not two different benefits of leverage. Fourth you account for interest deductibility but fail to factor in taxes on your investment earnings. Comparing post-tax interest with pre-tax investment returns is another apples-to-oranges comparison. Finally, you assume the mortgage is interest-only for 30 years, rather than amortized. This is not how most 30-year fixed mortgages in the US work at all – the vast majority of them, if not all, are amortized loans, not interest-only.

  10. What about cash flow? One reason we took the smallest morgatage we could was due to monthly cash flow. Money invested in the market should not really be touched for the long haul, otherwise returns can be seriously hampered. Being young, there are a lot of future demands on monthly cash flow likely to arise (children being an obvious one). We took the approach of making sure our cash flow was large enough that we could easily adjust our spending and investing patterns

    i didn’t see you factoring in investing into the market slowly after buying the house with cash. Assuming the morgatage payment was drip fed into the market in the house with cash scenario, how does that affect the numbers? I think this approach is most likely to get you the 11% return as well?

    • Thanks for your comment Ricky.

      Your cash flow going forward will make a difference, so you need to make sure you are covered for this. Our asssumption is that if someone is in a position to pay for their house in cash, then they are probably also in a position whereby the month-to-month payments on a mortgage wouldn’t be a problem.

      If you are in the unique position where you have the physical cash to buy a house outright, but your future monthly cash flows would be an issue, you would need to do a bit more thinking.

      You could argue that you could remove your dividends on your market investments each year to cover your mortgage interest payments, or something similar.

      I would estimate that a very small proportion of the population are in this position and so I probably won’t run the exact numbers and devise specific strategies, but my conclusion would probably still remain largely the same.

      Once you have bought the house with cash or with a mortgage, the future investments are identical.

      In the mortgage example, you have payments to make, but these are more than offset from the profits from the markets (subject to your previous point on cash flow). Therefore, this is considered the same as the cash only example.

      We also didn’t run the numbers for a repayment mortgage (rather than interest only) as this just shows a middle ground between the two extremes which we are examining in the article.

      I hope that answers your questions.
      moneystepper recently posted…What Was Initial Uptake Of Pension Freedoms?My Profile

      • Yes, agree that overall you are better off, almost no matter what you do.

        I am interested though, what is your stance on leveraging to invest? Based on the stated low risk of not achieving an 11% return in the long run, should someone leverage up at low rates, esp if against an asset of value they own (e.g. Remorgatage their house – central London flats bought for £200k now worth a million)? What about say a commercial loan @ 7%? Providing you can easily cover the monthly payments.

        I guess the biggest risk with this approach is the same thing that is likely to make you lose your job is also likely to drop the markets when you most need the cash – you will probably survive as the £170k won’t be wiped out (if investment is diverse) but your return will be massively impacted if you start withdrawing after it drops (even if it goes back up again). Cash/credit on hand, your ability to find a new job and holding your nerve will determine the size of impact.

        A lot of the ‘irrational’ approach is down to people’s perceptions (stock market risky, bricks and mortar safe). How does BTL tally up against stock market approach?

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